Bayesian random-effects meta-analysis of aggregate data on clinical events

To investigate intervention effects on rare events, meta-analysis techniques are commonly applied in order to assess the accumulated evidence. When it comes to adverse effects in clinical trials, these are often most adequately handled using survival methods. A common-effect model that is able to process data in commonly quoted formats in terms of hazard ratios has been proposed for this purpose. In order to accommodate potential heterogeneity between studies, we have extended the model by Holzhauer to a random-effects approach. The Bayesian model is described in detail, and applications to realistic data sets are discussed along with sensitivity analyses and Monte Carlo simulations to support the conclusions.

💡 Research Summary

This paper addresses the challenge of synthesizing evidence on rare adverse events in clinical trials when only aggregate data are available. Building on Holzhauer’s (2017) Bayesian common‑effect (CE) model, which treats all studies as sharing a single true hazard ratio (HR), the authors extend the framework to a random‑effects (RE) formulation that explicitly accounts for between‑study heterogeneity.

The authors first describe the typical structure of aggregate data for safety outcomes: total number of patients (n_ij), number of events (y_ij), number of fatal events (m_ij), number of early drop‑outs (z_ij), and follow‑up time (τ_ij) for each arm j of each trial i. They assume exponential waiting times for events and a Bernoulli model for fatal versus non‑fatal outcomes. In the CE model the log‑HR for each study, θ_i, is fixed to a common parameter μ. In the RE extension, θ_i is modeled as θ_i ∼ N(μ, τ²), where τ² captures the heterogeneity across studies. Prior distributions are chosen to be weakly informative: μ receives a diffuse Normal(0, 10⁴) prior, while τ is assigned a Half‑Normal or Half‑Cauchy prior, allowing the data to dominate inference. Historical control arms can be incorporated as single‑arm studies, preserving the hierarchical structure.

Inference is performed via Markov chain Monte Carlo (MCMC) using Stan. Convergence diagnostics (R̂, effective sample size) and model fit criteria (DIC, WAIC) are reported. Sensitivity analyses explore the impact of alternative prior specifications on posterior estimates of μ and τ, demonstrating robustness.

To evaluate performance, the authors conduct Monte‑Carlo simulations varying the number of studies (I = 5, 10, 20) and event rates. Across scenarios, the RE model consistently yields lower mean‑squared error and better coverage of the true HR than the CE model, especially when the number of studies is small and events are rare.

Two real‑world applications illustrate the methodology. The first revisits the rosiglitazone data set (54 trials plus 64 historical controls) previously analyzed with a CE model. The RE analysis reveals substantial heterogeneity (τ̂≈0.45) and produces a posterior HR estimate with a wider 95 % credible interval (approximately 0.78–1.32), reflecting uncertainty that the CE model under‑estimates. Inclusion of historical controls modestly sharpens the estimate of μ. The second example involves nine late‑stage oncology trials with very few events and considerable clinical diversity. Although τ̂ is smaller (≈0.20), the RE model still yields more conservative interval estimates, aligning with simulation findings that RE protects against over‑optimistic conclusions when data are sparse.

The discussion acknowledges limitations: the exponential assumption for event times may be unrealistic for some safety outcomes, and alternative survival distributions (e.g., Weibull) could be explored. The choice of priors, while weakly informative, still requires expert input, particularly for τ when data are limited. Nonetheless, the authors argue that the Bayesian RE framework offers a flexible, principled approach to meta‑analysis of rare events, allowing incorporation of external (historical) information and providing a transparent quantification of heterogeneity. This contributes valuable methodological guidance for regulatory and clinical decision‑making in contexts where individual patient data are unavailable and adverse events are infrequent.