A Generalization of the Mantel-Haenszel Estimator of Partial Association for 2 x J x K Tables

SUMMARY A generalization of the Mantel-Haenszel estimator of a common odds ratio for a series of 2 x 2 tables is proposed for the estimation of log linear partial association parameters for a series of 2 x J (J > 2) tables. The assumption of no three-way interaction among row, column, and stratifying variables is made. Two approximate covariance estimators are presented. Small-sample properties of these estimators are investigated by simulation studies. The results indicate that use of the proposed partial association technique produces estimates with negligible bias. Both covariance estimation techniques provide confidence intervals for functions of partial association parameters, for example, odds ratios or adjusted rates. A test of no three-way interaction results from these procedures.

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