Abstract: This paper proposes a single-index varying coefficient hazards model to identify biomarkers for risk stratification and treatment selection for individual patients. Our model accommodates multiple predictive biomarkers and allows for flexible nonlinear interactions between the multiple biomarkers and the treatment. We propose a global partial likelihood to estimate the varying-coefficient functions and the regression coefficients. The proposed estimators are shown to be consistent, asymptotically normal and semiparametrically efficient. The proposed approach is applied to a clinical trial on multiple myeloma patients for risk stratification and to investigate whether biomarkers would interact with treatment for each individual patient.

Key words and phrases: Cox proportional hazards model, global partial likelihood, semiparametric efficiency, single-index, varying coefficients.