Prior distributions for variance parameters in a sparse‐event meta‐analysis of a few small trials

Abstract

SummaryIn rare diseases, typically only a small number of patients are available for a randomized clinical trial. Nevertheless, it is not uncommon that more than one study is performed to evaluate a (new) treatment. Scarcity of available evidence makes it particularly valuable to pool the data in a meta‐analysis. When the primary outcome is binary, the small sample sizes increase the chance of observing zero events. The frequentist random‐effects model is known to induce bias and to result in improper interval estimation of the overall treatment effect in a meta‐analysis with zero events. Bayesian hierarchical modeling could be a promising alternative. Bayesian models are known for being sensitive to the choice of prior distributions for between‐study variance (heterogeneity) in sparse settings. In a rare disease setting, only limited data will be available to base the prior on, therefore, robustness of estimation is desirable. We performed an extensive and diverse simulation study, aiming to provide practitioners with advice on the choice of a sufficiently robust prior distribution shape for the heterogeneity parameter. Our results show that priors that place some concentrated mass on small τ values but do not restrict the density for example, the Uniform(−10, 10) heterogeneity prior on the log(τ2) scale, show robust 95% coverage combined with less overestimation of the overall treatment effect, across varying degrees of heterogeneity. We illustrate the results with meta‐analyzes of a few small trials.

A proposed framework to guide evidence synthesis practice for meta-analysis with zero-events studies

“…In a two-stage approach (also known as the standard meta-analysis approach), the study-specific effect sizes and standard errors are obtained or estimated from the included studies at the first stage, and then they are synthesized at the second stage [13,14]. Under the two-stage approach, available methods for zero-events include the continuity/empirical correction [7], Peto's OR [15], MH [16], two-stage Bayesian methods [17,18], the exact p-function method [19], the arcsine-based transformation (e.g., arcsine difference [20]), etc. Among these methods, Peto's OR is not applicable for dealing with double-zero-events studies.…”

Combined assessment of early and late‐phase outcomes in orphan drug development

“…Finally, in this work, we accounted for but did not estimate between‐study variance. Due to the only two available studies, a proper estimation of the between‐study outcome variability is currently known to be almost nonfeasible 14‐17 …”

“…Therefore, accounting for between-study variability may act as a less rough approach to minimize this decision-induced bias. A proper estimation of the between-trial early-phase outcome variance is not feasible with just two available studies, [14][15][16][17] therefore, in this article we choose not estimate but only account for this variance to aid towards the reduction of the bias.…”

Bayesian Approaches for Confirmatory Trials in Rare Diseases: Opportunities and Challenges

“…On the other hand, Bayesian models are known for being sensitive to the choice of heterogeneity prior distributions in sparse settings, therefore, the need to identify priors with robust properties is crucial. Pateras et al [32] proposed a general way to set prior distributions. Via simulations, they showed that a uniform heterogeneity prior, bounded between -10 and 10, on the log heterogeneity parameter scale shows appropriate 95% coverage and induces relatively acceptable under/over estimation of both the overall treatment effect and heterogeneity, across a wide range of heterogeneity levels.…”