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R/sensitivity_learning_table_flexible.R
In sl4bayesmeta: Sensitivity and learning for Bayesian meta-analysis
Defines functions
sensitivity_learning_table_flexible
Documented in
sensitivity_learning_table_flexible
sensitivity_learning_table_flexible <- function(df, tail_alpha_static=0.04550026, U1=1, U2=2,
tail_alpha_dynamic=0.5, rlmc1=0.25, rlmc2=0.5,
scale_effect="OR", type_sigma_ref="geometric",
mu_mean=0, mu_sd=4, grid_epsilon=0.00354){
# This flexible function enables a flexible change of all parameters and provides redundant programming.
# If necessary, this function can be split into parts without much recoding.
# It takes ca. 10 min to run this function.
# learning_sensitivity_table function (multiple calls of bayesmeta)
# computes a table containing the paremeters of heterogeneity priors HN, EXP, HC, LMX,
# descriptive statistics of posteriors,
# learning and sensitivity estimates for static 5%-tail HN(0.5)(U=1)- and HN(1)(U=2)-like scale parameters for for HN, EXP, HC, LMX heterogeneity priors
# learning and sensitivity for dynamically assigned scaling parameters for HN, EXP, HC, LMX for rlmc1 and rlmc2 adjusted at the median
# input:
# df: data frame in form compatible with data objects in the bayesmeta environment
## tail_alpha_static: P[HN(0.5)>1]=0.04550026, P[HN(1)>2]=0.04550026
# tail_alpha_static: =0.04550026 (recommended value)
## U1: threshold for P[HN(0.5)>1]=0.04550026
# U1: =1 (recommended value)
## U1: threshold for P[HN(1)>2]=0.04550026
# U2: =2 (recommended value)
## tail_alpha_dynamic=0.5: centering of Uref in the median P[tau>=Uref]=tail_alpha_tynamic=0.5 for a heterogeneity prior for tau
# tail_alpha_dynamic: =0.5 (recommended value)
## rlmc1=0.25: The Relative Latent Model Complexity (RLMC) set to 0.25 (empirically corresponding to HN(0.5))
#rlmc1: =0.25 (recommended value)
# rlmc2=0.5: The Relative Latent Model Complexity (RLMC) set to 0.5 (empirically corresponding to HN(1))
# rlmc2: =0.5 (recommended value)
## Method for the computation of the reference within-study standard deviation: either "geometric" or "harmonic"
# type_sigma_ref: ="geometric" (recommended value)
## grid_epsilon for sensitivity computation
## grid_epsilon=0.00354: grid_epsilon as suggested by Roos et al. (2015) corresponds to H(N(0,1),N(0.01,1))=0.00354
# grid_epsilon: =0.00354 (recommended value)
# output:
# table with the following columns:
# "U"
# "tail_prob"
# "par_val"
# "MRLMC"
# "median_post_OR"
# "95CrI_post_OR_low"
# "95CrI_post_OR_up"
# "length_95CrI_post_OR"
# "median_post_tau"
# "95CrI_post_tau_low"
# "95CrI_post_tau_up"
# "length_95CrI_post_tau"
# "L_mu"
# "L_tau"
# "S_mu"
# "S_tau"
# for HN, EXP, HC and LMX heterogeneity priors with the following scaling parameters (indicated in rows)
# "HN(0.5)_U1tail", "EXP_U1tail", "HC_U1tail", "LMX_U1tail": tail_alpha_static %-tail adjusted with threshold U=U1 (static)
# "HN_rlmc1", "EXP_rlmc1", "HC_rlmc1", "LMX_rlmc1": dynamically adjusted with target RLMC=rlmc1 and tail probability tail_alpha_dynamic
# "HN(1)_U2tail", "EXP_U2tail", "HC_U2tail", "LMX_U2tail":: tail_alpha_static %-tail adjusted with threshold U=U2 (static)
# "HN_rlmc2", "EXP_rlmc2", "HC_rlmc2", "LMX_rlmc2": dynamically adjusted with target RLMC=rlmc2 and tail probability tail_alpha_dynamic
# with bayesmeta
# library(bayesmeta)
# Version downloaded on 20180928
####---- parameters for learning and sensitivity computation (are now provided in the call of the flexible function) ----####
# # mu_mean: mean of the Normal prior for mu
# mu_mean <- 0
# # mu_sd: sd of the Normal prior for mu (according to Roever(2018) Bayesmeta-Paper (unit-information prior for log-odds-ratios))
# mu_sd <- 4
# ## static choice of the scale parameter for the heterogeneity prior for tau
# # 1-phalfnormal(q=1, scale=0.5) # P[HN(0.5)>1]=0.04550026
# # 1-phalfnormal(q=2, scale=1) # P[HN(1)>2]=0.04550026
# # tail_alpha_static: P[HN(0.5)>1]=0.04550026, P[HN(1)>2]=0.04550026
# tail_alpha_static <- 0.04550026
# # U1: thershold for P[HN(0.5)>1]=0.04550026
# U1 <- 1
# # U1: thershold for P[HN(1)>2]=0.04550026
# U2 <- 2
# ## dynamic choice of the scale parameter for the heterogeneity prior for tau
# # tail_alpha_dynamic=0.5: centering of Uref in the median P[tau>=Uref]=tail_alpha_tynamic=0.5 for a heterogeneity prior for tau
# tail_alpha_dynamic <- 0.5
# # rlmc1=0.25: The Relative Latent Model Complexity (RLMC) set to 0.25 (empirically corresponding to HN(0.5))
# rlmc1 <- 0.25
# # rlmc2=0.5: The Relative Latent Model Complexity (RLMC) set to 0.5 (empirically corresponding to HN(1))
# rlmc2 <- 0.5
# ## grid_epsilon for sensitivity computation
# # grid_epsilon=0.00354: grid_epsilon as suggested by Roos et al. (2015) corresponds to H(N(0,1),N(0.01,1))=0.00354
# grid_epsilon <- 0.00354
#
####---- epsilon-local grid for mu ----####
# normal (for mu)
# upper and lower epsilon grid values for a normal distribution with mean=0 according to equation (20) in Roos et al. (2015) expressed in terms of mu_sd
AAu_normal_mu <- mu_sd*(1+sqrt(1-(1-grid_epsilon^2)^4))/(1-grid_epsilon^2)^2
AAl_normal_mu <- mu_sd*(1-sqrt(1-(1-grid_epsilon^2)^4))/(1-grid_epsilon^2)^2
####---- create an object to collect the results ----####
tres<-matrix(NA, nrow=16, ncol=16)
if(!(scale_effect=="OR" || scale_effect=="logOR"))
warning(paste0("scale_effect must either be ", "OR", "or ","logOR",
sep=""))
colnames(tres)<-c("U", "tail_prob", "par_val", "MRLMC",
"median_post_OR", "95CrI_post_OR_low", "95CrI_post_OR_up", "length_95CrI_post_OR",
"median_post_tau", "95CrI_post_tau_low", "95CrI_post_tau_up", "length_95CrI_post_tau",
"L_mu", "L_tau", "S_mu", "S_tau")
rownames(tres)<-c("HN_U1tail", "EXP_U1tail", "HC_U1tail", "LMX_U1tail",
"HN_rlmc1", "EXP_rlmc1", "HC_rlmc1", "LMX_rlmc1",
"HN_U2tail", "EXP_U2tail", "HC_U2tail", "LMX_U2tail",
"HN_rlmc2", "EXP_rlmc2", "HC_rlmc2", "LMX_rlmc2")
####---- (HN(0.5)-like) static 0.05-tail adjustment with threshold U=1 (HN(0.5)) ----####
# prior parameters
tres[c(1:4),1]<-U1
tres[c(1:4),2]<-tail_alpha_static
tres[1,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN
tres[2,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP
tres[3,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC
tres[4,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX
# effective mrlmc
tres[1,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[2,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[3,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[4,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN05 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
tres[1,c(5:7)]<-exp(fit.bayesmeta.HN05$summary[c("median","95% lower","95% upper"),"mu"])
tres[1,c(9:11)]<-fit.bayesmeta.HN05$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
tres[2,c(5:7)]<-exp(fit.bayesmeta.EXP_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[2,c(9:11)]<-fit.bayesmeta.EXP_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
tres[3,c(5:7)]<-exp(fit.bayesmeta.HC_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[3,c(9:11)]<-fit.bayesmeta.HC_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
tres[4,c(5:7)]<-exp(fit.bayesmeta.LMX_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[4,c(9:11)]<-fit.bayesmeta.LMX_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN05_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[1,13]<-sqrt(1-integrate(integrand_HN05_mu, lower = -Inf, upper = Inf)$value)
tres[2,13]<-sqrt(1-integrate(integrand_EXP_HN05adj_mu, lower = -Inf, upper = Inf)$value)
tres[3,13]<-sqrt(1-integrate(integrand_HC_HN05adj_mu, lower = -Inf, upper = Inf)$value)
tres[4,13]<-sqrt(1-integrate(integrand_LMX_HN05adj_mu, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN05_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN))}
integrand_EXP_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP))}
