Asymptotic Confidence Intervals for the Relative Relapse Rate Under Random Censorship

Abstract

AbstractIn the present paper we determine asymptotic confidence intervals of relative relapse rates (RRR) in the case of stochastically right censorship. A practical problem which promotes this discussion is the investigation of the efficiency of a test medicine: The quotient of the mortality rates (called the RRR) of two groups of acute leukemia patients is used as its indicator whereby the patients of one group received the remedy. With this task we will pursue a recent paper by Rao et al. (1991) who assumed the Weibull distribution to be the model for relapse times in both groups. Furthermore, the observed samples are stochastically right censored with censoring distributions of Weibull type, too. We construct asymptotic confidence intervals for the distribution parameters on the basis of the ml estimator and a pseudo‐ml estimator from which the intervals for RRR follow. For the benefit of accuracy in the case of finite samples a bias correction is proposed. By means of a numerical example with the Freireich data (Freireich (1964)) the resulting intervals are compared with those of the approximative methods in Rao et al. (1991).