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. Research supported in part by MCyT Grants PB98-0182-C02-01 and BFM2002-00265 (ERDF support included) and XUGA Grant PGIDT00PX110501 PN for the first author and by the Ministry of the Flemish Community (Project BIL00/28, International Scientific and Technological Cooperation) and by the IAP research network nr P5/24 of the Belgian State (Federal Office for Scientific, Technical and Cultural Affairs) for the last two authors.