Integrating classification trees with local logistic regression in Intensive Care prognosis.

Health care effectiveness and efficiency are under constant scrutiny especially when treatment is quite costly as in the Intensive Care (IC). Currently there are various international quality of care programs for the evaluation of IC. At the heart of such quality of care programs lie prognostic models whose prediction of patient mortality can be used as a norm to which actual mortality is compared. The current generation of prognostic models in IC are statistical parametric models based on logistic regression. Given a description of a patient at admission, these models predict the probability of his or her survival. Typically, this patient description relies on an aggregate variable, called a score, that quantifies the severity of illness of the patient. The use of a parametric model and an aggregate score form adequate means to develop models when data is relatively scarce but it introduces the risk of bias. This paper motivates and suggests a method for studying and improving the performance behavior of current state-of-the-art IC prognostic models. Our method is based on machine learning and statistical ideas and relies on exploiting information that underlies a score variable. In particular, this underlying information is used to construct a classification tree whose nodes denote patient sub-populations. For these sub-populations, local models, most notably logistic regression ones, are developed using only the total score variable. We compare the performance of this hybrid model to that of a traditional global logistic regression model. We show that the hybrid model not only provides more insight into the data but also has a better performance. We pay special attention to the precision aspect of model performance and argue why precision is more important than discrimination ability.