Nonparametric Testing Methods for Treatment-Biomarker Interaction based on Local Partial-Likelihood
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In clinical trials, patients with different biomarker features may respond differently to the new treatments or drugs. In personalized medicine, it is important to study the interaction between treatment and biomarkers in order to clearly identify patients that benefit from the treatment. With the local partial likelihood estimation (LPLE) method proposed by Fan et al. (2006), the treatment effect can be modeled as a flexible function of the biomarker. In this paper, we propose a bootstrap test method for survival outcome data based on the LPLE, for assessing whether the treatment effect is a constant among all patients or varies as a function of the biomarker. The test method is called local partial likelihood bootstrap (LPLB) and is developed by bootstrapping the martingale residuals. The test statistic measures the amount of changes in treatment effects across the entire range of the biomarker and is derived based on asymptotic the- ories for martingales. The LPLB method is nonparametric, and is shown in simulations and data analysis examples to be flexible to identify treatment effects of any form in any biomarker defined subsets, and more powerful to detect treatment-biomarker interaction of complex forms than the Cox regression model with a simple interaction. We use data from a breast cancer and a prostate cancer clinical trial to illustrate the proposed LPLB test.