  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.
