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

TL;DR

This work addresses the challenge of synthesizing rare adverse-event data by extending Holzhauer's common-effect Bayesian model to a random-effects framework, enabling between-trial heterogeneity in time-to-event parameters while accommodating aggregated data inputs. It demonstrates how MAP priors and historical-data borrowing can refine inference in settings with many trials or sparse data, and it evaluates model performance through two real-data applications (rosiglitazone and oncology) plus extensive simulations. The findings show that random-effects models typically widen uncertainty to reflect heterogeneity, improve error control when heterogeneity is present, and that informative priors can enhance precision in small-sample or data-scarce scenarios. This approach supports more robust safety-effect conclusions in drug development where adverse events are rare and data reporting is heterogeneous, with potential extensions to more flexible time-to-event models and network contexts in the future.

Abstract

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.

Figures (8)

• Figure 1: An illustration of the five different possible patterns showing how fatal or non-fatal events and drop-out may occur over the course of a patient's follow-up time. Follow-up starts on the left, and during the trial duration, adverse events (fatal or non-fatal, $\times$) and drop-out ($\bigcirc$) may or may not occur in different orders. A fatal event or drop-out may terminate the follow-up (dashed lines). See Section \ref{['sec:study_design']} for more details.
• Figure 2: Typical scenarios for adverse event follow‐up in clinical trials (adopted from Figure 1 in Unkel et al.(2019)UnkelEtAl2019). The abbreviations are: AE, adverse event; TEAE, treatment-emergent adverse event; FU, follow-up; Saf-FU, safety follow-up; EoT, end of treatment; V$0$, visit at trial onset; V$1$,…,V$n$, visits during treatment. First occurrences of AEs are marked by triangles.
• Figure 3: Comparison of overall HR ($\varphi$) estimates from CE and RE models in the rosiglitazone example. Each line represents the 95% equal-tailed CI for $\varphi$, the square indicates the point estimate. Solid lines show the CIs for CE models, and dashed lines show RE models. Red and blue lines correspond to models with and without borrowing from historical trials, respectively. Models are first grouped by whether information is borrowed among trials in the main meta-analysis (stratified vs. non-stratified), and then the prior used for $\varphi$ ($\mathrm{Cauchy}(0.0, 0.37)$ or $\mathrm{Cauchy}(0.0, 2.5)$).
• Figure 4: Sensitivity analysis for RE models with varying priors on $\eta$ in case of a large number of trials in the rosiglitazone example. Blue lines correspond to models without borrowing from historical trials; red lines correspond to models with borrowing from historical trials. Each line represents the 95% equal-tailed CI for $\varphi$, the point estimate is indicated by a box on the line. Prior sensitivity (with respect to $\eta$) is quantified in terms of the $D_{\mathrm{CJS}}$ metric.
• Figure 5: Sensitivity analyses for RE models with varying priors on the heterogeneity $\eta$ in case of a small number of trials in the rosiglitazone example. Red and blue lines correspond to models with and without borrowing from historical trials. Each line represents the 95% equal-tailed CI for $\varphi$, the point estimate is indicated by a square. Prior sensitivity (with respect to $\eta$) is quantified in terms of the $D_{\mathrm{CJS}}$ metric.