Application of Bayesian predictive probability for interim futility analysis in single-arm phase II trial

Background

Bayesian predictive probability design, with a binary endpoint, is gaining attention for the phase II trial due to its innovative strategy. To make the Bayesian design more accessible, we elucidate this Bayesian approach with a R package to streamline a statistical plan, so biostatisticians and clinicians can easily integrate the design into clinical trial.

Methods

We utilize a Bayesian framework using Bayesian posterior probability and predictive probability to build a R package and develop a statistical plan for the trial design. With pre-defined sample sizes, the approach employs the posterior probability with a threshold to calculate the minimum number of responders needed at end of the study to claim efficacy. Then the predictive probability is applied to evaluate future success at interim stages and form stopping rule at each stage.

Results

An R package, ‘BayesianPredictiveFutility’, with associated graphical interface is developed for easy utilization of the trial design. The statistical tool generates a professional statistical plan with comprehensive results including a summary, details of study design, a series of tables and figures from stopping boundary for futility, Bayesian predictive probability, performance [probability of early termination (PET), type I error, and power], PET at each interim analysis, sensitivity analysis for predictive probability, posterior probability, sample size, and beta prior distribution. The statistical plan presents the methodology in a readable language fashion while preserving rigorous statistical arguments. The output formats (Word or PDF) are available to communicate with physicians or to be incorporated in the trial protocol. Two clinical trials in lung cancer are used to demonstrate its usefulness.

Conclusions

Bayesian predictive probability method presents a flexible design in clinical trial. The statistical tool brings an added value to broaden the application.

Designing phase II clinical trials to target subgroup of interest in a heterogeneous population: A case study using an R package

Phase II trials that evaluate target therapies based on a biomarker must be well designed in order to assess anti-tumor activity as well as clinical utility of the biomarker. Classical phase II designs do not deal with this molecular heterogeneity and can lead to an erroneous conclusion in the whole population, whereas a subgroup of patients may well benefit from the new therapy. Moreover, the target population to be evaluated in a phase III trial may be incorrectly specified. Alternative approaches are proposed in the literature that make it possible to include two subgroups according to biomarker status (negative/positive) in the same study. Jones, Parashar and Tournoux et al. propose different stratified adaptive two-stage designs to identify a subgroup of interest in a heterogeneous population that could possibly benefit from the experimental treatment at the end of the first or second stage. Nevertheless, these designs are rarely used in oncology research. After introducing these stratified adaptive designs, we present an R package (ph2hetero) implementing these methods. A case study is provided to illustrate both the designs and the use of the R package. These stratified adaptive designs provide a useful alternative to classical two-stage designs and may also provide options in contexts other than biomarker studies.

A Bayesian pick-the-winner design in a randomized phase II clinical trial

Purpose

Many phase II clinical trials evaluate unique experimental drugs/combinations through multi-arm design to expedite the screening process (early termination of ineffective drugs) and to identify the most effective drug (pick the winner) to warrant a phase III trial. Various statistical approaches have been developed for the pick-the-winner design but have been criticized for lack of objective comparison among the drug agents.

Methods

We developed a Bayesian pick-the-winner design by integrating a Bayesian posterior probability with Simon two-stage design in a randomized two-arm clinical trial. The Bayesian posterior probability, as the rule to pick the winner, is defined as probability of the response rate in one arm higher than in the other arm. The posterior probability aims to determine the winner when both arms pass the second stage of the Simon two-stage design.

Results

When both arms are competitive (i.e., both passing the second stage), the Bayesian posterior probability performs better to correctly identify the winner compared with the Fisher exact test in the simulation study. In comparison to a standard two-arm randomized design, the Bayesian pick-the-winner design has a higher power to determine a clear winner. In application to two studies, the approach is able to perform statistical comparison of two treatment arms and provides a winner probability (Bayesian posterior probability) to statistically justify the winning arm.

Conclusion

We developed an integrated design that utilizes Bayesian posterior probability, Simon two-stage design, and randomization into a unique setting. It gives objective comparisons between the arms to determine the winner.