Survival analysis in clinical trials: Past developments and future directions

The field of survival analysis emerged in the 20th century and experienced tremendous growth during the latter half of the century. The developments i n this field that have had the most profound impact on clinical trials are the Kaplan-Meier (1958, Journal of the American Statistical Association 53, 457-481) method for estimating the survival function, the log-rank statist ic (Mantel, 1966, Cancer Chemotherapy Report 50, 163-170) for comparing two survival distributions, and the Cox (1972, Journal of the Royal Statistica l Society, Series B 34, 187-220) proportional hazards model for quantifying the effects of covariates on the survival time. The counting-process marti ngale theory pioneered by Aalen (1975, Statistical inference for a family o f counting processes, Ph.D. dissertation, University of California, Berkele y) provides a unified framework for studying the small- and large-sample pr operties of survival analysis statistics. Significant progress has been ach ieved and further developments are expected in many other areas, including the accelerated failure time model, multivariate failure time data, interva l-censored data, dependent censoring, dynamic treatment regimes and causal inference, joint modeling of failure time and longitudinal data, and Baysia n methods.