integrand_HC_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC))}
integrand_LMX_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1))}
tres[1,14]<-sqrt(1-integrate(integrand_HN05_tau, lower = 0, upper = Inf)$value)
tres[2,14]<-sqrt(1-integrate(integrand_EXP_HN05adj_tau, lower = 0, upper = Inf)$value)
tres[3,14]<-sqrt(1-integrate(integrand_HC_HN05adj_tau, lower = 0, upper = Inf)$value)
tres[4,14]<-sqrt(1-integrate(integrand_LMX_HN05adj_tau, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN05adj<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN,
AA0_EXP=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP,
AA0_HC=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC,
AA0_LMX=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN05 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj$p_HN_l)})
fit.bayesmeta.HN05_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj$p_HN_u)})
integrand_HN05_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*fit.bayesmeta.HN05_mu_l$dposterior(mu=x))}
sens_HN05_l_base_mu<-sqrt(1-integrate(integrand_HN05_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*fit.bayesmeta.HN05_mu_u$dposterior(mu=x))}
sens_HN05_u_base_mu<-sqrt(1-integrate(integrand_HN05_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_mu<-max(sens_HN05_l_base_mu, sens_HN05_u_base_mu)
integrand_HN05_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*fit.bayesmeta.HN05_tau_l$dposterior(tau=x))}
sens_HN05_l_base_tau<-sqrt(1-integrate(integrand_HN05_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*fit.bayesmeta.HN05_tau_u$dposterior(tau=x))}
sens_HN05_u_base_tau<-sqrt(1-integrate(integrand_HN05_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_tau<-max(sens_HN05_l_base_tau, sens_HN05_u_base_tau)
# EXP
fit.bayesmeta.EXP_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj$p_EXP_l)})
fit.bayesmeta.EXP_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj$p_EXP_u)})
integrand_EXP_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_l$dposterior(mu=x))}
sens_EXP_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_u$dposterior(mu=x))}
sens_EXP_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_mu<-max(sens_EXP_HN05adj_l_base_mu, sens_EXP_HN05adj_u_base_mu)
integrand_EXP_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_l$dposterior(tau=x))}
sens_EXP_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_u$dposterior(tau=x))}
sens_EXP_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_tau<-max(sens_EXP_HN05adj_l_base_tau, sens_EXP_HN05adj_u_base_tau)
# HC
fit.bayesmeta.HC_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj$p_HC_l)})
fit.bayesmeta.HC_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj$p_HC_u)})
integrand_HC_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_l$dposterior(mu=x))}
sens_HC_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_u$dposterior(mu=x))}
sens_HC_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_mu<-max(sens_HC_HN05adj_l_base_mu, sens_HC_HN05adj_u_base_mu)
integrand_HC_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_l$dposterior(tau=x))}
sens_HC_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_u$dposterior(tau=x))}
sens_HC_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_tau<-max(sens_HC_HN05adj_l_base_tau, sens_HC_HN05adj_u_base_tau)
# LMX
fit.bayesmeta.LMX_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj$p_LMX_u, shape=1)})
integrand_LMX_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_l$dposterior(mu=x))}
sens_LMX_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_u$dposterior(mu=x))}
sens_LMX_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_mu<-max(sens_LMX_HN05adj_l_base_mu, sens_LMX_HN05adj_u_base_mu)
integrand_LMX_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_l$dposterior(tau=x))}
sens_LMX_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_u$dposterior(tau=x))}
sens_LMX_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_tau<-max(sens_LMX_HN05adj_l_base_tau, sens_LMX_HN05adj_u_base_tau)
tres[1,15]<-worst_sens_HN05_mu
tres[2,15]<-worst_sens_EXP_HN05adj_mu
tres[3,15]<-worst_sens_HC_HN05adj_mu
tres[4,15]<-worst_sens_LMX_HN05adj_mu
tres[1,16]<-worst_sens_HN05_tau
tres[2,16]<-worst_sens_EXP_HN05adj_tau
tres[3,16]<-worst_sens_HC_HN05adj_tau
tres[4,16]<-worst_sens_LMX_HN05adj_tau
####---- (HN(1)-like) static 0.05-tail adjustment with threshold U=2 (HN(1)) ----####
# prior parameters
tres[c(9:12),1]<-U2
tres[c(9:12),2]<-tail_alpha_static
tres[9,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN
tres[10,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP
tres[11,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC
tres[12,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX
# effective mrlmc
tres[9,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[10,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[11,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[12,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN1 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
tres[9,c(5:7)]<-exp(fit.bayesmeta.HN1$summary[c("median","95% lower","95% upper"),"mu"])
tres[9,c(9:11)]<-fit.bayesmeta.HN1$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
tres[10,c(5:7)]<-exp(fit.bayesmeta.EXP_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[10,c(9:11)]<-fit.bayesmeta.EXP_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
tres[11,c(5:7)]<-exp(fit.bayesmeta.HC_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[11,c(9:11)]<-fit.bayesmeta.HC_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
tres[12,c(5:7)]<-exp(fit.bayesmeta.LMX_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[12,c(9:11)]<-fit.bayesmeta.LMX_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN1_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[9,13]<-sqrt(1-integrate(integrand_HN1_mu, lower = -Inf, upper = Inf)$value)
tres[10,13]<-sqrt(1-integrate(integrand_EXP_HN1adj_mu, lower = -Inf, upper = Inf)$value)
tres[11,13]<-sqrt(1-integrate(integrand_HC_HN1adj_mu, lower = -Inf, upper = Inf)$value)
tres[12,13]<-sqrt(1-integrate(integrand_LMX_HN1adj_mu, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN1_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN))}
integrand_EXP_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP))}
integrand_HC_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC))}
integrand_LMX_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1))}
tres[9,14]<-sqrt(1-integrate(integrand_HN1_tau, lower = 0, upper = Inf)$value)
tres[10,14]<-sqrt(1-integrate(integrand_EXP_HN1adj_tau, lower = 0, upper = Inf)$value)
tres[11,14]<-sqrt(1-integrate(integrand_HC_HN1adj_tau, lower = 0, upper = Inf)$value)
tres[12,14]<-sqrt(1-integrate(integrand_LMX_HN1adj_tau, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN1adj<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN,
AA0_EXP=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP,
AA0_HC=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC,
AA0_LMX=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN1 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj$p_HN_l)})
fit.bayesmeta.HN1_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj$p_HN_u)})
integrand_HN1_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*fit.bayesmeta.HN1_mu_l$dposterior(mu=x))}
sens_HN1_l_base_mu<-sqrt(1-integrate(integrand_HN1_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*fit.bayesmeta.HN1_mu_u$dposterior(mu=x))}
sens_HN1_u_base_mu<-sqrt(1-integrate(integrand_HN1_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_mu<-max(sens_HN1_l_base_mu, sens_HN1_u_base_mu)
integrand_HN1_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*fit.bayesmeta.HN1_tau_l$dposterior(tau=x))}
sens_HN1_l_base_tau<-sqrt(1-integrate(integrand_HN1_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*fit.bayesmeta.HN1_tau_u$dposterior(tau=x))}
