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Five year post-transplant survival rate is an important indicator on qualityof care delivered by kidney transplant centers in the United States. To providea fair assessment of each transplant center, an effect that represents thecenter-specific care quality, along with patient level risk factors, is oftenincluded in the risk adjustment model. In the past, the center effects havebeen modeled as either fixed effects or Gaussian random effects, with variouspros and cons. Our numerical analyses reveal that the distributionalassumptions do impact the prediction of center effects especially when theeffect is extreme. To bridge the gap between these two approaches, we proposeto model the transplant center effect as a latent random variable with a finiteGaussian mixture distribution. Such latent Gaussian mixture models provide aconvenient framework to study the heterogeneity among the transplant centers.To overcome the weak identifiability issues, we propose to estimate the latentGaussian mixture model using a penalized likelihood approach, and developsequential locally restricted likelihood ratio tests to determine the number ofcomponents in the Gaussian mixture distribution. The fitted mixture modelprovides a convenient means of controlling the false discovery rate whenscreening for underperforming or outperforming transplant centers. Theperformance of the methods is verified by simulations and by the analysis ofthe motivating data example.

Latent Gaussian Mixture Models for Nationwide Kidney Transplant Center Evaluation