sensitivity_learning_table: Posterior, sensitivity and learning estimates for Bayesian...

In sl4bayesmeta: Sensitivity and learning for Bayesian meta-analysis

Description

Generates a table containing posterior, sensitivity and learning estimates and effective RLMC values for a meta-analysis data set with effect expressed as log-odds ratios or log-odds. Assumes a Bayesian normal-normal hierarchical model with different priors (half-normal, exponential, half-Cauchy and Lomax) for the between-study standard deviation. These priors are either 5 % tail-adjusted or adjusted to a target RLMC value.

Usage

sensitivity_learning_table(df)

Arguments

df	a data frame containing a column "y" with the estimates of the log-odds (ratios) for the individual studies, a column "sigma" with the corresponding standard errors and a column "labels" with labels for the studies

Details

The sensitivity measure used is epsilon-local sensitivity (Roos et al. 2015), which is based on the Hellinger distance. Here, learning refers to the ability of the data to modify the prior. It is quantified by the Hellinger distance between the prior and its marginal posterior. See Ott et al. (2020) for a description of the implemented methodology and some examples.

The shape parameter of the Lomax prior is fixed at 1. The reference thresholds used for the 5 % tail-adjustment are U=1 and U=2 and the target RLMC values considered are RLMC=0.25 and RLMC=0.5. The posterior estimates are obtained from the bayesmeta() function in the package bayesmeta.

Value

A matrix with the different estimates in the columns and one row per heterogeneity prior (i.e. the prior for the between-study standard deviation). The quantities given in the columns are as follows, where mu denotes the effect on the log-odds ratio or log-odds scale and tau the heterogeneity standard deviation:

U	reference threshold for prior adjustment
tail_prob	tail probability for prior adjustment
par_val	scale parameter value of the heterogeneity prior
MRLMC	median relative latent model complexity estimated from MC sampling
median_post_mu	posterior median for the effect mu
95CrI_post_mu_low	lower end point of the 95 % shortest credible interval (CrI) for the effect mu
95CrI_post_mu_up	upper end point of the 95 % shortest CrI for the effect mu
length_95CrI_post_mu	length of the 95 % shortest CrI for the effect mu
median_post_tau	posterior median for tau
95CrI_post_tau_low	lower end point of the 95 % shortest CrI for tau
95CrI_post_tau_up	upper end point of the 95 % shortest CrI for tau
length_95CrI_post_tau	length of the 95 % shortest CrI for tau
L_mu	learning estimate for the effect mu
L_tau	learning estimate for tau
S_mu	sensitivity estimate for the effect mu
S_tau	sensitivity estimate for tau

The following heterogeneity priors are given in the rows (from top to bottom):

HN(0.5)_U1tail5perz, EXP_U1tail5perz, HC_U1tail5perz, LMX_U1tail5perz	half-normal, exponential, half-Caucy and Lomax prior, all 5 %-tail adjusted with threshold U=1 (static)
HN_mrlmc025, EXP_mrlmc025, HC_mrlmc025, LMX_mrlmc025	median-adjusted with target RLMC=0.25 (dynamic)
HN(1)_U2tail5perz, EXP_U2tail5perz, HC_U2tail5perz, LMX_U2tail5perz	5 %-tail adjusted with threshold U=2 (static)
HN_mrlmc050, EXP_mrlmc050, HC_mrlmc050, LMX_mrlmc050	median-adjusted with target RLMC=0.50 (dynamic)

Warning

This function takes ca. 5-10 minutes to run on the acute graft rejection data set given in the example below.

Note

This function covers the 5%-tail and the RLMC-based adjustment of heterogeneity priors, but not the 50%-tail adjustment (which is not based on RLMC) considered in Ott et al. (2020). That adjustment can be studied by using the function sensitivity_learning_table_flexible.

For effects which are not on the log-odds (ratio) scale, the prior for the effect needs to be adjusted, but otherwise the same code can be used if a Bayesian normal-normal hierarchical model is appropriate.

References

Ott, M., Hunanyan, S., Held, L., Roos, M. Sensitivity quantification in Bayesian meta-analysis. Manuscript revised for Research Synthesis Methods. 2020.

Roos, M., Martins, T., Held, L., Rue, H. (2015). Sensitivity analysis for Bayesian hierarchical models. Bayesian Analysis 10(2), 321–349. https://projecteuclid.org/euclid.ba/1422884977

See Also

bayesmeta in package bayesmeta, pri_par_adjust_static,
pri_par_adjust_dynamic, effective_rlmc,
sensitivity_learning_table_flexible

Examples

# 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))), # log-OR
                 sigma = sqrt(1/rT+1/(nT-rT)+1/rC+1/(nC-rC)), # SE(log-OR)
                 labels = c(1:2))
  
# compute the table for the AGR data
# warning: it takes ca. 5-10 minutes to run this function
# on the above data set!
sensitivity_learning_table(df)

sl4bayesmeta documentation built on Feb. 18, 2020, 3:02 p.m.