Randomized Play-the-Winner Rule for Ordered Categorical Data

Abstract

Randomized clinical trials allocating equal numbers of subjects to each of two treatments are regarded as the “gold standard” for comparing treatments [Ivanova, A. V. (2003). A play-the-winner type urn design with reduced variability. Metrika 58:1–13]. However, if the treatment difference is large, and the end point of the study is potentially dangerous, it does not seem appropriate to expose the large number of study patients to the inferior arm. To circumvent such a situation, implementation of a data-dependent treatment allocation rule that continuously updates the knowledge by accommodating the results of the previous treatment responses during the trial is the order of the day. The objective of such a rule is to protect the study patients from paying a handsome price for the benefit of future patients. A particular adaptive design, the randomized play-the-winner (RPW) rule [Zelen, M. (1969). Play-the-winner rule and the controlled clinical trial. J. Am. Statist. Assoc. 64:131–146], [Wei, L. J., Durham, S. (1978). The randomized play-the-winner rule in medical trials. J. Am. Statist. Assoc. 73:830–843], [Wei. L. J. (1979). The generalized Polya's urn for sequential medical trials. Ann. Statist. 7:291–296], and [Cornell, R. G., Landenberger, B. D., Bartlett, R. G. (1986). Randomized play-the-winner clinical trials. Commun. Statist. Part A—Theory Methods 25:159–178 to quote a few], is often advocated to preserve the ethical aspect of the clinical trials. It has been generally observed that, in case of adaptive design, the loss of power for testing the equality of two treatments is negligible in comparison with 50–50 randomization [Yao, Q., Wei, L. J. (1996). Play the winner for phase II/III clinical trials. Statist. Med. 15:2413–2423]. Following Wei (1979), many researchers have produced a volume of articles based on this RPW rule. However, all the previous works are either for dichotomized data or for continuous data after being dichotomized based on some threshold value. The present paper provides a technique for comparing two such treatments, based on the RPW rule, when both treatment responses are polychotomous in nature and are measured on an ordinal scale. Different exact and asymptotic results related to the proposed technique from a frequentist point of view are studied. The problem has also been addressed under restricted alternative. Simulation studies have also been performed to study the power of the test and saving in sample from being treated by the inferior treatment. The results are compared with the 50–50 allocation scheme. A real-life data set, as mentioned in the case of the first investigator of Boss and Brownie [Boos, D. D., Brownie C. (1992). A rank based mixed model approach to multisite clinical trials. Biometrics 48:61–72] has also been analyzed in light of adaptive design to ensure preservation of the ethical aspect.