Confidence Intervals for the Relative Relapse Rate of Placebo VS 6‐Mercaptopurine Group of Acute Leukemia Patients Under a Random Censorship Model

Abstract

The present paper considers a random censorhip model in which the remission times of acute leukemia patients in a study are randomly censored according to a given probability distribution and constructs confidence intervals for the Relative Relapse Rate [RRR] of the placebo versus 6‐Mercaptopurine group of acute leukemia patients. Two important models are discussed for the probability distributions of the remission times‐the exponential and the Weibull distributions. The censoring distributions are also regarded as following exponential and Weibull distributions. Several methods are used to construct the confidence intervals including its maximum likelihood estimator and its approximate sampling distribution. Sprott'S and Cox'S methods as well as the Box‐Cox transformations are also utilized. These methods are used to illustrate the construction of the confidence intervals with the FREIREICH et al. data (1964) involving a placebo and a 6‐MP group of acute leukemia patients. The results of the present paper provide valuable alternatives to the usual parametric and nonparametric tests for the treatment effect, that are discussed in the literature, such as Gehan'S test, Logrank test, and the Mantel‐Haenszel test.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1002/bimj.4710330512

Keywords

Censoring mechanism, Control and treatment groups, Exponential and Weibull distributions, Remission times

Publication Date

1-1-1991

Journal Title

Biometrical Journal

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