Stochastic frailty models for modeling and forecasting mortality

In many countries life expectancy gains have been substantially higher than predicted by even recent forecasts. This is primarily due to increasing rates of improvement in old-age mortality not captured by existing models. In this paper we show how the concept of frailty can be used to model both changing rates of improvement and the deceleration of mortality at old ages, also seen in data. We present a "fragilization" method by which frailty can be added to standard mortality models. The aim is to improve the modeling and forecasting of old-age mortality while preserving the structure of the original model and the underlying stochastic processes. Estimation is based on a general pseudo-likelihood approach which allows the use of essentially any frailty distribution and mortality model. We also consider a class of generalized stochastic frailty models with both frailty and non-frailty terms, and we describe how these models can be estimated by the EM-algorithm. The method is applied to the Lee-Carter model and a parametric time-series model. For both applications the effect of adding frailty is illustrated with mortality data for US males.