Predictive classification concerns identifying subgroups based on a continuous biomarker through the estimation of an unknown cutpoint and assessing whether these subgroups differ in treatment effect. 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 does not exist, the cutpoint is non-identifiable under the null. We propose profile score-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 the inconsistency of the standard bootstrap for the non-identifiable case. The proposed method is applied to a dataset from a clinical trial on advanced colorectal cancer.