title: Interpretation and estimation of summary ratios under heterogeneity.
abstract: Of the several types of summary odds ratios in use in epidemiology, only those proposed by Mantel and Haenszel and Miettinen do not assume homogeneity (constancy) of stratum-specific parameters. Under heterogeneity, Miettinen's estimators consistently estimate meaningful epidemiologic parameters, whereas the asymptotic expectation of the Mantel-Haenszel odds ratio varies according to irrelevant features of the sampling design. Although one can modify the Mantel-Haenszel summary to overcome the latter problem, one can also extend the Miettinen estimators to sparse data and thus limit the use of Mantel-Haenszel summaries to situations in which the homogeneity hypothesis is reasonable. This paper provides formulae for the extended Miettinen estimators and large-sample variances and confidence limits for summary ratios under heterogeneity.
mesh_terms: D004812:Epidemiologic Methods; D006801:Humans; D011336:Probability; D012494:Sampling Studies; D013223:Statistics as Topic