On doubly robust estimation in a semiparametric odds ratio model.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Conditional odds ratio models are crucial for analyzing associations between variables, especially in the presence of unmeasured confounding.
• Semiparametric models offer flexibility by allowing parts of the model to be non-parametrically specified.
• Doubly robust estimation provides reliable results even when one of the model components is misspecified.

Purpose of the Study:

• To develop and evaluate doubly robust estimators for parameters in semiparametric conditional odds ratio models.
• To assess the consistency, asymptotic normality, and efficiency of these estimators under various model assumptions.
• To provide a computationally simpler alternative to existing estimation methods.

Main Methods:

• The study proposes novel estimators based on the principle of doubly robust estimation.
• Asymptotic properties (consistency and normality) are derived under a union model framework.
• Efficiency is investigated at the intersection submodel where both nuisance functions are correctly specified.

Main Results:

• The proposed estimators are shown to be consistent and asymptotically normal under a union model.
• For outcomes with finite support, the estimators achieve semiparametric efficiency.
• For general outcomes, the estimators are nearly efficient at the intersection submodel.
• The methods avoid the complex alternating conditional expectations algorithm.

Conclusions:

• The developed doubly robust estimators offer a robust and efficient approach for semiparametric conditional odds ratio models.
• These methods are practical due to their ease of implementation and computational advantages.
• The findings contribute to the advancement of statistical inference in complex modeling scenarios.