Baseline Survival Function Estimators under Proportional Hazards Assumption

Cox (1972) proposed the partial likelihood technique to estimate the risk coefficients of proportional hazards regression model without specify the baseline hazards function. Once the risk coefficients β are estimated, we may interest in estimating the corresponding baseline survival function. Therefore, Breslow (1972) and Kalbfleisch & Prentice (1973) provided two different procedures as the baseline survival function estimators. However, these two estimators have some drawbacks. Breslow’s estimator may give negative value, and Kalbfleisch & Prentice’s estimator has no close form when ties data is presented. In this work, we propose another estimator which is also based on NPMLE technique as Breslow’s and Kalbfleisch & Prentice’s estimators, however, it has a close form in all cases and never give negative value. To compare these three estimators, we run a series of simulations to see the finite sample performance of them under some specified models.