For many medical conditions several treatment options may be available for treating patients. We consider evaluating markers based on a simple treatment selection policy that incorporates information on the patient's marker value exceeding a threshold. For example, colon cancer patients may be treated by surgery alone or surgery plus chemotherapy. The c-myc gene expression level may be used as a biomarker for treatment selection. Although traditional regression methods may assess the effect of the marker and treatment on outcomes, it is appealing to quantify more directly the potential impact on the population of using the marker to select treatment. A useful tool is the selection impact (SI) curve proposed by Song and Pepe (2004, Biometrics 60, 874-883) for binary outcomes. However, the current SI method does not deal with continuous outcomes, nor does it allow to adjust for other covariates that are important for treatment selection. In this paper, we extend the SI curve for general outcomes, with a specific focus on survival time. We further propose the covariate specific SI curve to incorporate covariate information in treatment selection. Nonparametric and semiparametric estimators are developed accordingly. We show that the proposed estimators are consistent and asymptotically normal. The performance is illustrated by simulation studies and through an application to data from a cancer clinical trial.
Song, Xiao and Zhou, Xiao-Hua , "Evaluating Markers for Treatment Selection Based on Survival Time" (June 2009). UW Biostatistics Working Paper Series. Working Paper 349.