sens_HN1_u_base_tau<-sqrt(1-integrate(integrand_HN1_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_tau<-max(sens_HN1_l_base_tau, sens_HN1_u_base_tau)
# EXP
fit.bayesmeta.EXP_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj$p_EXP_l)})
fit.bayesmeta.EXP_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj$p_EXP_u)})
integrand_EXP_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_l$dposterior(mu=x))}
sens_EXP_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_u$dposterior(mu=x))}
sens_EXP_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_mu<-max(sens_EXP_HN1adj_l_base_mu, sens_EXP_HN1adj_u_base_mu)
integrand_EXP_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_l$dposterior(tau=x))}
sens_EXP_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_u$dposterior(tau=x))}
sens_EXP_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_tau<-max(sens_EXP_HN1adj_l_base_tau, sens_EXP_HN1adj_u_base_tau)
# HC
fit.bayesmeta.HC_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj$p_HC_l)})
fit.bayesmeta.HC_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj$p_HC_u)})
integrand_HC_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_l$dposterior(mu=x))}
sens_HC_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_u$dposterior(mu=x))}
sens_HC_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_mu<-max(sens_HC_HN1adj_l_base_mu, sens_HC_HN1adj_u_base_mu)
integrand_HC_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_l$dposterior(tau=x))}
sens_HC_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_u$dposterior(tau=x))}
sens_HC_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_tau<-max(sens_HC_HN1adj_l_base_tau, sens_HC_HN1adj_u_base_tau)
# LMX
fit.bayesmeta.LMX_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj$p_LMX_u, shape=1)})
integrand_LMX_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_l$dposterior(mu=x))}
sens_LMX_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_u$dposterior(mu=x))}
sens_LMX_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_mu<-max(sens_LMX_HN1adj_l_base_mu, sens_LMX_HN1adj_u_base_mu)
integrand_LMX_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_l$dposterior(tau=x))}
sens_LMX_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_u$dposterior(tau=x))}
sens_LMX_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_tau<-max(sens_LMX_HN1adj_l_base_tau, sens_LMX_HN1adj_u_base_tau)
tres[9,15]<-worst_sens_HN1_mu
tres[10,15]<-worst_sens_EXP_HN1adj_mu
tres[11,15]<-worst_sens_HC_HN1adj_mu
tres[12,15]<-worst_sens_LMX_HN1adj_mu
tres[9,16]<-worst_sens_HN1_tau
tres[10,16]<-worst_sens_EXP_HN1adj_tau
tres[11,16]<-worst_sens_HC_HN1adj_tau
tres[12,16]<-worst_sens_LMX_HN1adj_tau
####---- dynamic 0.5-tail adjustment with rlmc=0.25 ----####
# prior parameters
U_ref025<-sqrt(rlmc1/(1-rlmc1))*sigma_ref(df, type_sigma_ref=type_sigma_ref)
tres[c(5:8),1] <- U_ref025
tres[c(5:8),2] <- tail_alpha_dynamic
tres[5,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN
tres[6,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP
tres[7,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC
tres[8,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX
# effective mrlmc
tres[5,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[6,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[7,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[8,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN05_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
tres[5,c(5:7)]<-exp(fit.bayesmeta.HN05_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[5,c(9:11)]<-fit.bayesmeta.HN05_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
tres[6,c(5:7)]<-exp(fit.bayesmeta.EXP_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[6,c(9:11)]<-fit.bayesmeta.EXP_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
tres[7,c(5:7)]<-exp(fit.bayesmeta.HC_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[7,c(9:11)]<-fit.bayesmeta.HC_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
tres[8,c(5:7)]<-exp(fit.bayesmeta.LMX_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[8,c(9:11)]<-fit.bayesmeta.LMX_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN05_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[5,13]<-sqrt(1-integrate(integrand_HN05_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[6,13]<-sqrt(1-integrate(integrand_EXP_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[7,13]<-sqrt(1-integrate(integrand_HC_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[8,13]<-sqrt(1-integrate(integrand_LMX_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN05_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN))}
integrand_EXP_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP))}
integrand_HC_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC))}
integrand_LMX_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1))}
tres[5,14]<-sqrt(1-integrate(integrand_HN05_tau_dyn, lower = 0, upper = Inf)$value)
tres[6,14]<-sqrt(1-integrate(integrand_EXP_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[7,14]<-sqrt(1-integrate(integrand_HC_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[8,14]<-sqrt(1-integrate(integrand_LMX_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN05adj_dyn<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN,
AA0_EXP=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP,
AA0_HC=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC,
AA0_LMX=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN05_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj_dyn$p_HN_l)})
fit.bayesmeta.HN05_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj_dyn$p_HN_u)})
integrand_HN05_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*fit.bayesmeta.HN05_mu_l_dyn$dposterior(mu=x))}
sens_HN05_l_base_mu_dyn<-sqrt(1-integrate(integrand_HN05_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*fit.bayesmeta.HN05_mu_u_dyn$dposterior(mu=x))}
sens_HN05_u_base_mu_dyn<-sqrt(1-integrate(integrand_HN05_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_mu_dyn<-max(sens_HN05_l_base_mu_dyn, sens_HN05_u_base_mu_dyn)
integrand_HN05_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*fit.bayesmeta.HN05_tau_l_dyn$dposterior(tau=x))}
sens_HN05_l_base_tau_dyn<-sqrt(1-integrate(integrand_HN05_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*fit.bayesmeta.HN05_tau_u_dyn$dposterior(tau=x))}
sens_HN05_u_base_tau_dyn<-sqrt(1-integrate(integrand_HN05_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_tau_dyn<-max(sens_HN05_l_base_tau_dyn, sens_HN05_u_base_tau_dyn)
# EXP
fit.bayesmeta.EXP_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj_dyn$p_EXP_l)})
fit.bayesmeta.EXP_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj_dyn$p_EXP_u)})
integrand_EXP_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_EXP_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_EXP_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_mu_dyn<-max(sens_EXP_HN05adj_l_base_mu_dyn, sens_EXP_HN05adj_u_base_mu_dyn)
integrand_EXP_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_EXP_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_EXP_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_tau_dyn<-max(sens_EXP_HN05adj_l_base_tau_dyn, sens_EXP_HN05adj_u_base_tau_dyn)
# HC
fit.bayesmeta.HC_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj_dyn$p_HC_l)})
fit.bayesmeta.HC_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj_dyn$p_HC_u)})
integrand_HC_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_HC_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_HC_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_mu_dyn<-max(sens_HC_HN05adj_l_base_mu_dyn, sens_HC_HN05adj_u_base_mu_dyn)
integrand_HC_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_HC_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_HC_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_tau_dyn<-max(sens_HC_HN05adj_l_base_tau_dyn, sens_HC_HN05adj_u_base_tau_dyn)
