Likelihood Ratio Based Con dence Intervals in Survival Analysis

Con dence intervals for the survival function and the cumulative hazard function are considered. These con dence intervals are based on an inversion of the likelihood ratio statistic. To do this two extensions of the likelihood, each of which yields meaningful likelihood ratio hypothesis tests and subsequent con dence intervals, are considered. The choice of the best extension is di cult. In the failure time setting, the binomial extension is best in constructing con dence intervals concerning the survival function and the Poisson extension is best in constructing con dence intervals concerning the cumulative hazard. Simulations indicate that these two methods perform as well as or better than competitors based on asymptotic normality of the estimator.