Describing heterogeneous effects in stratified ordinal contingency tables, with application to multi-center clinical trials
Standard models for a set of contingency tables with ordered response categories assume a common effect within or between tables, described by a certain type of odds ratio. In practice, heterogeneity usually occurs among such odds ratios, even if its extent is minor in magnitude. This article presents models that summarize the effect while simultaneously describing the degree of heterogeneity. For cases in which the levels of the stratification factor are a sample, such as many multi-center clinical trials, we recommend the use of random effects models. These treat the true stratum-specific ordinal log odds ratios as a sample with some unknown mean and standard deviation. For the random effects distribution, we consider both normality and a nonparametric approach. In using these more realistic models permitting heterogeneity, it can be more difficult to establish significance of effects because of the extra variability inherent in the model. The primary focus is three-way contingency tables with an ordinal response and a stratification factor, but we also briefly discuss models for describing heterogeneity within contingency tables.
odds ratio random effect adjacent-categories logit association models cumulative logit gausshermite quadrature nonparametric mixture model proportional odds model treatment-by-center interaction