Statistical methods for breast cancer survival using the restricted mean survival time - Summary Breast cancer is a complex and heterogeneous disease where the roles of many prognostic factors, including androgen receptor (AR) which is an emerging potential prognostic biomarker, remain unclear in its clinical pro- gression. The Nurses' Health Studies (NHS), which motivated this application, are large prospective cohort studies conducted to investigate the risk factors for major chronic diseases in women including breast cancer. The data from the NHS contain invaluable information for breast cancer research such as lifestyle, hormonal, and genetic risk factors, as well as clinical outcomes such as breast cancer diagnosis, recurrence, and death. In many epidemiologic studies on breast cancer survival, including the NHS, the hazard ratio (HR), which is esti- mated based on the proportional hazards (PH) model, has been the most routinely used effect measure despite its limitations. In the NHS data, the PH assumption in the association between AR expression and breast cancer survival was found to be violated. The interpretation of HR is challenging and the result is often misleading if the PH assumption is violated, which makes it difficult to assess AR's prognostic values. Recently, summary metrics based on the restricted mean survival time (RMST), which is defined as the life expectancy up to a specific time point, have attracted substantial attention as useful alternatives to the HR. The RMST has many advantageous features such as its straightforward interpretation and robustness. Specifically, we can assess the prognostic factor's effects in terms of absolute effect, which is clinically more interpretable than the HR, without assuming PH using the RMST-based regression model. In this project, we propose to develop novel statistical methods based on RMST to fully utilize the rich data from the NHS and to gain a better understanding of the complex effect of AR on breast cancer progression and survival. Under Aim 1, we will develop a flexible regression method based on RMST that estimates the varying covariate effects across a range of time. The proposed regression method will be used to elucidate the clinical significance of AR in survival by different subtypes of breast cancers. Under Aim 2, we will develop a model-free approach to summarize the bivariate survival data (i.e., time from an initial event to an intermediate event and from the intermediate event to a failure event). The metrics developed under Aim 2 will be used to study residual survival after breast cancer recurrence and facilitate comparisons between groups by AR status for different breast cancer subtypes. These novel sta- tistical approaches will be applied to data from the NHS to obtain new knowledge about the prognostic values of AR and potentially lead to better targeted therapies.
