Statistical Test for Ordered Categorical Data in Clinical Trials
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Statistical Test for Ordered Categorical Data in Clinical Trials Shein-Chrng Chow Duke University School of Medicine, Durham, North Carolina Sir-Keung Tse City University ofHong Kong. Hong Kong Chinyon Yong Yunnan University, Yunnan, China
Dennis Cosmatos Wyeth Research, Collegeville, Pennsylvania Eric Chi Amgen, lnc., Thousand Oaks, California
Key Words Clinical trials; Likelihood ratio test; Multinomial model; Ordered categorical data; Sample size determination Correspondence Address Shein-Chung Chow, Department of Biostatistics and Bioinfonnatics. Duke University School of Medicine, 2400 Pratt St., Room 031I , Terrace Level, Durham, NC 27715 (email: sheinchung.chow@ dukexdu).
In clinical trials, subjects are often classified into ordered categories (eg, worsening, no change, and improvement) based on their posttreatment clinical response changes from baseline. The usual approach in using a multinomial model for assessing treatment efects between treatment groups is not efficient because it demands intense computation to evaluate the corresponding probabilities across these ordered categories. In this studv, we propose to model the response probabilities via a parametric form, and the Comparison of these probabilities
INTRODUCTION In clinical trials for comparing an active treatment and a standard therapy, it is not uncommon to classify the responses into some ordered categories. For example, based on some prespecified evaluability criteria, the investigator may classify the responses into three categories such as worsening, no change, and improving. In practice, as a simple approach, the proportions of responses between treatments are usually compared to assess treatment effect by category. This approach, however, is not statistically justifiable. In addition, it is a concern that a pattern of results in which the active treatment increased both the proportion of failures (worsening) and the proportion of successes (improvement) would be statistically significant and difficult to interpret. For testing one-sided alternatives for ordered categorical data models, several methods utilizing chi-square statistics have been proposed in the literature (1-5). Cohen (6) discussed the problem of comparing the effectiveness of two treatments, say, whether a test treatment is more effective than a control treatment, based on categorical responses. Cohen (6) considered a multinomial model to describe the probabilities of the responses falling into the various cateInf-ti~n
is translated into the comparison of the associated model parameters. Maximum likelihood estimates are then derived and the required sample size for achieving a desired statistical power at a prespeciied level of significance is also obtained. A simulation study is performed to evduatefinitesamplesize performance.An example concerning the evaluation of the efficacy of a test treatment for subjects with moderate to severe Crohn disease that is refmdory to steroids and immunosuppressants is presented to illustrate the proposed method.
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