Modelling of lung cancer survival data for critical illness insurances

Abstract

Modelling of critical illness survival data, being primary developed in the context of, e.g. health insurance contracts, also plays an important role in the currently analysed problems related to secondary insurance market. The aim of this contribution is two-fold. In the first part we describe how to construct a multiple state model for critical illness insurances, which takes into account that a probability of death for a dread disease sufferer depends on the duration of the disease and the survival probabilities are related to the disease stage. Then, in the second part, we focus on modelling of the probabilistic structure of the analysed model for a particular case of dread disease. Based on the actual data for the Lower Silesian Voivodship in Poland, we estimate the transition probabilities for the derived model in case of the risk of lung cancer. For this purpose we use the methodology developed for the construction of multi-state life tables, such as binomial, Poisson and ordinal logistic regression models. The obtained results can be directly used to build the multiple increment–decrement tables, which are useful to valuation not only critical illness insurances and life insurances with accelerated death benefits option but also to viatical settlement contracts and health-related expenses.