Estimating the survival function in the proportional hazards regression model: A study of the small sample size properties

To study the small sample performance in the proportional hazards regression model of four estimators of the survival function and three procedures for constructing confidence intervals, a Monte Carlo simulation study was conducted. We conclude that even with a sample size of 50 and with 25-50% censoring it is possible to give reliable estimates of survival probabilities, except perhaps in the extreme right tail of the distribution. The choice of the best estimator is not clearcut though an estimator based on the product integral of Breslow's cumulative hazard estimator tended to have a slightly better overall performance. For the confidence interval a log-log transformation is strongly recommended.