I am working on a project and I want to use the methodology Center for Medicare and Medicaid Services uses to risk standardize adverse outcomes by medical providers, according to case mix. The outcomes are generally binary and the risk model is obtained by regular logistic regression. Then they use the variables significant in the logistic model in a generalized linear mixed model (PROC GLIMMIX) with a random effect for provider, to determine the standardized risk for each provider. The standardized risk is calculated for each provider by dividing the sum of the predicted risks by the sum of the expected risks and that quantity is multiplied by the average unadjusted risk of the population.
My problem comes in replicating the hierarchical bootstrap they use to get the confidence intervals on the standardized risk. It appears that they bootstrap at the hospital level and then take a random draw from the estimated distribution of the random effect to estimate the predicted risk for each case within each provider in each bootstrap sample. I am not satisfied with the results I get when I try to reproduce their methodology. I need someone who is familiar with SAS macro code to go over my code and their code to see whether I am doing everything correctly. Also, I need reassurance that their methods are robust to small sample sizes and low risks like I have for some of my providers.
If you are interested in consulting on this project, please contact me at singalb@trinity-health.org
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Bonita Singal
Senior Research Biostatistician
St. Joseph Mercy Health System
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