d2BC_S_I_HC_raw: Sensitivity and Identification measure expressed by the...
In si4bayesmeta: Sensitivity and Identification for the Bayesian Meta-Analysis

Description Usage Arguments Details Value References See Also Examples

Returns the second derivative of the Bhattacharyya coefficient for a Bayesian NNHM with respect to Priori and Likelihood perturbations given a HC heterogeneity prior.

1	d2BC_S_I_HC_raw(df, hh, rlmc = 0.5, mu_mean = 0, mu_sd = 4)

`df`	original base data frame in a `bayesmeta` format
`hh`	the step for the numerical computation of derivatives of BC with respect to changing RLMC in a Bayesian NNHM
`rlmc`	the value of the target RLMC, usually set to 0.25, 0.5 or 0.75
`mu_mean`	mean of the normal prior for mu
`mu_sd`	sd of the normal prior for mu

Provides the Sensitivity and Identification estimates according to Roos et al. (2020). Sensitivity quantification is performed by a HC heterogeneity prior perturbation in a Bayesian NNHM with a fixed likelihood. Identification quantification is obtained by likelihood perturbation in a Bayesian NNHM with a fixed HC heterogeneity prior. The measure is based on the computation of second derivatives of the Bhattacharyya coefficient with respect to RLMC at a base RLMC value.

Table with the S-I (sensitivity-identification) measure: with sensitivity ("S_d2BC_P") and identification ("I_d2BC_L").

Roos, M., Hunanyan, S., Bakka, H., Rue, H. (2020). Sensitivity and identification quantification by a relative latent model complexity perturbation in the Bayesian meta-analysis. Manuscript submitted to Research Synthesis Methods.

pri_par_adjust_HC, d2BC, descr_extract, bayesmeta in package bayesmeta

# Acute Graft rejection (AGR) data analyzed in Friede et al. (2017),  
# Sect. 3.2, URL: https://doi.org/10.1002/bimj.201500236
# First study: experimental group: 14 cases out of 61; 
# control group: 15 cases out of 20 
# Second study: experimental group: 4 cases out of 36; 
# control group: 11 cases out of 36 

rT<-c(14,4)
nT<-c(61,36)
rC<-c(15,11)
nC<-c(20,36)
  
df = data.frame(y = log((rT*(nC-rC))/(rC*(nT-rT))), 
            sigma = sqrt(1/rT+1/(nT-rT)+1/rC+1/(nC-rC)), 
                  labels = c(1:2))
  
# Set the normal prior parameter values for mu according to Roever 2018, bayesmeta
# Suitable for logOR and log-odds scale with the unit information argument  
mu_mean<-0
mu_sd<-4

# set a global parameter for 
#RLMC perturbation

hh0<-0.0044 # new value obtained empirically 
#by adjusting it for the 
#epsilon-local sensitivity approach
#with grid_epsilon=0.00354 for RLMC adjusted HN, HC 
#heterogeneity priors with targets (0.25,0.5,0.75) 
#for NNHM 

# Fix the value of the target RLMC
t_RLMC_025<-0.25

res_d2BC_S_I_rlmc025_HC_raw <- 
  d2BC_S_I_HC_raw(df=df, hh=hh0, rlmc=t_RLMC_025, mu_mean=mu_mean, mu_sd=mu_sd)
res_d2BC_S_I_rlmc025_HC_raw