A Bayesian Optimal Phase II Design for Randomized Immunotherapy Trials with Delayed Treatment Effects

2025-08-29

AI Summary

Immunotherapies often exhibit delayed treatment effects, leading to non-proportional hazards in conventional phase II trials, resulting in reduced statistical power and inflated Type I error rates. To address this, we propose DTE-BOP2, a Bayesian optimal design that—uniquely—models the time-to-effect separation (S) as a truncated gamma-distributed random variable, relaxing the restrictive assumption of immediate efficacy. We establish that statistical power primarily depends on the ratio of median survival times before and after separation. DTE-BOP2 integrates the BOP2 framework, Bayesian adaptive decision rules, a weighted log-rank test, and borrowing from historical controls, supporting both expert-elicited priors and default parameterization. Simulation studies demonstrate that DTE-BOP2 maintains precise Type I error control across diverse delayed-effect scenarios and achieves higher power with smaller sample sizes compared to standard BOP2 and piecewise weighted methods. An open-source R package is available on CRAN (DTEBOP2).

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Bayesian Learning

Application Category

• Responsible Web: Data and user privacy-enhancing technologies for the Web
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Immunotherapy has transformed cancer treatment, yet its delayed therapeutic effects often lead to non-proportional hazards, rendering many conventional phase II designs underpowered and prone to type I error inflation. To address this issue, we propose a novel Bayesian Optimal Phase II design (DTE-BOP2) that explicitly models the uncertainty in the separation timing of treatment effect. The treatment separation timepoint (denoted by S) is endowed with a truncated-Gamma prior, whose parameters can be elicited from experts or inferred from historical data, with default settings available when prior knowledge is scarce. Built upon the BOP2 framework (Zhou et al. 2017, 2020), our design retains operational simplicity while incorporating type I error control and maintaining the power. Extensive simulations demonstrate that DTE-BOP2 uniformly controls type I error at the nominal level across a wide range of treatment effect separation timepoint S. We further observe that the power decreases monotonically as S increases. Importantly, we find that the power is primarily driven by the relative magnitude of treatment benefit before and after the separation time, i.e., the ratio of medians, rather than their absolute values. Compared to the original BOP2, the piecewise weighted log-rank, and the conventional log-rank tests, DTE-BOP2 achieves higher power with smaller sample sizes while preserving type I error robustness across plausible delay scenarios. An open-source R package, DTEBOP2 (CRAN), with detailed vignettes, enables investigators to implement the design and analyse phase-II trials exhibiting delayed treatment effects.

Problem

• Addresses underpowered phase II trials due to delayed immunotherapy effects
• Models uncertainty in treatment effect separation timing using Bayesian methods
• Controls type I error while improving power with smaller sample sizes

Innovation

• Bayesian Optimal Phase II design for delayed effects
• Truncated-Gamma prior models treatment separation timing
• Controls type I error while maintaining power efficiency