# LMX
fit.bayesmeta.LMX_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj_dyn$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj_dyn$p_LMX_u, shape=1)})
integrand_LMX_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_LMX_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_LMX_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_mu_dyn<-max(sens_LMX_HN05adj_l_base_mu_dyn, sens_LMX_HN05adj_u_base_mu_dyn)
integrand_LMX_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_LMX_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_LMX_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_tau_dyn<-max(sens_LMX_HN05adj_l_base_tau_dyn, sens_LMX_HN05adj_u_base_tau_dyn)
tres[5,15]<-worst_sens_HN05_mu_dyn
tres[6,15]<-worst_sens_EXP_HN05adj_mu_dyn
tres[7,15]<-worst_sens_HC_HN05adj_mu_dyn
tres[8,15]<-worst_sens_LMX_HN05adj_mu_dyn
tres[5,16]<-worst_sens_HN05_tau_dyn
tres[6,16]<-worst_sens_EXP_HN05adj_tau_dyn
tres[7,16]<-worst_sens_HC_HN05adj_tau_dyn
tres[8,16]<-worst_sens_LMX_HN05adj_tau_dyn
####---- dynamic 0.5-tail adjustment with rlmc=0.5 ----####
# prior parameters
U_ref05<-sqrt(rlmc2/(1-rlmc2))*sigma_ref(df, type_sigma_ref=type_sigma_ref)
tres[c(13:16),1]<-U_ref05
tres[c(13:16),2]<-tail_alpha_dynamic
tres[13,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN
tres[14,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP
tres[15,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC
tres[16,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX
# effective mrlmc
tres[13,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[14,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[15,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[16,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN1_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
tres[13,c(5:7)]<-exp(fit.bayesmeta.HN1_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[13,c(9:11)]<-fit.bayesmeta.HN1_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
tres[14,c(5:7)]<-exp(fit.bayesmeta.EXP_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[14,c(9:11)]<-fit.bayesmeta.EXP_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
tres[15,c(5:7)]<-exp(fit.bayesmeta.HC_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[15,c(9:11)]<-fit.bayesmeta.HC_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
tres[16,c(5:7)]<-exp(fit.bayesmeta.LMX_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[16,c(9:11)]<-fit.bayesmeta.LMX_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN1_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[13,13]<-sqrt(1-integrate(integrand_HN1_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[14,13]<-sqrt(1-integrate(integrand_EXP_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[15,13]<-sqrt(1-integrate(integrand_HC_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[16,13]<-sqrt(1-integrate(integrand_LMX_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN1_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN))}
integrand_EXP_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP))}
integrand_HC_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC))}
integrand_LMX_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1))}
tres[13,14]<-sqrt(1-integrate(integrand_HN1_tau_dyn, lower = 0, upper = Inf)$value)
tres[14,14]<-sqrt(1-integrate(integrand_EXP_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[15,14]<-sqrt(1-integrate(integrand_HC_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[16,14]<-sqrt(1-integrate(integrand_LMX_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN1adj_dyn<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN,
AA0_EXP=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP,
AA0_HC=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC,
AA0_LMX=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN1_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj_dyn$p_HN_l)})
fit.bayesmeta.HN1_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj_dyn$p_HN_u)})
integrand_HN1_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*fit.bayesmeta.HN1_mu_l_dyn$dposterior(mu=x))}
sens_HN1_l_base_mu_dyn<-sqrt(1-integrate(integrand_HN1_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*fit.bayesmeta.HN1_mu_u_dyn$dposterior(mu=x))}
sens_HN1_u_base_mu_dyn<-sqrt(1-integrate(integrand_HN1_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_mu_dyn<-max(sens_HN1_l_base_mu_dyn, sens_HN1_u_base_mu_dyn)
integrand_HN1_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*fit.bayesmeta.HN1_tau_l_dyn$dposterior(tau=x))}
sens_HN1_l_base_tau_dyn<-sqrt(1-integrate(integrand_HN1_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*fit.bayesmeta.HN1_tau_u_dyn$dposterior(tau=x))}
sens_HN1_u_base_tau_dyn<-sqrt(1-integrate(integrand_HN1_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_tau_dyn<-max(sens_HN1_l_base_tau_dyn, sens_HN1_u_base_tau_dyn)
# EXP
fit.bayesmeta.EXP_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj_dyn$p_EXP_l)})
fit.bayesmeta.EXP_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj_dyn$p_EXP_u)})
integrand_EXP_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_EXP_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_EXP_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_mu_dyn<-max(sens_EXP_HN1adj_l_base_mu_dyn, sens_EXP_HN1adj_u_base_mu_dyn)
integrand_EXP_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_EXP_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_EXP_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_tau_dyn<-max(sens_EXP_HN1adj_l_base_tau_dyn, sens_EXP_HN1adj_u_base_tau_dyn)
# HC
fit.bayesmeta.HC_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj_dyn$p_HC_l)})
fit.bayesmeta.HC_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj_dyn$p_HC_u)})
integrand_HC_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_HC_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_HC_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_mu_dyn<-max(sens_HC_HN1adj_l_base_mu_dyn, sens_HC_HN1adj_u_base_mu_dyn)
integrand_HC_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_HC_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_HC_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_tau_dyn<-max(sens_HC_HN1adj_l_base_tau_dyn, sens_HC_HN1adj_u_base_tau_dyn)
# LMX
fit.bayesmeta.LMX_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj_dyn$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj_dyn$p_LMX_u, shape=1)})
integrand_LMX_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_LMX_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_LMX_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_mu_dyn<-max(sens_LMX_HN1adj_l_base_mu_dyn, sens_LMX_HN1adj_u_base_mu_dyn)
integrand_LMX_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_LMX_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_LMX_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_tau_dyn<-max(sens_LMX_HN1adj_l_base_tau_dyn, sens_LMX_HN1adj_u_base_tau_dyn)
tres[13,15]<-worst_sens_HN1_mu_dyn
tres[14,15]<-worst_sens_EXP_HN1adj_mu_dyn
tres[15,15]<-worst_sens_HC_HN1adj_mu_dyn
tres[16,15]<-worst_sens_LMX_HN1adj_mu_dyn
tres[13,16]<-worst_sens_HN1_tau_dyn
tres[14,16]<-worst_sens_EXP_HN1adj_tau_dyn
tres[15,16]<-worst_sens_HC_HN1adj_tau_dyn
tres[16,16]<-worst_sens_LMX_HN1adj_tau_dyn
#### Computation of the length of 95%CrI
tres[,8]<-tres[,7]-tres[,6] #length_95CrI_post_OR
tres[,12]<-tres[,11]-tres[,10] #length_95CrI_post_tau
# transformation of effect estimates to log scale
if(scale_effect=="logOR")
tres <- or2logor(tres)
return(tres)
}
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Defines functions sensitivity_learning_table_flexible
Documented in sensitivity_learning_table_flexible
sensitivity_learning_table_flexible <- function(df, tail_alpha_static=0.04550026, U1=1, U2=2,
