Outcome‐dependent sampling in cluster‐correlated data settings with application to hospital profiling

Hospital readmission is a key marker of quality of healthcare and an important policy measure, used by the Centers for Medicare and Medicaid Services to determine, in part, reimbursement rates. Currently, analyses of readmissions are based on a logistic–normal generalized linear mixed model that permits estimation of hospital‐specific measures while adjusting for case mix differences. Recent moves to identify and address healthcare disparities call for expanding case mix adjustment to include measures of socio‐economic status while minimizing additional burden to hospitals associated with collecting data on such measures. Towards resolving this dilemma, we propose that detailed socio‐economic data be collected on a subsample of patients via an outcome‐dependent sampling scheme, specifically the cluster‐stratified case–control design. Estimation and inference, for both the fixed and the random‐effects components, are performed via pseudo‐maximum‐likelihood wherein inverse probability weights are incorporated in the usual integrated likelihood to account for the design. In comprehensive simulations, cluster‐stratified case–control sampling proves to be an efficient design whenever interest lies in fixed or random effects of a generalized linear mixed model and covariates are unobserved or expensive to collect. The methods are motivated by and illustrated with an analysis of N = 889661 Medicare beneficiaries hospitalized between 2011 and 2013 with congestive heart failure at one of K = 3116 hospitals. Results highlight that the framework proposed provides a means of mitigating disparities in terms of which hospitals are indicated as being poor performers, relative to a naive analysis that fails to adjust for missing case mix variables.