Application of survival analysis methods to long-term care insurance

With the introduction of compulsory long-term care (LTC) insurance in Germany in 1995, a large claims portfolio with a significant proportion of censored observations became available. In first part of this paper we present an analysis of part of this portfolio using the Cox [Journal of the Royal Statistics Society B 34 (1972) 187] proportional hazard model to estimate transition intensities. It is shown that this approach allows the inclusion of censored observations as well as the inclusion of time dependent risk factors such as time spent in LTC. This is in contrast to the more commonly used Poisson regression with graduation approach (see e.g., Renshaw and Haberman [Journal of the Institute Actuaries 17 (1995) 1]), where censored observations and time dependent risk factors are ignored. In the second part we show how these estimated transition intensities can be used in a multiple state Markov process (see Haberman and Pitacco [Actuarial Models for Disability Insurance, Chapman & Hall, CRC Press, Boca Raton, FL, 1999]) to calculate premiums for LTC insurance plans.