Wednesday, March 01, 2023 Bootstrap adjusted predictive classification for identification of subgroups with differential treatment effects under generalized linear models Na L, Yanglei S, Lin CD, Dongsheng T. Bootstrap adjusted predictive classification for identification of subgroups with differential treatment effects under generalized linear models (ONLINE). Electronic Journal of Statistics 17: 548-606, 2023. https://doi.org/10.1214/23-EJS2108 Predictive classification considered in this paper concerns the problem of identifying subgroups based on a continuous biomarker through estimation of an unknown cutpoint and assessing whether these subgroups differ in treatment effect relative to some clinical outcome. The problem is considered under a generalized linear model framework for clinical outcomes and formulated as testing the significance of the interaction between the treatment and the subgroup indicator. When the main effect of the subgroup indicator does not exist, the cutpoint is non-identifiable under the null. Existing procedures are not adaptive to the identifiability issue, and do not work well when the main effect is small. In this work, we propose profile score-type and Wald-type test statistics, and further m-out-of-n bootstrap techniques to obtain their critical values. The proposed procedures do not rely on the knowledge about the model identifiability, and we establish their asymptotic size validity and study the power under local alternatives in both cases. Further, we show that the standard bootstrap is inconsistent for the non-identifiable case. Simulation results corroborate our theory, and the proposed method is applied to a dataset from a clinical trial on advanced colorectal cancer.
