A comparison of marginal odds ratio estimators

Area of Science:

• Biostatistics
• Epidemiology
• Causal Inference

Background:

• Propensity scores are widely used for estimating causal effects, particularly under linearity assumptions.
• Binary outcomes and exposures present challenges, as standard assumptions like collapsibility may not hold.
• Existing methods for marginal odds ratio estimation with propensity scores require further investigation.

Purpose of the Study:

• To examine propensity score utilization for binary exposure and outcome variables, focusing on the marginal odds ratio.
• To evaluate the performance of various propensity score-based estimators, including Mantel-Haenszel and doubly robust methods.
• To assess estimator performance under conditions of low exposure prevalence and model misspecification.

Main Methods:

• Review of propensity score stratification and matching for Mantel-Haenszel estimator calculation.
• Investigation of a marginal odds ratio estimator employing doubly robust methods.
• Comparative performance analysis of different estimators under simulated conditions.
• Application of estimators to a real-world case study on Medicare plan type and quality of care.

Main Results:

• The Mantel-Haenszel estimator, when used with propensity score stratification or matching, is not consistent for the marginal or conditional odds ratio.
• Doubly robust estimators demonstrate favorable performance compared to other methods, especially under model misspecification.
• The study highlights the importance of choosing appropriate estimators for binary data in causal inference.

Conclusions:

• Standard propensity score methods may yield biased results for marginal odds ratios with binary data.
• Doubly robust estimators offer a more reliable approach for causal effect estimation in such settings.
• Accurate causal inference requires careful consideration of estimator choice and potential biases, as demonstrated in the Medicare quality of care case study.