Single-Index Mixed-Effects Model for Asymmetric Bivariate Clustered Data

Area of Science:

• Biostatistics
• Dental Research
• Epidemiology

Background:

• Periodontal disease (PD) progression studies often use linear mixed models (LMMs) with bivariate endpoints like probed pocket depth (PPD) and clinical attachment level (CAL).
• Violations of normality assumptions in LMMs can lead to imprecise inferences, and the linear assumption may not capture the true response-covariate relationship.
• Existing methods may not provide a comprehensive summary of PD risk from covariates.

Purpose of the Study:

• To develop a non-linear mixed model framework for analyzing asymmetric, clustered bivariate responses (PPD and CAL) in periodontal disease.
• To provide a one-number summary of PD risk by modeling non-linear covariate relationships.
• To address limitations of traditional LMMs in handling non-normal and non-linear data in PD research.

Main Methods:

• Utilized a non-linear mixed model with multivariate asymmetric Laplace distribution (ALD) for random terms.
• Employed a single-index model with polynomial spline approximations to capture non-linear relationships.
• Developed an EM-type algorithm for maximum-likelihood estimation and established large sample theoretical properties.
• Validated the approach through simulation studies and application to a PD study in Type-2 diabetic African-Americans.

Main Results:

• The proposed model and estimation algorithm effectively handle asymmetric, heavy-tailed data, including outliers.
• Simulation studies demonstrated the efficiency of the estimators in finite-sample scenarios.
• The methodology provides a more accurate assessment of periodontal disease progression and risk.

Conclusions:

• The novel non-linear mixed model offers a robust framework for analyzing complex periodontal disease data.
• This approach improves risk assessment and provides a more nuanced understanding of PD progression, particularly in diabetic populations.
• The developed EM-type algorithm ensures efficient and reliable statistical inference.