Two-stage stratified designs with survival outcomes and adjustment for misclassification in predictive biomarkers

Biomarker stratified clinical trial designs are versatile tools to assess biomarker clinical utility and address its relationship with clinical endpoints. Due to imperfect assays and/or classification rules, biomarker status is prone to errors. To account for biomarker misclassification, we consider a two-stage stratified design for survival outcomes with an adjustment for misclassification in predictive biomarkers. Compared to continuous and/or binary outcomes, the test statistics for survival outcomes with an adjustment for biomarker misclassification is much more complicated and needs to take special care. We propose to use the information from the observed biomarker status strata to construct adjusted log-rank statistics for true biomarker status strata. These adjusted log-rank statistics are then used to develop sequential tests for the global (composite) hypothesis and component-wise hypothesis. We discuss the power analysis with the control of the type-I error rate by using the correlations between the adjusted log-rank statistics within and between the design stages. Our method is illustrated with examples of the recent successful development of immunotherapy in nonsmall-cell lung cancer.