Interpretation and estimation of summary ratios under heterogeneity

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Summary odds ratios are crucial in epidemiology for synthesizing results across strata.
• Existing methods like Mantel-Haenszel and Miettinen offer alternatives to assuming homogeneity of effects.
• Heterogeneity in stratum-specific parameters presents challenges for standard meta-analysis techniques.

Purpose of the Study:

• To compare Miettinen's and Mantel-Haenszel's summary odds ratio estimators under parameter heterogeneity.
• To present extended Miettinen estimators applicable to sparse data scenarios.
• To provide methods for calculating variances and confidence limits for summary ratios when heterogeneity is present.

Main Methods:

• The study evaluates the asymptotic properties of Miettinen and Mantel-Haenszel estimators under heterogeneity.
• Formulae for extended Miettinen estimators are derived for sparse data.
• Methods for calculating large-sample variances and confidence limits are presented.

Main Results:

• Miettinen's estimators consistently estimate meaningful epidemiologic parameters even with heterogeneity.
• The Mantel-Haenszel odds ratio's expectation can be influenced by sampling design under heterogeneity.
• Extended Miettinen estimators offer a robust alternative for sparse data when homogeneity is not assumed.

Conclusions:

• Miettinen's estimators are preferred over Mantel-Haenszel when stratum-specific parameter heterogeneity is suspected.
• The extended Miettinen estimators provide a valuable tool for meta-analysis in epidemiological studies with sparse data and heterogeneity.
• The Mantel-Haenszel method should be reserved for situations where the homogeneity hypothesis is likely to hold.