Estimating restricted mean survival time and expected life-years lost in the presence of competing risks within flexible parametric survival models

摘要

In observational studies of time-to-event data, researchers are often interested in decomposing the overall probability of death into component parts due to the event of interest, and competing, but mutually exclusive outcome events. For example, in cancer studies, it is of interest to partition the overall probability of death into the probability of death due to cancer and the probability of death due to other causes. These are referred to as cause-specific cumulative incidence functions (CIFs) and are often chosen as the primary estimand of interest. The cause-specific CIF gives the probability of dying from the cause of interest at a particular time whilst also being at risk of dying from other causes of death [1, 2]. In order to arrive at these quantities and to circumvent bias, methods that appropriately account for the competing nature of the events must be applied. The restricted mean failure time (RMFT) has been proposed as an alternative summary measure that is based on the area under the all-cause probability of death up to a specific time-point[3]. In an analogous way to the decomposition into cause-specific CIFs, the RMFT can be further partitioned to give the expected number of life years lost due to a specific cause before a given time-point. In this paper, we describe how the aforementioned measures can be obtained using a flexible parametric model (FPM) as the estimation approach by modelling covariate effects either using (1) the direct relationship with the cause-specific CIF on the subdistribution hazards (SDHs) scale, or (2) modelling all cause-specific hazard functions (CSHs) to obtain each cause-specific CIF [4–7]. Choosing FPMs as the estimation method allows us to estimate effects conditional on covariates, and effects averaged over specific covariate distributions.