Discussion paper // Sonderforschungsbereich 386 der Ludwig-Maximilians-Universität München 357
In this paper we quantify the inception selection effect of diagnosis in a large German long term care (LCT) portfolio. First we are interested in modeling transition intensities, which will then be used in a multistate model set up to estimate 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 diagnosis 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.
semiparametric hazard model survival analysis long term care insurance multistate model inception selection