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 merits and demerits.

We propose two new methods that allow flexible random effects distributions. The first one is a Generalized Linear Mixed Model (GLMM) with normal mixture random effects. By allowing random effects to be non homogeneous, the shrinkage effects is reduced and the predicted random effects are much closer to the truth. In addition, modeling random effects as normal mixture will essentially clustering it into different groups, which provides a natural way of evaluating the performance in the transplant center case. To decide the number of components, we do a sequential hypothesis tests.

In the second method, we propose a subgroup analysis on the random effects under the framework of GLMM. Each level of the random effect is allowed to be a cluster by itself, but clusters that are close to each other will be merged into big ones. This method provides more precise and stable estimation than fixed effects model while it has a much more flexible distributions for random effects than a GLMM with Gaussian assumption. In addition, the other effects in the model will be selected via lasso type penalty.