Generalized Linear Mixed Models with Gaussian Mixture Random Effects: Inference and Application.

Area of Science:

• Biostatistics
• Health Services Research
• Medical Informatics

Background:

• Clustered data, such as patient outcomes within healthcare facilities, presents unique statistical challenges.
• Evaluating healthcare provider performance, like kidney transplant centers, requires accounting for patient-level factors and facility-level variations.
• Existing models may struggle with identifiability and accurately assessing heterogeneity among providers.

Purpose of the Study:

• To propose a novel class of generalized linear mixed models incorporating Gaussian mixture random effects for clustered data.
• To address weak identifiability issues inherent in mixture models.
• To develop methods for determining the optimal number of mixture components and controlling false discovery rates in provider screening.

Main Methods:

• A penalized Expectation Maximization (EM) algorithm is employed for model fitting.
• Sequential locally restricted likelihood ratio tests are developed to ascertain the number of Gaussian mixture components.
• The model integrates patient-level risk factors and models transplant center effects using a finite Gaussian mixture.

Main Results:

• The proposed model effectively handles clustered data and Gaussian mixture random effects.
• The penalized EM algorithm overcomes identifiability challenges.
• Likelihood ratio tests provide a robust method for selecting the number of mixture components.

Conclusions:

• The developed statistical framework offers a powerful tool for analyzing heterogeneity in clustered data, exemplified by kidney transplant center performance.
• The model facilitates accurate evaluation of transplant center quality by considering patient risk factors and center-specific effects.
• This approach enables reliable screening of transplant centers for non-standard performance while controlling the false discovery rate.