The multistate life table with duration‐dependence

A method for generalizing the multistate, or increment‐decrement, life table to include rates which depend upon duration of exposure to risk, as well as upon age, is proposed. The method is built upon the linear approximation, called the linear integration hypothesis, developed mainly by Rogers and his colleagues. Although the use of rates indexed by duration categories leads to a substantial increase in the state space of the model, it is possible to arrange the rates in such a way that matrices to be inverted are no larger than those encountered in the usual multistate life table. In the more general approach it is possible to derive several new summary indices of the life‐table cohort's history, such as the mean and median time in current status, at any age. The method is illustrated using a simple four‐state marital‐status model which has appeared often in the literature; here, rates of divorce and widowhood vary by duration of marriage as well as age.