Subgroup Testing in the Change-Plane Cox Model

Survival outcomes are frequently observed in numerous biomedical and epidemiological studies. The impact of treatment on these outcomes may vary across subgroups characterized by other covariates, for example, immune checkpoint blockade therapy may have different effects on the survival of solid tumor patients based on their tumor mutational burden. In such scenarios, change-plane Cox models provide a suitable approach to identify subgroups that exhibit an improved treatment effect in the analysis of survival data. While some literature is available for testing the presence of a change plane in these models, the existing methods primarily rely on the score test, which has limited power in small sample situations. In this paper, we introduce a novel method based on the likelihood ratio test to enhance the power. The asymptotic distributions of the proposed test statistic under both the null and local alternative hypotheses are established. Furthermore, the finite sample performance of the proposed approach is comprehensively evaluated through extensive simulation studies. Finally, the proposed test is applied to analyze nonsmall cell lung cancer data, further demonstrating its practical utility.