Estimation of treatment effects in all-comers randomized clinical trials with a predictive marker

Recent advances in genomics and biotechnologies have accelerated the development of molecularly targeted treatments and accompanying markers to predict treatment responsiveness. However, it is common at the initiation of a definitive phase III clinical trial that there is no compelling biological basis or early trial data for a candidate marker regarding its capability in predicting treatment effects. In this case, it is reasonable to include all patients as eligible for randomization, but to plan for prospective subgroup analysis based on the marker. One analysis plan in such all-comers designs is the so-called fallback approach that first tests for overall treatment efficacy and then proceeds to testing in a biomarker-positive subgroup if the first test is not significant. In this approach, owing to the adaptive nature of the analysis and a correlation between the two tests, a bias will arise in estimating the treatment effect in the biomarker-positive subgroup after a non-significant first overall test. In this article, we formulate the bias function and show a difficulty in obtaining unbiased estimators for a whole range of an associated parameter. To address this issue, we propose bias-corrected estimation methods, including those based on an approximation of the bias function under a bounded range of the parameter using polynomials. We also provide an interval estimation method based on a bivariate doubly truncated normal distribution. Simulation experiments demonstrated a success in bias reduction. Application to a phase III trial for lung cancer is provided.