Bootstrap Adjustment to Minimum p-Value Method for Predictive Classification

Abstract

In medical studies, the minimum p-value method is often used to determine a cutpoint of a continuous biomarker for predictive classification and to assess whether a subset of patients may have different treatment effect than other patients. This method, however, suffers from an issue of type I error inflation when the estimated cutpoint is treated as known. In this paper, we propose bootstrap-based procedures to obtain the valid p-value for the minimum p-value test statistic when the treatment effect is measured by a continuous outcome under both random and fixed designs, regardless of whether the cutpoint is identifiable. In the fixed design case, the test statistic is the supremum of a non-centered random process, whose mean function (i.e. bias) diverges as the sample size goes to infinity even under the null hypothesis. The proposed bootstrap statistic matches asymptotically the diverging bias, and we apply the high-dimensional Gaussian approximation results to establish the asymptotic size validity, as well as the power consistency under local alternatives. The proposed method is applied to a dataset from a clinical trial on advanced colorectal cancer.