Assessing Latent Risk Based on Joint Modelling of Multiple Health Insurance Outcomes of Mixed Types

Our research is motivated by an insurance study involving 788 insurance subscribers who made claims resulting from ischemic heart disease. Four different types of health services used by these subscribers as well as the corresponding total cost were observed for two years. Health care utilizations vary a lot even for subscribers of the same personal characteristics. The research question of primary interest is how to capture patient-specific latent risks beyond what can be explained by known personal characteristics. In this study, we characterize unobserved latent risks by random effects in our joint Tweedie mixed models for multiple health outcomes of mixed types. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach is illustrated with the analysis of the health insurance study of 788 ischemic heart disease patients. Applying cluster analysis to the patient-specific latent risks predicted by our model, we were able to classify patients into a high risk group of 36 patients, a medium risk group of 256 patients and a low risk group of 496 patients. The finding is of important policy relevance since the losses suffered by a few are known to be spread over many in an insurance system. Grouping of patients and prioritization of specific groups based on subject-specific latent risks facilitates resource allocation and pricing.