Modeling of transition intensities and probabilities in a German long term care portfolio with known diagnosis

In this paper a semiparametric hazard model introduced by Cox
(1972) is used to model transitions intensities for a long term
care (LTC) data set. The main focus is the inclusion of the
diagnoses which led to LTC as explanatory variables. Modern model
diagnostic techniques are applied to check the model assumptions.
Fractional Polynomials proposed by Royston and Altman (1994) are
used to model the functional form of continuous covariates. Time
dependency is examined graphically by using scaled Schoenfeld
residuals (see Grambsch and Therneau(1994)). It is shown that the
inclusion of diagnoses significantly improves the estimated
transition probabilities on which premiums are based. As an
alternative approach a piecewise exponential model is fitted and
compared to the semiparametric hazard model.