Mixed Semi-Continuous Copula Additive Regression Models with Applications in Insurance and Health Care

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Insurance and health care data often present a high proportion of zeros with possible skewed positive values. For example, insurance claims and medical expenditures are among those continuous skewed data with a spike at zero. Furthermore, these data are interconnected and researcher might wish to model them jointly. For instance, the interest can be in modelling simultaneously different types of medical expenditure (inpatient and outpatient), health outcomes (quality adjusted life years, QALYs) and costs, and multiple types of coverage provided by the same insurance policy, while accounting for both their dependence and the particular nature of their distributions (high proportion of zeros with positive values). Accounting for both features is indeed critical for many reasons including obtaining unbiased estimates, reliable confidence intervals, providing reliable predictions, to name but a few. Our aim is to propose a powerful, flexible and sophisticated approach that can deal with the nature of these data in an effective and efficient way while producing comprehensible results that are easy to interpret and understand, particularly by risk analysts and health decision makers.