Nonparametric estimation and testing in a cure model.

Nonparametric generalized maximum likelihood product limit point estimators and confidence intervals are given for a cure model with random censorship. One-, two-, and K-sample likelihood ratio tests for inference on the cure rates are developed. In the two-sample case its power is compared to the power of several alternatives, including the log-rank and Gray and Tsiatis (1989, Biometrics 45, 899-904) tests. Implications for the use of the likelihood ratio test in a clinical trial designed to compare cure rates are discussed.