# Latent Gaussian Mixture Models for Nationwide Kidney Transplant Center Evaluation

## TL;DR

This paper introduces a novel latent Gaussian mixture model to evaluate kidney transplant centers nationwide, improving the assessment of center effects by capturing heterogeneity and addressing distributional assumptions.

## Contribution

It proposes a penalized likelihood estimation method for latent Gaussian mixture models and develops tests to determine the number of mixture components, enhancing center effect analysis.

## Key findings

- Distributional assumptions affect center effect predictions.
- The mixture model effectively captures heterogeneity among centers.
- Simulation and real data validate the proposed approach.

## Abstract

Five year post-transplant survival rate is an important indicator on quality of care delivered by kidney transplant centers in the United States. To provide a fair assessment of each transplant center, an effect that represents the center-specific care quality, along with patient level risk factors, is often included in the risk adjustment model. In the past, the center effects have been modeled as either fixed effects or Gaussian random effects, with various pros and cons. Our numerical analyses reveal that the distributional assumptions do impact the prediction of center effects especially when the effect is extreme. To bridge the gap between these two approaches, we propose to model the transplant center effect as a latent random variable with a finite Gaussian mixture distribution. Such latent Gaussian mixture models provide a convenient framework to study the heterogeneity among the transplant centers. To overcome the weak identifiability issues, we propose to estimate the latent Gaussian mixture model using a penalized likelihood approach, and develop sequential locally restricted likelihood ratio tests to determine the number of components in the Gaussian mixture distribution. The fitted mixture model provides a convenient means of controlling the false discovery rate when screening for underperforming or outperforming transplant centers. The performance of the methods is verified by simulations and by the analysis of the motivating data example.