Landmark risk prediction of residual life for breast cancer survival

Abstract

The importance of developing personalized risk prediction estimates has become increasingly evident in recent years. In general, patient populations may be heterogenous and represent a mixture of different unknown subtypes of disease. When the source of this heterogeneity and resulting subtypes of disease are unknown, accurate prediction of survival may be difficult. However, in certain disease settings, the onset time of an observable short-term event may be highly associated with these unknown subtypes of disease and thus may be useful in predicting long-term survival. One approach to incorporate short-term event information along with baseline markers for the prediction of long-term survival is through a landmark Cox model, which assumes a proportional hazards model for the residual life at a given landmark point. In this paper, we use this modeling framework to develop procedures to assess how a patient's long-term survival trajectory may change over time given good short-term outcome indications along with prognosis on the basis of baseline markers. We first propose time-varying accuracy measures to quantify the predictive performance of landmark prediction rules for residual life and provide resampling-based procedures to make inference about such accuracy measures. Simulation studies show that the proposed procedures perform well in finite samples. Throughout, we illustrate our proposed procedures by using a breast cancer dataset with information on time to metastasis and time to death. In addition to baseline clinical markers available for each patient, a chromosome instability genetic score, denoted by CIN25, is also available for each patient and has been shown to be predictive of survival for various types of cancer. We provide procedures to evaluate the incremental value of CIN25 for the prediction of residual life and examine how the residual life profile changes over time. This allows us to identify an informative landmark point, t(0) , such that accurate risk predictions of the residual life could be made for patients who survive past t(0) without metastasis.

Keywords: biomarkers; disease prognosis; landmark prediction; predictive accuracy; risk prediction; survival analysis.