Hazard ratio estimation for two-sample case under interval-censored failure time data

This paper discusses two-sample comparison in the case of interval-censored failure time data. For the problem, one common approach is to employ some nonparametric test procedures, which usually give some p-values but not a direct or exact quantitative measure of the survival or treatment difference of interest. In particular, these procedures cannot provide a hazard ratio estimate, which is commonly used to measure the difference between the two treatments or samples. For interval-censored data, a few nonparametric test procedures have been developed, but it does not seem to exist as a procedure for hazard ratio estimation. Corresponding to this,we present two procedures for nonparametric estimation of the hazard ratio of the two samples for interval-censored data situations. They are generalizations of the corresponding procedures for right-censored failure time data. An extensive simulation study is conducted to evaluate the performance of the two procedures and indicates that they work reasonably well in practice. For illustration, they are applied to a set of interval-censored data arising from a breast cancer study.