Relative hazard rate estimation for right censored and left truncated data

In medical research differences among treatment groups are a common focus of study. The concept of relative hazard rate is a tool for comparing two groups in terms of their difference in risk rates. A kernel estimator is proposed in the case where both samples are subject to left truncation and right censoring and an iid representation is obtained in this setup. The asymptotic distribution and the asymptotic mean squared error of the estimator are obtained. An application to the famous Channing House data set illustrates the theory.