Maximum Likelihood Assessment of Clinical Trials Based on an Ordered Categorical Response

A unified maximum likelihood (ML) methodology is developed for assessing simultaneously both the statistical significance of treatment effects and the model fit when the response variable contains ordered categories. In general, for any treatment by response table it is shown that the better the model fit the more significant the treatment effect. The paper begins by examining the fit for different logit model extensions to data derived under the assumption of an underlying bivariate normal. It is shown that the “parallel log-odds” model (I) based on adjacent odds often provides a parsimonious description of the data which fits better than the “proportional odds” model (2) based on cumulative odds. Using additional data from a published clinical study, the fit and descriptive utility of more general models (3,4) using an extended ML algorithm (5) are also examined. The paper concludes with some extensions to multi-way tables, where one or more covariates are present.