A Bayesian joint model for zero-inflated integers and left-truncated event times with a time-varying association: Applications to senior health care

Population aging in most industrialized societies has led to a dramatic increase in emergency medical demand among the elderly. In the context of private health care, an optimal allocation of the medical resources for seniors is commonly done by forecasting their life spans. Accounting for each subject's particularities is therefore indispensable, so the available data must be processed at an individual level. We use a large and unique dataset of insured parties aged 65 and older to appropriately relate the emergency care usage with mortality risk. Longitudinal and time-to-event processes are jointly modeled, and their underlying relationship can therefore be assessed. Such an application, however, requires some special features to also be considered. First, longitudinal demand for emergency services exhibits a nonnegative integer response with an excess of zeros due to the very nature of the data. These subject-specific responses are handled by a zero-inflated version of the hierarchical negative binomial model. Second, event times must account for the left truncation derived from the fact that policyholders must reach the age of 65 before they may begin to be observed. Consequently, a delayed entry bias arises for those individuals entering the study after this age threshold. Third, and as the main challenge of our analysis, the association parameter between both processes is expected to be age-dependent, with an unspecified association structure. This is well-approximated through a flexible functional specification provided by penalized B-splines. The parameter estimation of the joint model is derived under a Bayesian scheme.

Joint Modelling of Survival and Emergency Medical Care Usage in Spanish Insureds Aged 65+

BACKGROUND

We study the longevity and medical resource usage of a large sample of insureds aged 65 years or older drawn from a large health insurance dataset. Yearly counts of each subject's emergency room and ambulance service use and hospital admissions are made. Occurrence of mortality is also monitored. The study aims to capture the simultaneous dependence between their demand for healthcare and survival.

METHODS

We demonstrate the benefits of taking a joint approach to modelling longitudinal and survival processes by using a large dataset from a Spanish medical mutual company. This contains historical insurance information for 39,137 policyholders aged 65+ (39.5% men and 60.5% women) across the eight-year window of the study. The joint model proposed incorporates information on longitudinal demand for care in a weighted cumulative effect that places greater emphasis on more recent than on past service demand.

RESULTS

A strong significant and positive relationship between the exponentially weighted demand for emergency, ambulance and hospital services is found with risk of death (alpha = 1.462, p < 0.001). Alternative weighting specifications are tested, but in all cases they show that a joint approach indicates a close connection between health care demand and time-to-death. Additionally, the model allows us to predict individual survival curves dynamically as new information on demand for services becomes known.

CONCLUSIONS

The joint model fitted demonstrates the utility of analysing demand for medical services and survival simultaneously. Likewise, it allows the personalized prediction of survival in advanced age subjects.