MANTEL-HAENSZEL-TYPE INFERENCE FOR CUMULATIVE ODDS RATIOS WITH A STRATIFIED ORDINAL RESPONSE

This article proposes a Mantel-Haenszel-type estimator of an assumed c ommon cumulative odds ratio in a proportional odds model for an ordina l response with several 2 x c contingency tables. It is useful, for in stance, for comparing two treatments on an ordinal response for data f rom several centers when the data are highly sparse. The estimator has behavior similar to the Mantel-Haenszel estimator of a common odds ra tio for several 2 x 2 tables. It is consistent under the ordinary asym ptotic framework in which the number of tables is fixed and, unlike th e maximum likelihood (ML) estimator, also under sparse asymptotics in which the number of tables grows with the sample size. Simulations rev eal a considerable difference between it and the ML estimator when eac h table has few observations. Efficiency comparisons suggest that litt le efficiency loss occurs compared to the ML estimator when the data a re not sparse. Tests and estimators are presented for detecting and ha ndling heterogeneity in the odds ratios, and generalizations are avail able for stratified r x c contingency tables.