A Note on Marginalization of Regression Parameters from Mixed Models of Binary Outcomes

• Published in: Biometrics Vol. 74; no. 1; pp. 354 - 361
• Main Authors: Hedeker, Donald, du Toit, Stephen H. C., Demirtas, Hakan, Gibbons, Robert D.
• Format: Journal Article
• Language: English
• Published: United States Wiley-Blackwell 01.03.2018; Blackwell Publishing Ltd
• Subjects: BIOMETRIC PRACTICE; biometry; clinical trials; Clustered data; Computer Simulation; Data Interpretation, Statistical; Drug addiction; Estimates; Humans; Longitudinal data; Longitudinal Studies; Mathematical models; Models, Statistical; Multilevel models; Parameters; Population‐averaged estimates; Regression; Regression Analysis; Smoking; smoking (habit); Smoking Cessation; Social exclusion; Subject‐specific estimates; Treatment Outcome; Population-averaged estimates; Clustered data; Longitudinal data; Subject-specific estimates; Multilevel models
• ISSN: 0006-341X; 1541-0420; 1541-0420
• DOI: 10.1111/biom.12707

This article discusses marginalization of the regression parameters in mixed models for correlated binary outcomes. As is well known, the regression parameters in such models have the "subject-specific" (SS) or conditional interpretation, in contrast to the "population-averaged" (PA) or marginal estimates that represent the unconditional covariate effects. We describe an approach using numerical quadrature to obtain PA estimates from their SS counterparts in models with multiple random effects. Standard errors for the PA estimates are derived using the delta method. We illustrate our proposed method using data from a smoking cessation study in which a binary outcome (smoking, Y/N) was measured longitudinally. We compare our estimates to those obtained using GEE and marginalized multilevel models, and present results from a simulation study.