tail_alpha_dynamic=0.5, rlmc1=0.25, rlmc2=0.5,
scale_effect="OR", type_sigma_ref="geometric",
mu_mean=0, mu_sd=4, grid_epsilon=0.00354){
# This flexible function enables a flexible change of all parameters and provides redundant programming.
# If necessary, this function can be split into parts without much recoding.
# It takes ca. 10 min to run this function.
# learning_sensitivity_table function (multiple calls of bayesmeta)
# computes a table containing the paremeters of heterogeneity priors HN, EXP, HC, LMX,
# descriptive statistics of posteriors,
# learning and sensitivity estimates for static 5%-tail HN(0.5)(U=1)- and HN(1)(U=2)-like scale parameters for for HN, EXP, HC, LMX heterogeneity priors
# learning and sensitivity for dynamically assigned scaling parameters for HN, EXP, HC, LMX for rlmc1 and rlmc2 adjusted at the median
# input:
# df: data frame in form compatible with data objects in the bayesmeta environment
## tail_alpha_static: P[HN(0.5)>1]=0.04550026, P[HN(1)>2]=0.04550026
# tail_alpha_static: =0.04550026 (recommended value)
## U1: threshold for P[HN(0.5)>1]=0.04550026
# U1: =1 (recommended value)
## U1: threshold for P[HN(1)>2]=0.04550026
# U2: =2 (recommended value)
## tail_alpha_dynamic=0.5: centering of Uref in the median P[tau>=Uref]=tail_alpha_tynamic=0.5 for a heterogeneity prior for tau
# tail_alpha_dynamic: =0.5 (recommended value)
## rlmc1=0.25: The Relative Latent Model Complexity (RLMC) set to 0.25 (empirically corresponding to HN(0.5))
#rlmc1: =0.25 (recommended value)
# rlmc2=0.5: The Relative Latent Model Complexity (RLMC) set to 0.5 (empirically corresponding to HN(1))
# rlmc2: =0.5 (recommended value)
## Method for the computation of the reference within-study standard deviation: either "geometric" or "harmonic"
# type_sigma_ref: ="geometric" (recommended value)
## grid_epsilon for sensitivity computation
## grid_epsilon=0.00354: grid_epsilon as suggested by Roos et al. (2015) corresponds to H(N(0,1),N(0.01,1))=0.00354
# grid_epsilon: =0.00354 (recommended value)
# output:
# table with the following columns:
# "U"
# "tail_prob"
# "par_val"
# "MRLMC"
# "median_post_OR"
# "95CrI_post_OR_low"
# "95CrI_post_OR_up"
# "length_95CrI_post_OR"
# "median_post_tau"
# "95CrI_post_tau_low"
# "95CrI_post_tau_up"
# "length_95CrI_post_tau"
# "L_mu"
# "L_tau"
# "S_mu"
# "S_tau"
# for HN, EXP, HC and LMX heterogeneity priors with the following scaling parameters (indicated in rows)
# "HN(0.5)_U1tail", "EXP_U1tail", "HC_U1tail", "LMX_U1tail": tail_alpha_static %-tail adjusted with threshold U=U1 (static)
# "HN_rlmc1", "EXP_rlmc1", "HC_rlmc1", "LMX_rlmc1": dynamically adjusted with target RLMC=rlmc1 and tail probability tail_alpha_dynamic
# "HN(1)_U2tail", "EXP_U2tail", "HC_U2tail", "LMX_U2tail":: tail_alpha_static %-tail adjusted with threshold U=U2 (static)
# "HN_rlmc2", "EXP_rlmc2", "HC_rlmc2", "LMX_rlmc2": dynamically adjusted with target RLMC=rlmc2 and tail probability tail_alpha_dynamic
# with bayesmeta
# library(bayesmeta)
# Version downloaded on 20180928
####---- parameters for learning and sensitivity computation (are now provided in the call of the flexible function) ----####
# # mu_mean: mean of the Normal prior for mu
# mu_mean <- 0
# # mu_sd: sd of the Normal prior for mu (according to Roever(2018) Bayesmeta-Paper (unit-information prior for log-odds-ratios))
# mu_sd <- 4
# ## static choice of the scale parameter for the heterogeneity prior for tau
# # 1-phalfnormal(q=1, scale=0.5) # P[HN(0.5)>1]=0.04550026
# # 1-phalfnormal(q=2, scale=1) # P[HN(1)>2]=0.04550026
# # tail_alpha_static: P[HN(0.5)>1]=0.04550026, P[HN(1)>2]=0.04550026
# tail_alpha_static <- 0.04550026
# # U1: thershold for P[HN(0.5)>1]=0.04550026
# U1 <- 1
# # U1: thershold for P[HN(1)>2]=0.04550026
# U2 <- 2
# ## dynamic choice of the scale parameter for the heterogeneity prior for tau
# # tail_alpha_dynamic=0.5: centering of Uref in the median P[tau>=Uref]=tail_alpha_tynamic=0.5 for a heterogeneity prior for tau
# tail_alpha_dynamic <- 0.5
# # rlmc1=0.25: The Relative Latent Model Complexity (RLMC) set to 0.25 (empirically corresponding to HN(0.5))
# rlmc1 <- 0.25
# # rlmc2=0.5: The Relative Latent Model Complexity (RLMC) set to 0.5 (empirically corresponding to HN(1))
# rlmc2 <- 0.5
# ## grid_epsilon for sensitivity computation
# # grid_epsilon=0.00354: grid_epsilon as suggested by Roos et al. (2015) corresponds to H(N(0,1),N(0.01,1))=0.00354
# grid_epsilon <- 0.00354
#
####---- epsilon-local grid for mu ----####
# normal (for mu)
# upper and lower epsilon grid values for a normal distribution with mean=0 according to equation (20) in Roos et al. (2015) expressed in terms of mu_sd
AAu_normal_mu <- mu_sd*(1+sqrt(1-(1-grid_epsilon^2)^4))/(1-grid_epsilon^2)^2
AAl_normal_mu <- mu_sd*(1-sqrt(1-(1-grid_epsilon^2)^4))/(1-grid_epsilon^2)^2
####---- create an object to collect the results ----####
tres<-matrix(NA, nrow=16, ncol=16)
if(!(scale_effect=="OR" || scale_effect=="logOR"))
warning(paste0("scale_effect must either be ", "OR", "or ","logOR",
sep=""))
colnames(tres)<-c("U", "tail_prob", "par_val", "MRLMC",
"median_post_OR", "95CrI_post_OR_low", "95CrI_post_OR_up", "length_95CrI_post_OR",
"median_post_tau", "95CrI_post_tau_low", "95CrI_post_tau_up", "length_95CrI_post_tau",
"L_mu", "L_tau", "S_mu", "S_tau")
rownames(tres)<-c("HN_U1tail", "EXP_U1tail", "HC_U1tail", "LMX_U1tail",
"HN_rlmc1", "EXP_rlmc1", "HC_rlmc1", "LMX_rlmc1",
"HN_U2tail", "EXP_U2tail", "HC_U2tail", "LMX_U2tail",
"HN_rlmc2", "EXP_rlmc2", "HC_rlmc2", "LMX_rlmc2")
####---- (HN(0.5)-like) static 0.05-tail adjustment with threshold U=1 (HN(0.5)) ----####
# prior parameters
tres[c(1:4),1]<-U1
tres[c(1:4),2]<-tail_alpha_static
tres[1,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN
tres[2,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP
tres[3,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC
tres[4,3]<-pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX
# effective mrlmc
tres[1,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[2,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[3,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[4,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN05 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
tres[1,c(5:7)]<-exp(fit.bayesmeta.HN05$summary[c("median","95% lower","95% upper"),"mu"])
tres[1,c(9:11)]<-fit.bayesmeta.HN05$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
tres[2,c(5:7)]<-exp(fit.bayesmeta.EXP_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[2,c(9:11)]<-fit.bayesmeta.EXP_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
tres[3,c(5:7)]<-exp(fit.bayesmeta.HC_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[3,c(9:11)]<-fit.bayesmeta.HC_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
tres[4,c(5:7)]<-exp(fit.bayesmeta.LMX_HN05adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[4,c(9:11)]<-fit.bayesmeta.LMX_HN05adj$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN05_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN05adj_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[1,13]<-sqrt(1-integrate(integrand_HN05_mu, lower = -Inf, upper = Inf)$value)
tres[2,13]<-sqrt(1-integrate(integrand_EXP_HN05adj_mu, lower = -Inf, upper = Inf)$value)
tres[3,13]<-sqrt(1-integrate(integrand_HC_HN05adj_mu, lower = -Inf, upper = Inf)$value)
tres[4,13]<-sqrt(1-integrate(integrand_LMX_HN05adj_mu, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN05_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN))}
integrand_EXP_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP))}
integrand_HC_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC))}
integrand_LMX_HN05adj_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1))}
tres[1,14]<-sqrt(1-integrate(integrand_HN05_tau, lower = 0, upper = Inf)$value)
tres[2,14]<-sqrt(1-integrate(integrand_EXP_HN05adj_tau, lower = 0, upper = Inf)$value)
tres[3,14]<-sqrt(1-integrate(integrand_HC_HN05adj_tau, lower = 0, upper = Inf)$value)
tres[4,14]<-sqrt(1-integrate(integrand_LMX_HN05adj_tau, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN05adj<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN,
AA0_EXP=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP,
AA0_HC=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC,
AA0_LMX=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN05 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN05_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj$p_HN_l)})
fit.bayesmeta.HN05_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj$p_HN_u)})
integrand_HN05_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*fit.bayesmeta.HN05_mu_l$dposterior(mu=x))}
sens_HN05_l_base_mu<-sqrt(1-integrate(integrand_HN05_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(mu=x)*fit.bayesmeta.HN05_mu_u$dposterior(mu=x))}
sens_HN05_u_base_mu<-sqrt(1-integrate(integrand_HN05_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_mu<-max(sens_HN05_l_base_mu, sens_HN05_u_base_mu)
integrand_HN05_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*fit.bayesmeta.HN05_tau_l$dposterior(tau=x))}
