On Cox proportional hazards model performance under different sampling schemes

Cox's proportional hazards model (PH) is an acceptable model for survival data analysis. This work investigates PH models' performance under different efficient sampling schemes for analyzing time to event data (survival data). We will compare a modified Extreme, and Double Extreme Ranked Set Sampling (ERSS, and DERSS) schemes with a simple random sampling scheme. Observations are assumed to be selected based on an easy-to-evaluate baseline available variable associated with the survival time. Through intensive simulations, we show that these modified approaches (ERSS and DERSS) provide more powerful testing procedures and more efficient estimates of hazard ratio than those based on simple random sampling (SRS). We also showed theoretically that Fisher's information for DERSS is higher than that of ERSS, and ERSS is higher than SRS. We used the SEER Incidence Data for illustration. Our proposed methods are cost saving sampling schemes.