We introduce a duration model that allows for unobserved cumulative individual-specific shocks, which are likely to be important in explaining variations in duration outcomes, such as length of life and time spent unemployed. The model is also a useful tool in situations where researchers observe a great deal of information about individuals when first interviewed in surveys but little thereafter. We call this model the a??increasingly mixed proportional hazarda?? (IMPH) model. We compare and contrast this model with the mixed proportional hazard (MPH) model, which continues to be the workhorse of applied single-spell duration analysis in economics and the other social sciences. We apply the IMPH model to study the relationships among socioeconomic status, health shocks, and mortality, using 19 waves of data drawn from the German Socio-Economic Panel (SOEP). The IMPH model is found to fit the data statistically better than the MPH model, and unobserved health shocks and socioeconomic status are shown to play powerful roles in predicting longevity.