Bayesian Design and Analysis of Precision Trials with Partial Borrowing

With the advancement of precision medicine there is an increasing need for design and analysis methods in clinical trials with the objective of investigating effect heterogeneity and estimating subgroup effects. As this requires precise estimation of interaction effects, borrowing information from external data sources including retrospective studies and early phase clinical trials to enrich the trial in sparse subgroups is pertinent. Motivated by a trial in gastric cancer we consider a practical design and analysis framework for borrowing from external data sources that only partially inform the inference. As the analysis model we propose an individually weighted model where the external data are weighted based on their fit with the target population based on the distribution of a set of covariates. In a simulation study we assess the performance of the model under various scenarios and make comparisons to dynamic borrowing. In addition, we provide a Bayesian design framework where design priors are extracted from the external data to determine decision boundaries and sample sizes. The design procedure is demonstrated within the context of our motivating example.

💡 Research Summary

The paper addresses a pressing challenge in precision medicine: estimating treatment effects for small patient sub‑groups where the trial alone lacks sufficient power. To augment information, the authors propose a Bayesian framework that partially borrows external data (e.g., from early‑phase studies or retrospective cohorts) while protecting against bias caused by population differences.

The core of the methodology is an “individually weighted” power prior. For each external subject a similarity weight ωₙ is computed based on how closely that subject’s covariate profile matches the internal trial population. The similarity is quantified through a posterior predictive similarity function: a probabilistic model q(z|ξ) is fitted to the covariates Z observed in the internal data, the posterior π(ξ|Z_I) is obtained, and ωₙ = ∫ q(zₙ|ξ)π(ξ|Z_I)dξ. This weight raises the external likelihood contribution to the prior, yielding

π_IW(θ) ∝ π₀(θ)·∏_{n=1}^{N_E} f(θ; dₙ)^{ωₙ}.

Because external datasets can be much larger than the trial, the authors introduce a truncation rule. A cutoff ω₀ is selected so that the sum of retained weights does not exceed the internal sample size (∑ ωₙ I(ωₙ>ω₀) ≤ N_I). This prevents a flood of low‑weight observations from overwhelming the analysis.

The analysis model is a generalized linear model with prognostic covariates x and effect‑modifier covariates s:

g(E