The Bayesian Time Machine: Accounting for temporal drift in multi-arm platform trials

Abstract

Background: Multi-arm platform trials investigate multiple agents simultaneously, typically with staggered entry and exit of experimental treatment arms versus a shared control arm. In such settings, there is considerable debate whether to limit analyses for a treatment arm to concurrent randomized control subjects or to allow comparisons to both concurrent and non-concurrent (pooled) control subjects. The potential bias from temporal drift over time is at the core of this debate.

Methods: We propose time-adjusted analyses, including a "Bayesian Time Machine," to model potential temporal drift in the entire study population, such that primary analyses can incorporate all randomized control subjects from the platform trial. We conduct a simulation study to assess performance relative to utilizing concurrent or pooled controls.

Results: In multi-arm platform trials with staggered entry, analyses adjusting for temporal drift (either Bayesian or frequentist) have superior estimation of treatment effects and favorable testing properties compared to analyses using either concurrent or pooled controls. The Bayesian Time Machine generally provides estimates with greater precision and smaller mean square error than alternative approaches, at the risk of small bias and small Type I error inflation.

Conclusions: The Bayesian Time Machine provides a compromise between bias and precision by smoothing estimates across time and leveraging all available data for the estimation of treatment effects. Prior distributions controlling the behavior of dynamic smoothing across time must be pre-specified and carefully calibrated to the unique context of each trial, appropriately accounting for the population, disease, and endpoints.

Keywords: Bayesian Time Machine; Temporal drift; adaptive platform trial; concurrent controls; multi-arm clinical trials; non-concurrent controls; staggered entry.