sens_HN05_l_base_tau<-sqrt(1-integrate(integrand_HN05_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HN05$dposterior(tau=x)*fit.bayesmeta.HN05_tau_u$dposterior(tau=x))}
sens_HN05_u_base_tau<-sqrt(1-integrate(integrand_HN05_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_tau<-max(sens_HN05_l_base_tau, sens_HN05_u_base_tau)
# EXP
fit.bayesmeta.EXP_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj$p_EXP_l)})
fit.bayesmeta.EXP_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj$p_EXP_u)})
integrand_EXP_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_l$dposterior(mu=x))}
sens_EXP_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_u$dposterior(mu=x))}
sens_EXP_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_mu<-max(sens_EXP_HN05adj_l_base_mu, sens_EXP_HN05adj_u_base_mu)
integrand_EXP_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_l$dposterior(tau=x))}
sens_EXP_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_u$dposterior(tau=x))}
sens_EXP_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_tau<-max(sens_EXP_HN05adj_l_base_tau, sens_EXP_HN05adj_u_base_tau)
# HC
fit.bayesmeta.HC_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj$p_HC_l)})
fit.bayesmeta.HC_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj$p_HC_u)})
integrand_HC_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_l$dposterior(mu=x))}
sens_HC_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_u$dposterior(mu=x))}
sens_HC_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_mu<-max(sens_HC_HN05adj_l_base_mu, sens_HC_HN05adj_u_base_mu)
integrand_HC_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_l$dposterior(tau=x))}
sens_HC_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_u$dposterior(tau=x))}
sens_HC_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_tau<-max(sens_HC_HN05adj_l_base_tau, sens_HC_HN05adj_u_base_tau)
# LMX
fit.bayesmeta.LMX_HN05adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U1, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj$p_LMX_u, shape=1)})
integrand_LMX_HN05adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_l$dposterior(mu=x))}
sens_LMX_HN05adj_l_base_mu<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_u$dposterior(mu=x))}
sens_LMX_HN05adj_u_base_mu<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_mu<-max(sens_LMX_HN05adj_l_base_mu, sens_LMX_HN05adj_u_base_mu)
integrand_LMX_HN05adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_l$dposterior(tau=x))}
sens_LMX_HN05adj_l_base_tau<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_u$dposterior(tau=x))}
sens_LMX_HN05adj_u_base_tau<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_tau<-max(sens_LMX_HN05adj_l_base_tau, sens_LMX_HN05adj_u_base_tau)
tres[1,15]<-worst_sens_HN05_mu
tres[2,15]<-worst_sens_EXP_HN05adj_mu
tres[3,15]<-worst_sens_HC_HN05adj_mu
tres[4,15]<-worst_sens_LMX_HN05adj_mu
tres[1,16]<-worst_sens_HN05_tau
tres[2,16]<-worst_sens_EXP_HN05adj_tau
tres[3,16]<-worst_sens_HC_HN05adj_tau
tres[4,16]<-worst_sens_LMX_HN05adj_tau
####---- (HN(1)-like) static 0.05-tail adjustment with threshold U=2 (HN(1)) ----####
# prior parameters
tres[c(9:12),1]<-U2
tres[c(9:12),2]<-tail_alpha_static
tres[9,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN
tres[10,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP
tres[11,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC
tres[12,3]<-pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX
# effective mrlmc
tres[9,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[10,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[11,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[12,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN1 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
tres[9,c(5:7)]<-exp(fit.bayesmeta.HN1$summary[c("median","95% lower","95% upper"),"mu"])
tres[9,c(9:11)]<-fit.bayesmeta.HN1$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
tres[10,c(5:7)]<-exp(fit.bayesmeta.EXP_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[10,c(9:11)]<-fit.bayesmeta.EXP_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
tres[11,c(5:7)]<-exp(fit.bayesmeta.HC_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[11,c(9:11)]<-fit.bayesmeta.HC_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
tres[12,c(5:7)]<-exp(fit.bayesmeta.LMX_HN1adj$summary[c("median","95% lower","95% upper"),"mu"])
tres[12,c(9:11)]<-fit.bayesmeta.LMX_HN1adj$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN1_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN1adj_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[9,13]<-sqrt(1-integrate(integrand_HN1_mu, lower = -Inf, upper = Inf)$value)
tres[10,13]<-sqrt(1-integrate(integrand_EXP_HN1adj_mu, lower = -Inf, upper = Inf)$value)
tres[11,13]<-sqrt(1-integrate(integrand_HC_HN1adj_mu, lower = -Inf, upper = Inf)$value)
tres[12,13]<-sqrt(1-integrate(integrand_LMX_HN1adj_mu, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN1_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN))}
integrand_EXP_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP))}
integrand_HC_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC))}
integrand_LMX_HN1adj_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1))}
tres[9,14]<-sqrt(1-integrate(integrand_HN1_tau, lower = 0, upper = Inf)$value)
tres[10,14]<-sqrt(1-integrate(integrand_EXP_HN1adj_tau, lower = 0, upper = Inf)$value)
tres[11,14]<-sqrt(1-integrate(integrand_HC_HN1adj_tau, lower = 0, upper = Inf)$value)
tres[12,14]<-sqrt(1-integrate(integrand_LMX_HN1adj_tau, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN1adj<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN,
AA0_EXP=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP,
AA0_HC=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC,
AA0_LMX=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN1 <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HN)})
fit.bayesmeta.HN1_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj$p_HN_l)})
fit.bayesmeta.HN1_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj$p_HN_u)})
integrand_HN1_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*fit.bayesmeta.HN1_mu_l$dposterior(mu=x))}
sens_HN1_l_base_mu<-sqrt(1-integrate(integrand_HN1_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(mu=x)*fit.bayesmeta.HN1_mu_u$dposterior(mu=x))}
sens_HN1_u_base_mu<-sqrt(1-integrate(integrand_HN1_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_mu<-max(sens_HN1_l_base_mu, sens_HN1_u_base_mu)
integrand_HN1_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*fit.bayesmeta.HN1_tau_l$dposterior(tau=x))}
sens_HN1_l_base_tau<-sqrt(1-integrate(integrand_HN1_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HN1$dposterior(tau=x)*fit.bayesmeta.HN1_tau_u$dposterior(tau=x))}
sens_HN1_u_base_tau<-sqrt(1-integrate(integrand_HN1_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_tau<-max(sens_HN1_l_base_tau, sens_HN1_u_base_tau)
# EXP
fit.bayesmeta.EXP_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj$p_EXP_l)})
fit.bayesmeta.EXP_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj$p_EXP_u)})
integrand_EXP_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_l$dposterior(mu=x))}
sens_EXP_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_u$dposterior(mu=x))}
sens_EXP_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_mu<-max(sens_EXP_HN1adj_l_base_mu, sens_EXP_HN1adj_u_base_mu)
integrand_EXP_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_l$dposterior(tau=x))}
sens_EXP_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_u$dposterior(tau=x))}
sens_EXP_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_tau<-max(sens_EXP_HN1adj_l_base_tau, sens_EXP_HN1adj_u_base_tau)
# HC
fit.bayesmeta.HC_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_HC)})
fit.bayesmeta.HC_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj$p_HC_l)})
fit.bayesmeta.HC_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj$p_HC_u)})
integrand_HC_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_l$dposterior(mu=x))}
sens_HC_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_u$dposterior(mu=x))}
sens_HC_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_mu<-max(sens_HC_HN1adj_l_base_mu, sens_HC_HN1adj_u_base_mu)
integrand_HC_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_l$dposterior(tau=x))}
sens_HC_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_u$dposterior(tau=x))}
sens_HC_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_tau<-max(sens_HC_HN1adj_l_base_tau, sens_HC_HN1adj_u_base_tau)
# LMX
fit.bayesmeta.LMX_HN1adj <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_static(UU=U2, tail_prob=tail_alpha_static)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_l <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_u <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj$p_LMX_u, shape=1)})
integrand_LMX_HN1adj_l_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_l$dposterior(mu=x))}
sens_LMX_HN1adj_l_base_mu<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_mu <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_u$dposterior(mu=x))}
