Panel data with survival: Hospitalization of HIV-positive patients

This article provides an analysis of the hospitalization experience of a panel of HIV-positive patients. It is part of a program of work designed to study the medical expenditures of such patients and their variation both between people and over time. We model the joint distribution of the inpatient episodes and the survival times of a panel of patients over 15 months. The model induces correlation between hospitalization and death via an unmeasured, person-specific, frailty term, and it allows rates of hospitalization and of death each to be affected by time-invariant and time-varying covariates. We subject the model to a variety of predictive tests and show that it is generally consistent with the data. We study and present estimates of the time variation in the rate of hospitalization. We also report the effects of a large number of covariates on rates of hospitalization and mortality. The model generalizes fairly easily in a number of ways, one of which is to handle vector-valued measures of medical expenditure and of other outcomes, such as the employment record, associated with the illness and evolving through time. Our model thus points toward a general solution to the problem of analyzing panel data in which the outcome variables of interest are correlated with the rate of mortality.