The inception selection effect of diagnosis in a German long term care portfolio

In this paper we quantify the inception selection effect of
diagnosis in a large German long term care (LTC) portfolio. First
we are interested in modeling transition intensities, which will
then be used in a multistate model set up to estimate transition
probabilities. Finally we use these probability estimates as the
basis for premium calculations. For the estimation of transition
intensities we use semiparametric hazard models introduced by Cox
(1972) allowing the inclusion of diagnosis as explanatory variable.
Using modern model diagnostics we build a statistical model for the
transition intensities and show that the resulting transition
probability estimates including diagnosis perform better than when
diagnosis is neglected. To quantify the inception selection effect
of diagnosis we show how these improved transition probability
estimates affect the premiums in an LTC insurance contract. In
particular for younger age groups higher premiums are obtained when
the diagnoses are taken into account compared to a model which
disregards diagnosis. This demonstrates the actuarial need for
allowing for an inception selection effect of diagnosis.