|Title||Subgroup Detection and Sample Size Calculation with Proportional Hazards Regression for Survival Data|
|Year of Publication||2016|
In this paper, we propose a testing procedure for detecting and estimating the subgroup with an enhanced treatment effect in survival data analysis. Here, we consider a new proportional hazards model which includes a nonparametric component for the covariate effect in the control group and a subgroup-treatment interaction effect defined by a change-plane. We develop a score-type test for detecting the existence of the subgroup, which is doubly robust against misspecification of the baseline effect model or the propensity score but not both under mild assumptions for censoring. When the null hypothesis of no subgroup is rejected, the change-plane parameters that define the subgroup can be estimated based on supremum of the normalized score statistic. The asymptotic distributions of the proposed test statistic under the null and local alternative hypotheses are established. Based on established asymptotic distributions, we further propose a sample size calculation formula for detecting a given subgroup effect and derive a numerical algorithm for implementing the sample size calculation in clinical trial designs. The performance of the proposed approach is evaluated by simulation studies. An application to a cancer clinical trial data is also given for illustration.