Two-Stage Adaptive Enrichment Designs with Survival Outcomes and Adjustment for Misclassification in Predictive Biomarkers

Biomarker enrichment clinical trial designs are versatile tools to assess the treatment effect and increase the efficiency of clinical trials. In this paper, we propose a two-stage enrichment clinical trial design with survival outcomes, and consider the situation where the biomarker assay and classification are possibly subject to errors. Specifically, the first stage is a randomized design, stratified by the biomarker appeared status. Depending on the result of the interim analysis and a pre-specified futility criterion, the second stage can be either enriched with only the biomarker appeared positive patients, or remain as the stratified design with both biomarker appeared positive and biomarker appeared negative patients. Compared to continuous and binary outcomes, test statistics to account for biomarker misclassification are much more complicated and require special care. We develop log-rank statistics for the interim and final analyses, with an adjustment for the sensitivity and specificity of the biomarker assay. Control of Type I error rate is achieved by considering correlations between adjusted log-rank statistics from the same and/or different stages. R code is developed to calculate critical values, global/marginal power, and sample size. Our method is illustrated with examples of a recently successful development of immunotherapy in non-small-cell lung cancer.