Classification and estimation of case-mix adjusted performance indices for binary outcomes

In this paper, we propose a general class of indices that can be used for comparing the performances of organizations providing a given public service to citizens, such as universities, hospitals, nursing homes, employment agencies or other institutions. In particular, we handle the case where evaluation is performed by assessing the probability that a given event has happened as a result of the service provided to users requiring it. Indices are designed for settings where users can be divided into groups with similar characteristics in order to account for case-mix, that is, for the different composition of users within each organization with respect to personal features influencing the probability of the event at hand. For the proposed class, we build a taxonomy leading to nine index types. These different types constitute a useful toolbox to satisfy specific needs and/or criteria set by the evaluator in applied contexts. A general inferential framework is also discussed to deal with settings where, whatever the index chosen, its value has to be estimated from sample data. A simulation study based on a real-world dataset is presented to assess the behavior of indices’ estimators.