Joint Modeling of Longitudinal and Time-to-Event Data with Applications in Health Insurance

Abstract

[eng] Health insurance companies accumulate a great wealth of historical data, including policyholder characteristics (age, residence, etc.), death event information, and the frequency and type of medical claims made by each individual, which can be used as an indirect measure of subject's health status. At the same time, the aging processes occurring in most of developed countries generate an interest in assessing the relationship between emergency care demand and survival rate, especially for policyholders over 65. Theoretically, the amount needed by insurance companies to cover the costs of policyholders requiring frequent emergency care should be compensated by a lower survival rate, but this compensation is ambiguous due to heterogeneity between subjects. Indeed, aging and mortality rates are influenced by subject-specific socioeconomic and biological variables, which may vary considerably between individuals, and within a single subject. Consequently, there is both a medical and economic necessity to assess how the individual medical demand of elderly subjects will evolve over time, as their age-related high rate of chronic disease make them require additional medical resources. On one hand, insurance prices are measured in terms of premiums, so individual health status must be considered in order to allow the elderly to sign actuarially fair contracts. On the other hand, an insurance company providing pensions and insurance needs to plan for unexpected costs derived from people having lifespans above mean expectations. Under this interdependency scheme, the joint models for longitudinal and time-to-event data proposed in this thesis provide useful tools to properly address the underlying relationship between the emergency medical demand and the hazard for death event. This thesis makes a contribution to the statistical methodology in the field of joint modeling techniques, which were applied to a large longitudinal dataset, the HI Dataset, provided by a Spanish medical insurance company. From this dataset, we collected those subjects over 65 and living in Barcelona (Spain). For each subject, we have the historical emergency claims information within the study window, as well as the time-to-event information. The longitudinal outcome is of discrete nature, usually restricted to a small range of non-negative integer values which are affected by some degree of overdispersion, i.e. the observed variance exceeds the mean. Additionally, counts with a large number of zeros become quite common due to the incomplete nature of health insurance data. All those subjects entering after the age of 65 are considered as delayed entries, and their time-to-event data are subject to left truncation in addition to the potential (non-informative) right censoring. Then, the implemented joint models must account for the special characteristics of our observed longitudinal response, departing from the common Gaussian responses, together with the specific time-to-event data pattern. There are three main tasks at hand in the joint analysis of the two considered outcomes: 1. To implement a joint model which allows for the handling of longitudinal counts, also considering potential subject-specific overdispersion by means of a model which considers a zero excess (zero inflation). Moreover, survival times can also be subject to both left truncation and right censoring. 2. To assess the functional form to associate each individual's expected longitudinal response with their death risk, investigating the effect of the cumulative longitudinal response on the current death hazard. 3. As a central focus of this thesis, to propose the existence of a time-dependent relationship between the longitudinal process and the time-to-event outcome. This is defined using Bayesian P-splines in order for any specific shape to be conferred. All the analyses included in this thesis have been implemented under the Bayesian framework, in the R and JAGS free-software environments.