Calculation of LTC Premiums based on direct estimates of transition probabilities

In this paper we model the life-history of LTC patients using a
Markovian multi-state model in order to calculate premiums for a
given LTC-plan. Instead of estimating the transition intensities in
this model we use the approach suggested by Andersen et al. (2003)
for a direct estimation of the transition probabilities. Based on
the Aalen-Johansen estimator, an almost unbiased estimator for the
transition matrix of a Markovian multi-state model, we calculate
so-called pseudo-values, known from Jackknife methods. Further, we
assume that the relationship between these pseudo-values and the
covariates of our data are given by a GLM with the logit as
link-function. Since the GLMs do not allow for correlation between
successive observations we use instead the "Generalized Estimating
Equations" (GEEs) to estimate the parameters of our regression
model. The approach is illustrated using a representative sample
from a German LTC portfolio.