HC_accuracy: Sensitivity-based identification and classification of...

In pa4bayesmeta: Prior Accuracy for Bayesian Meta-Analysis

Description

This function implements the algorithm for sensitivity-based identification and classification of inaccurate half-Cauchy heterogeneity priors proposed in Ott et al. (2021). It classifies the specified half-Cauchy heterogeneity prior as either anticonservative (puts more than half of its probability mass on too small heterogeneity values) or conservative (puts more than half of its probability mass on too large heterogeneity values). Assumes a Bayesian normal-normal hierarchical model.

Usage

HC_accuracy(df, scale.HC = 1, mu.mean = 0, mu.sd = 4, 
            tail.prob = 0.5, grid.epsilon = 0.00354)

Arguments

df	data frame with one column "y" containing the effect estimates for the individual studies and a column "sigma" containing the standard errors of these estimates
scale.HC	scale parameter of the half-Cauchy prior of interest
mu.mean	mean of the normal prior for the effect mu. Defaults to 0.
mu.sd	standard deviation of the normal prior for the effect mu. Defaults to 4.
tail.prob	probability mass of the prior above the reference threshold. Defaults to 0.5, which corresponds to the 50%-RLMC-based adjustment of priors.
grid.epsilon	value for epsilon, a tuning parameter for epsilon-local sensitivity computation (see pri_par_epsilon_grid for details). Defaults to 0.00354.

Details

This algorithm proceeds as follows: First, it computes the effective median RLMC for the HC prior with scale parameter scale.HC and the data set df. Second, it applies the 50%-RLMC-based adjustment to obtain a HN prior with the same median RLMC for the data set df. Third, it computes epsilon-local sensitivity estimates for these two HN and HC priors and the data set df. Finally, comparing the two sensitivity estimates leads to the decision: If the sensitivity estimate for the HN prior is larger than the sensitivity estimate for the HC prior, then both the HN and HC prior are classfied as anticonservative. If the sensitivity estimate for the HC prior is larger than the sensitivity estimate for the HN prior, then both the HN and HC prior are classfied as conservative.

This is a special case of the algorithm described in Ott et al. (2021, Section 5), see also the Supplementary Material of that manuscript (Section 4.6) for more information.

Using HC heterogeneity priors as "weakly informative" priors has been suggested in Gelman (2006). The standard half-Cauchy heterogeneity prior (scale.HC = 1) has for example been used in Bodnar et al. (2017).

Value

A list of the following 4 elements:

param	a list of the following two scale parameter values (non-negative real numbers): HN: scale parameter of the adjusted HN prior HC: scale parameter of the specified HC prior
mrlmc_HC	the effective median RLMC for the specified HC prior
S_tau	a list of the following two epsilon-local sensitivity estimates with respect to the heterogeneity parameter tau: `S(tau)^HN`: sensitivity estimate for the HN prior `S(tau)^HC`: sensitivity estimate for the HC prior
decision	a string specifiying the decision if the HN and HC priors are anticonservative or conservative

References

Ott, M., Hunanyan, S., Held, L., Roos, M. Sensitivity-based identification of inaccurate heterogeneity priors in Bayesian meta-analysis. Submitted to Statistical Methods in Medical Research. 2021.

Ott, M., Hunanyan, S., Held, L., Roos, M. Supplementary Material: Sensitivity-based identification of inaccurate heterogeneity priors in Bayesian meta-analysis. Submitted to Statistical Methods in Medical Research. 2021.

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (Comment on article by Browne and Draper). Bayesian Analysis 1(3), 515–534. https://doi.org/10.1214/06-BA117A

Bodnar, O., Link, A., Arendacka, B., Possolo, A., Elster C. (2017). Bayesian estimation in random effects meta-analysis using a non-informative prior. Statistics in Medicine 36(2), 378–399. https://doi.org/10.1002/sim.7156

See Also

HN_accuracy, prior_accuracy, effective_rlmc, pri_par_adjust

Examples

# load the steriod-resistant rejection (SRR) data analyzed in Friede et al. (2017)
data(srr)

# sensitivity-based accuracy estimation & classification for
# the HC(1) prior and the SRR data
HC_accuracy(df = srr, scale.HC = 1,
            mu.mean = 0, mu.sd = 4)

pa4bayesmeta documentation built on Aug. 1, 2021, 3 p.m.