On evaluating how well a biomarker can predict treatment response with survival data

One of the objectives of personalized medicine is to take treatment decisions based on a biomarker measurement. Therefore, it is often interesting to evaluate how well a biomarker can predict the response to a treatment. To do so, a popular methodology consists of using a regression model and testing for an interaction between treatment assignment and biomarker. However, the existence of an interaction is not sufficient for a biomarker to be predictive. It is only necessary. Hence, the use of the marker-by-treatment predictiveness curve has been recommended. In addition to evaluate how well a single continuous biomarker predicts treatment response, it can further help to define an optimal threshold. This curve displays the risk of a binary outcome as a function of the quantiles of the biomarker, for each treatment group. Methods that assume a binary outcome or rely on a proportional hazard model for a time-to-event outcome have been proposed to estimate this curve. In this work, we propose some extensions for censored data. They rely on a time-dependent logistic model, and we propose to estimate this model via inverse probability of censoring weighting. We present simulations results and three applications to prostate cancer, liver cirrhosis, and lung cancer data. They suggest that a large number of events need to be observed to define a threshold with sufficient accuracy for clinical usefulness. They also illustrate that when the treatment effect varies with the time horizon which defines the outcome, then the optimal threshold also depends on this time horizon.