A note on marginalization of regression parameters from mixed models of binary outcomes

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Mixed-Effects Models

Background:

• Mixed models for correlated binary outcomes typically yield subject-specific (SS) or conditional interpretations of regression parameters.
• Population-averaged (PA) or marginal estimates, representing unconditional covariate effects, are often preferred for population-level inference.
• Existing methods for obtaining PA estimates from SS estimates in complex models can be computationally intensive or limited in scope.

Purpose of the Study:

• To describe a novel approach using numerical quadrature to derive population-averaged (PA) estimates from subject-specific (SS) regression parameters.
• To extend the estimation of PA parameters to mixed models with multiple random effects for correlated binary outcomes.
• To provide a method for calculating standard errors of the PA estimates using the delta method.

Main Methods:

• Utilized numerical quadrature to approximate integrals required for transforming SS estimates to PA estimates.
• Employed the delta method for deriving standard errors of the population-averaged estimates.
• Applied the method to longitudinal smoking cessation data and compared results with Generalized Estimating Equations (GEE) and marginalized multilevel models.

Main Results:

• The proposed numerical quadrature approach successfully obtained population-averaged estimates from subject-specific parameters in a mixed model with correlated binary outcomes.
• Standard errors for the PA estimates were derived, enabling statistical inference.
• The method demonstrated comparable performance to existing techniques like GEE and marginalized multilevel models in simulation studies.

Conclusions:

• The numerical quadrature method offers a viable and effective approach for estimating population-averaged effects in complex mixed models for binary longitudinal data.
• This method enhances the interpretability of regression parameters by providing marginal effects relevant for public health and policy.
• The approach is robust and can be applied to various scenarios involving correlated binary outcomes, as supported by simulation results.