sens_LMX_HN1adj_u_base_mu<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_mu, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_mu<-max(sens_LMX_HN1adj_l_base_mu, sens_LMX_HN1adj_u_base_mu)
integrand_LMX_HN1adj_l_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_l$dposterior(tau=x))}
sens_LMX_HN1adj_l_base_tau<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_tau <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_u$dposterior(tau=x))}
sens_LMX_HN1adj_u_base_tau<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_tau, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_tau<-max(sens_LMX_HN1adj_l_base_tau, sens_LMX_HN1adj_u_base_tau)
tres[9,15]<-worst_sens_HN1_mu
tres[10,15]<-worst_sens_EXP_HN1adj_mu
tres[11,15]<-worst_sens_HC_HN1adj_mu
tres[12,15]<-worst_sens_LMX_HN1adj_mu
tres[9,16]<-worst_sens_HN1_tau
tres[10,16]<-worst_sens_EXP_HN1adj_tau
tres[11,16]<-worst_sens_HC_HN1adj_tau
tres[12,16]<-worst_sens_LMX_HN1adj_tau
####---- dynamic 0.5-tail adjustment with rlmc=0.25 ----####
# prior parameters
U_ref025<-sqrt(rlmc1/(1-rlmc1))*sigma_ref(df, type_sigma_ref=type_sigma_ref)
tres[c(5:8),1] <- U_ref025
tres[c(5:8),2] <- tail_alpha_dynamic
tres[5,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN
tres[6,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP
tres[7,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC
tres[8,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX
# effective mrlmc
tres[5,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[6,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[7,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[8,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN05_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
tres[5,c(5:7)]<-exp(fit.bayesmeta.HN05_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[5,c(9:11)]<-fit.bayesmeta.HN05_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
tres[6,c(5:7)]<-exp(fit.bayesmeta.EXP_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[6,c(9:11)]<-fit.bayesmeta.EXP_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
tres[7,c(5:7)]<-exp(fit.bayesmeta.HC_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[7,c(9:11)]<-fit.bayesmeta.HC_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
tres[8,c(5:7)]<-exp(fit.bayesmeta.LMX_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[8,c(9:11)]<-fit.bayesmeta.LMX_HN05adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN05_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN05adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[5,13]<-sqrt(1-integrate(integrand_HN05_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[6,13]<-sqrt(1-integrate(integrand_EXP_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[7,13]<-sqrt(1-integrate(integrand_HC_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[8,13]<-sqrt(1-integrate(integrand_LMX_HN05adj_mu_dyn, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN05_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN))}
integrand_EXP_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP))}
integrand_HC_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC))}
integrand_LMX_HN05adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1))}
tres[5,14]<-sqrt(1-integrate(integrand_HN05_tau_dyn, lower = 0, upper = Inf)$value)
tres[6,14]<-sqrt(1-integrate(integrand_EXP_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[7,14]<-sqrt(1-integrate(integrand_HC_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[8,14]<-sqrt(1-integrate(integrand_LMX_HN05adj_tau_dyn, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN05adj_dyn<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN,
AA0_EXP=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP,
AA0_HC=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC,
AA0_LMX=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN05_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN05_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj_dyn$p_HN_l)})
fit.bayesmeta.HN05_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN05adj_dyn$p_HN_u)})
integrand_HN05_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*fit.bayesmeta.HN05_mu_l_dyn$dposterior(mu=x))}
sens_HN05_l_base_mu_dyn<-sqrt(1-integrate(integrand_HN05_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(mu=x)*fit.bayesmeta.HN05_mu_u_dyn$dposterior(mu=x))}
sens_HN05_u_base_mu_dyn<-sqrt(1-integrate(integrand_HN05_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_mu_dyn<-max(sens_HN05_l_base_mu_dyn, sens_HN05_u_base_mu_dyn)
integrand_HN05_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*fit.bayesmeta.HN05_tau_l_dyn$dposterior(tau=x))}
sens_HN05_l_base_tau_dyn<-sqrt(1-integrate(integrand_HN05_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN05_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN05_dyn$dposterior(tau=x)*fit.bayesmeta.HN05_tau_u_dyn$dposterior(tau=x))}
sens_HN05_u_base_tau_dyn<-sqrt(1-integrate(integrand_HN05_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN05_tau_dyn<-max(sens_HN05_l_base_tau_dyn, sens_HN05_u_base_tau_dyn)
# EXP
fit.bayesmeta.EXP_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj_dyn$p_EXP_l)})
fit.bayesmeta.EXP_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN05adj_dyn$p_EXP_u)})
integrand_EXP_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_EXP_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_EXP_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_mu_dyn<-max(sens_EXP_HN05adj_l_base_mu_dyn, sens_EXP_HN05adj_u_base_mu_dyn)
integrand_EXP_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_EXP_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_EXP_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN05adj_tau_dyn<-max(sens_EXP_HN05adj_l_base_tau_dyn, sens_EXP_HN05adj_u_base_tau_dyn)
# HC
fit.bayesmeta.HC_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj_dyn$p_HC_l)})
fit.bayesmeta.HC_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN05adj_dyn$p_HC_u)})
integrand_HC_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_HC_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_HC_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_mu_dyn<-max(sens_HC_HN05adj_l_base_mu_dyn, sens_HC_HN05adj_u_base_mu_dyn)
integrand_HC_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_HC_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_HC_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN05adj_tau_dyn<-max(sens_HC_HN05adj_l_base_tau_dyn, sens_HC_HN05adj_u_base_tau_dyn)
# LMX
fit.bayesmeta.LMX_HN05adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc1, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj_dyn$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN05adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN05adj_dyn$p_LMX_u, shape=1)})
integrand_LMX_HN05adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_l_dyn$dposterior(mu=x))}
sens_LMX_HN05adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN05adj_mu_u_dyn$dposterior(mu=x))}
sens_LMX_HN05adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_mu_dyn<-max(sens_LMX_HN05adj_l_base_mu_dyn, sens_LMX_HN05adj_u_base_mu_dyn)
integrand_LMX_HN05adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_l_dyn$dposterior(tau=x))}
sens_LMX_HN05adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN05adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN05adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN05adj_tau_u_dyn$dposterior(tau=x))}
sens_LMX_HN05adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN05adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN05adj_tau_dyn<-max(sens_LMX_HN05adj_l_base_tau_dyn, sens_LMX_HN05adj_u_base_tau_dyn)
tres[5,15]<-worst_sens_HN05_mu_dyn
tres[6,15]<-worst_sens_EXP_HN05adj_mu_dyn
tres[7,15]<-worst_sens_HC_HN05adj_mu_dyn
tres[8,15]<-worst_sens_LMX_HN05adj_mu_dyn
tres[5,16]<-worst_sens_HN05_tau_dyn
tres[6,16]<-worst_sens_EXP_HN05adj_tau_dyn
tres[7,16]<-worst_sens_HC_HN05adj_tau_dyn
tres[8,16]<-worst_sens_LMX_HN05adj_tau_dyn
####---- dynamic 0.5-tail adjustment with rlmc=0.5 ----####
# prior parameters
U_ref05<-sqrt(rlmc2/(1-rlmc2))*sigma_ref(df, type_sigma_ref=type_sigma_ref)
tres[c(13:16),1]<-U_ref05
tres[c(13:16),2]<-tail_alpha_dynamic
tres[13,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN
tres[14,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP
tres[15,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC
tres[16,3]<-pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX
# effective mrlmc
tres[13,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfnormal(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN),
MM=1000000, output="sample", step=0.03))
tres[14,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rexp(n=MM, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP),
MM=1000000, output="sample", step=0.03))
tres[15,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rhalfcauchy(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC),
MM=1000000, output="sample", step=0.03))
tres[16,4]<- median(effective_rlmc(df=df, r.tau.prior=function(MM)rlomax(n=MM, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1),
MM=1000000, output="sample", step=0.03))
# posteriors for base HN, EXP, HC and LMX heterogeneity priors
fit.bayesmeta.HN1_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
