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For stratified clinical trials with an ordinal response, this article considers two diagnostics strategies for evaluating the heterogeneity of the ordinal odds ratios across multi-centers in proportional odds models. The first strategy assumes multi-centers as a sample from a population and then uses a proportional odds model allowing random effects to model the heterogeneity among the ordinal log odds ratios. It gives an overall view of the heterogeneity across multi-centers. The second strategy applies the influence measure to the Mantel–Haenszel type estimators of the ordinal odds ratios. It shows the detail of heterogeneity in each of the multi-centers. At the end, this article uses a multi-center clinical trials example to illustrate both strategies.

In this paper, we will consider the influence analysis of a contingency table in which cell counts are generated by a clustered sampling model. We discuss the estimation procedures for obtaining maximum likelihood estimates and diagnostical methods for a contingency table derived from a cluster sampling model. In particular, we consider diagnostic and influence analysis in a cluster sampling model.