Likelihood ratio based confidence bands in survival analysis.

摘要

Thomas and Grunkemeier (1975) introduced a nonparametric likelihood ratio approach to confidence interval estimation of survival probabilities based on right censored data. We construct simultaneous confidence bands for survival, cumulative hazard rate and quantile functions using this approach. The boundaries of the bands for survival functions are contained within (0,1). A procedure essentially equivalent to a bias correction is developed. The resulting increase in coverage accuracy is illustrated by an example and a simulation study. We look at various versions of likelihood ratio based (LR) confidence bands for the survival function and compare them with the Hall-Wellner band and Nair's equal precision band. We show that LR bands for the cumulative hazard rate function and the quantile function can be obtained by employing a functional and the inverse transformation of the survival function respectively to an LR band for the survival function. At the mean time, the test-based and reflected methods are shown to be valid for constructing bands for the quantile function. The various confidence bands for the quantile function are illustrated through an example.