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

Abstract

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.

Fig 1. Subject-specific longitudinal evolution of weighted cumulative exposure and dynamic survival probability for a woman aged 80 at study entry.

The plot is distributed in four panels showing the first four successive measuring points, at ages 80.5, 81.5, 82.5 and 83.5 years, respectively. The left-hand side of each panel depicts the cumulative area under the true biomarker path until the time of measurement, while the right-hand side shows the median predicted survival probabilities over 200 Monte Carlo samples. The shaded region in the survival estimate is limited by the 95% pointwise confidence intervals.