Applying Meta-Analytic-Predictive Priors with the R Bayesian Evidence Synthesis Tools

Abstract

Use of historical data in clinical trial design and analysis has shown various advantages such as reduction of number of subjects and increase of study power. The metaanalytic-predictive (MAP) approach accounts with a hierarchical model for between-trial heterogeneity in order to derive an informative prior from historical data. In this paper, we introduce the package RBesT (R Bayesian evidence synthesis tools) which implements the MAP approach with normal (known sampling standard deviation), binomial and Poisson endpoints. The hierarchical MAP model is evaluated by Markov chain Monte Carlo (MCMC). The MCMC samples representing the MAP prior are approximated with parametric mixture densities which are obtained with the expectation maximization algorithm. The parametric mixture density representation facilitates easy communication of the MAP prior and enables fast and accurate analytical procedures to evaluate properties of trial designs with informative MAP priors. The paper first introduces the framework of robust Bayesian evidence synthesis in this setting and then explains how RBesT facilitates the derivation and evaluation of an informative MAP prior from historical control data. In addition we describe how the meta-analytic framework relates to further applications including probability of success calculations.

Summarizing empirical information on between-study heterogeneity for Bayesian random-effects meta-analysis

“…Another way to set up an overdispersed predictive distribution might be to fit a mixture distribution based on a small number of components, say 2-4. 29 For the present example, both maximum-likelihood as well as moment estimation again yield estimates of 8.2 for the degreesof-freedom ( ), and of 0.20 for the scale ( ) here; see also the corresponding distribution sketched in Figure 2. Table 2 also contrasts summary statistics of the predictive distribution (based on MCMC) to the half-normal or half-Student-fits.…”

“…In the following, we will consider these three approaches for practical application. Note that the third approach is essentially the one also implemented by Rhodes et al 19 and Turner et al, 20 or, in a related context, by Weber et al 29…”

Software for Bayesian Statistics

“…Most of the papers in the special issue perform Bayesian inference by using Markov chain Monte Carlo (MCMC) algorithms. For simulating values from the posterior distributions, they use the BUGS language via JAGS (see e.g., Bonner et al 2021;Erler et al 2021;Mayrink et al 2021;Weber et al 2021), Stan (see e.g., Bürkner 2021;Merkle et al 2021;Weber et al 2021), or nimble (Michaud et al 2021;Bonner et al 2021), interfaced with R by means of the corresponding packages rjags (Plummer, Stukalov, and Denwood 2021), rstan (Stan Development Team 2021) and nimble (de . Alternatively, other papers (e.g., Corradin et al 2021;Hosszejni and Kastner 2021;Knaus et al 2021;Venturini and Piccarreta 2021) write sampling functions in C++ which are then integrated into R by using the Rcpp (Eddelbuettel and François 2011) and RcppArmadillo (Eddelbuettel and Sanderson 2014) packages.…”

“…Finally, some papers do not use MCMC but numerical approximations such as Eggleston et al (2021), Fasiolo et al (2021 and Van Niekerk et al (2021). Two papers (Kuschnig and Vashold 2021;Weber et al 2021) also implement priors for specific Bayesian models.…”

Using horseshoe prior for incorporating multiple historical control data in randomized controlled trials

“…In the framework of meta-analytic approaches, there are two methods of evaluating θ CC: the meta-analytic predictive (MAP) approach and the meta-analytic combined (MAC) approach. The 10 package can deal easily with the MAP approach and this supports normal, binary, and Poisson endpoints, but has not yet dealt with time-to-event endpoints. Hence, the MAC approach is applied as the meta-analytic approach in this study because its computational cost is lower than that of the MAP approach.…”