Testing overall and subpopulation treatment effects with measurement errors

There is a growing interest in the discovery of important predictors from many potential biomarkers for therapeutic use. In particular, a biomarker has predictive value for treatment if the treatment is only effective for patients whose biomarker values exceed a certain threshold. However, biomarker expressions are often subject to measurement errors, which may blur the biomarker's predictive capability in patient classification and, as a consequence, may lead to inappropriate treatment decisions. By taking into account the measurement errors, we propose a new testing procedure for the overall and subpopulation treatment effects in the multiple testing framework. The proposed method bypasses the permutation or other resampling procedures that become computationally infeasible in the presence of measurement errors. We conduct simulation studies to examine the erformance of the proposed method, and illustrate it with a data example.