tres[13,c(5:7)]<-exp(fit.bayesmeta.HN1_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[13,c(9:11)]<-fit.bayesmeta.HN1_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.EXP_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
tres[14,c(5:7)]<-exp(fit.bayesmeta.EXP_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[14,c(9:11)]<-fit.bayesmeta.EXP_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.HC_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
tres[15,c(5:7)]<-exp(fit.bayesmeta.HC_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[15,c(9:11)]<-fit.bayesmeta.HC_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
fit.bayesmeta.LMX_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
tres[16,c(5:7)]<-exp(fit.bayesmeta.LMX_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"mu"])
tres[16,c(9:11)]<-fit.bayesmeta.LMX_HN1adj_dyn$summary[c("median","95% lower","95% upper"),"tau"]
# learning quantification
# mu
integrand_HN1_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_EXP_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_HC_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
integrand_LMX_HN1adj_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*dnorm(x, mean=mu_mean, sd=mu_sd))}
tres[13,13]<-sqrt(1-integrate(integrand_HN1_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[14,13]<-sqrt(1-integrate(integrand_EXP_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[15,13]<-sqrt(1-integrate(integrand_HC_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
tres[16,13]<-sqrt(1-integrate(integrand_LMX_HN1adj_mu_dyn, lower = -Inf, upper = Inf)$value)
# tau
integrand_HN1_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*dhalfnormal(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN))}
integrand_EXP_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*dexp(x, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP))}
integrand_HC_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*dhalfcauchy(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC))}
integrand_LMX_HN1adj_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*dlomax(x, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1))}
tres[13,14]<-sqrt(1-integrate(integrand_HN1_tau_dyn, lower = 0, upper = Inf)$value)
tres[14,14]<-sqrt(1-integrate(integrand_EXP_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[15,14]<-sqrt(1-integrate(integrand_HC_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
tres[16,14]<-sqrt(1-integrate(integrand_LMX_HN1adj_tau_dyn, lower = 0, upper = Inf)$value)
# epsilon-local grid for A*|X| scaled distributions for tau
gr2p_HN1adj_dyn<-pri_par_epsilon_grid(AA0_HN=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN,
AA0_EXP=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP,
AA0_HC=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC,
AA0_LMX=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX,
grid_epsilon=grid_epsilon)
# sensitivity quantification
# HN
fit.bayesmeta.HN1_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfnormal(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HN)})
fit.bayesmeta.HN1_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj_dyn$p_HN_l)})
fit.bayesmeta.HN1_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfnormal(t, scale=gr2p_HN1adj_dyn$p_HN_u)})
integrand_HN1_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*fit.bayesmeta.HN1_mu_l_dyn$dposterior(mu=x))}
sens_HN1_l_base_mu_dyn<-sqrt(1-integrate(integrand_HN1_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(mu=x)*fit.bayesmeta.HN1_mu_u_dyn$dposterior(mu=x))}
sens_HN1_u_base_mu_dyn<-sqrt(1-integrate(integrand_HN1_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_mu_dyn<-max(sens_HN1_l_base_mu_dyn, sens_HN1_u_base_mu_dyn)
integrand_HN1_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*fit.bayesmeta.HN1_tau_l_dyn$dposterior(tau=x))}
sens_HN1_l_base_tau_dyn<-sqrt(1-integrate(integrand_HN1_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HN1_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HN1_dyn$dposterior(tau=x)*fit.bayesmeta.HN1_tau_u_dyn$dposterior(tau=x))}
sens_HN1_u_base_tau_dyn<-sqrt(1-integrate(integrand_HN1_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HN1_tau_dyn<-max(sens_HN1_l_base_tau_dyn, sens_HN1_u_base_tau_dyn)
# EXP
fit.bayesmeta.EXP_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dexp(t, rate=1/pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_EXP)})
fit.bayesmeta.EXP_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj_dyn$p_EXP_l)})
fit.bayesmeta.EXP_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dexp(t, rate=1/gr2p_HN1adj_dyn$p_EXP_u)})
integrand_EXP_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_EXP_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.EXP_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_EXP_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_mu_dyn<-max(sens_EXP_HN1adj_l_base_mu_dyn, sens_EXP_HN1adj_u_base_mu_dyn)
integrand_EXP_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_EXP_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_EXP_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.EXP_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.EXP_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_EXP_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_EXP_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_EXP_HN1adj_tau_dyn<-max(sens_EXP_HN1adj_l_base_tau_dyn, sens_EXP_HN1adj_u_base_tau_dyn)
# HC
fit.bayesmeta.HC_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dhalfcauchy(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_HC)})
fit.bayesmeta.HC_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj_dyn$p_HC_l)})
fit.bayesmeta.HC_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dhalfcauchy(t, scale=gr2p_HN1adj_dyn$p_HC_u)})
integrand_HC_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_HC_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.HC_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_HC_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_mu_dyn<-max(sens_HC_HN1adj_l_base_mu_dyn, sens_HC_HN1adj_u_base_mu_dyn)
integrand_HC_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_HC_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_HC_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.HC_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.HC_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_HC_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_HC_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_HC_HN1adj_tau_dyn<-max(sens_HC_HN1adj_l_base_tau_dyn, sens_HC_HN1adj_u_base_tau_dyn)
# LMX
fit.bayesmeta.LMX_HN1adj_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAl_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_mu_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=AAu_normal_mu,
tau.prior=function(t){dlomax(t, scale=pri_par_adjust_dynamic(df=df, rlmc=rlmc2, tail_prob=tail_alpha_dynamic, type_sigma_ref=type_sigma_ref)$p_LMX, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_l_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj_dyn$p_LMX_l, shape=1)})
fit.bayesmeta.LMX_HN1adj_tau_u_dyn <- bayesmeta(y=df[,"y"],
sigma=df[,"sigma"],
labels=df[,"labels"],
mu.prior.mean=mu_mean, mu.prior.sd=mu_sd,
tau.prior=function(t){dlomax(t, scale=gr2p_HN1adj_dyn$p_LMX_u, shape=1)})
integrand_LMX_HN1adj_l_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_l_dyn$dposterior(mu=x))}
sens_LMX_HN1adj_l_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_mu_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(mu=x)*fit.bayesmeta.LMX_HN1adj_mu_u_dyn$dposterior(mu=x))}
sens_LMX_HN1adj_u_base_mu_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_mu_dyn, lower = -Inf, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_mu_dyn<-max(sens_LMX_HN1adj_l_base_mu_dyn, sens_LMX_HN1adj_u_base_mu_dyn)
integrand_LMX_HN1adj_l_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_l_dyn$dposterior(tau=x))}
sens_LMX_HN1adj_l_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_l_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
integrand_LMX_HN1adj_u_base_tau_dyn <- function(x) {sqrt(fit.bayesmeta.LMX_HN1adj_dyn$dposterior(tau=x)*fit.bayesmeta.LMX_HN1adj_tau_u_dyn$dposterior(tau=x))}
sens_LMX_HN1adj_u_base_tau_dyn<-sqrt(1-integrate(integrand_LMX_HN1adj_u_base_tau_dyn, lower = 0, upper = Inf)$value)/grid_epsilon
worst_sens_LMX_HN1adj_tau_dyn<-max(sens_LMX_HN1adj_l_base_tau_dyn, sens_LMX_HN1adj_u_base_tau_dyn)
tres[13,15]<-worst_sens_HN1_mu_dyn
tres[14,15]<-worst_sens_EXP_HN1adj_mu_dyn
tres[15,15]<-worst_sens_HC_HN1adj_mu_dyn
tres[16,15]<-worst_sens_LMX_HN1adj_mu_dyn
tres[13,16]<-worst_sens_HN1_tau_dyn
tres[14,16]<-worst_sens_EXP_HN1adj_tau_dyn
tres[15,16]<-worst_sens_HC_HN1adj_tau_dyn
tres[16,16]<-worst_sens_LMX_HN1adj_tau_dyn
#### Computation of the length of 95%CrI
tres[,8]<-tres[,7]-tres[,6] #length_95CrI_post_OR
tres[,12]<-tres[,11]-tres[,10] #length_95CrI_post_tau
# transformation of effect estimates to log scale
if(scale_effect=="logOR")
tres <- or2logor(tres)
return(tres)
}
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