Performance evaluation of nursing homes using finite mixtures of logistic models and M-quantile regression for binary data

Evaluating the performance of health care institutions is of paramount interest and it is often conducted using generalized linear mixed models. In this paper, we focus on the evaluation of Nursing Homes for elderly residents in a region of Italy and concentrate on binary outcomes (death and worsening). We propose to use a routinely assessed covariate such as the Resource Utilization Group to account for case-mix. We fit finite mixtures of logistic models to check the assumption of normality of the random effects in the generalized linear mixed model approach and to obtain a clustering of the Nursing Homes with respect to their performance. Since the distribution of the random effects is very skew, we propose to use scores based on robust M-Quantile regression for binary data and estimate their standard error using block-bootstrap. A sensitivity analysis is also conducted to evaluate the assumption of missing at random for non-observed data on discharged residents.