A risk set adjustment for proportional hazards modeling of combined cohort data

Sporting careers observed over a preset time interval can be partitioned into two distinct subsamples. These samples consist of individuals whose careers had already commenced at the start of the time interval (prevalent subsample) and individuals whose careers began during the time interval (incident subsample) as well the respective individual-level covariate data such as salary, height, weight, performance statistics, draft position, etc. Under the assumption of a proportional hazards model, we propose a partial likelihood estimator to model the effect of covariates on survival via an adjusted risk set sampling procedure for when the incident cohort data is used in conjunction with the prevalent cohort data. We use simulated failure time data to validate the combined cohort proportional hazards methodology and illustrate our model using an NBA data set for career durations measured between 1990 and 2008.