Randomized Play The Winner Rule For Ordered Categorical Data – A Follow-up Model in Clinical Trials
by
Aditya Chatterjee
Department of Statistics, The University of Burdwan, Burdwan 713104, West Bengal, India
Coauthors: Gopaldeb Chattopadhyay (Bureau of Applied Economics and Statistics,Government of West Bengal,India)

Comparison of a new drug with a standard or placebo drug through clinical trials is a very common problem of interest in the pharmaceutical industries. In many such trials the treatment responses are measured on an ordinal scale rather than on a continuous scale. A number of authors over the past decades have considered techniques for analyzing such type of ordered categorical data. A simple scoring system called ridits (relative to an identified distribution) that was first introduced by Bross(1958) may be used towards analyzing such data where cumulative probability scores instead of arbitrarily selected scores are considered. Brockett and Levine (1977) noticed that the ridit scores, estimated from the data, have the property that if we combine two adjacent categories and redefine the scores by the same method, then the scores for the remaining categories remain unchanged. Ridit analysis has been successfully applied to the study of automobile accident (Bross(1960)), cancer (Wynder, Bross, Hirayama(1960)), schizophrenia (Spitzer et. al. (1965)), preference studies ( Pouolard et. al.(1997)).

The technique of data-dependent allocation of treatments to the patients are of paramount interest with regard to clinical trials. For example, if the subjects enter into a system sequentially, the problem of allocation of treatments among the entering subjects requires thorough scrutiny. Further, as the subjects are human beings, from ethical point of view, it is desirable to carry out a test procedure with smaller number of patients being treated by the inferior treatment in course of the decision-making. With this idea in mind Zelen (1969) introduced the concept of play-the-winner rule for dichotomous treatment responses. Later Wei and Durham (1978) and Wei (1979) modified this idea and introduced randomized-play-the-winner rule. One of the major requirements in such sequential trials is that the outcomes are known relatively quickly and the treatment responses are dichotomous. In fact the method provided by Wei (1988), holds only if the treatment responses are dichotomous and instantaneous. Following Wei, Chattopadhyay (2002) proposed a test procedure for more than two treatment response categories. However, that procedure is not suitable when the treatment response of all previously treated patients are not readily available with the clinician before treating a particular patient, i.e. when the treatment responses are not instantaneous. In practice, treatment responses are not always instantaneous and often it is required to follow up the patients after certain time period since administering the drug.

In the present paper our aim is to provide a suitable test procedure for comparing two treatments (say treatment A and treatment B) when the treatment responses are ordered categorical in nature and each patient is followed up after certain time period (say, D days) from the date of administering the treatment. On an average this rule also allows more patients to be treated by better treatment in course of decision making, thus preserving the ethical issue of clinical trial. At the same time the treatment responses are not required to be instantaneous. Various small sample and asymptotic empirical results of the test have been derived. Moreover power and ASN studies have been done by simulation to establish the claims.

Date received: November 8, 2002