Application of the Cox proportional hazards model and competing risks models to critical illness insurance data

Abstract

A commercial insurance company in the Czech Republic provided data on critical illness insurance. The survival analysis was used to study the influence of the gender of an insured person, the age at which the person entered into an insurance contract, and the region where the insured person lived on the occurrence of an insured event. The main goal of the research was to investigate whether the influence of explanatory variables is estimated differently when two different approaches of analysis are used. The two approaches used were (1) the Cox proportional hazard model that does not assign a specific cause, such as a certain diagnosis, to a critical illness insured event and (2) the competing risks models. Regression models related to these approaches were estimated by R software. The results, which are discussed and compared in the paper, show that insurance companies might benefit from offering policies that consider specific diagnoses as the cause of insured events. They also show that in addition to age, the gender of the client plays a key role in the occurrence of such insured events.