Models of mortality and aging depend on assumptions about physiological change even if they are not made explicit. Standard models, like the Gompertz, often fail to describe mortality at extreme ages, suggesting a need for biologically more detailed and flexible models. One solution is to model the interaction of time-varying covariates with mortality to better describe the age dependence of mortality, test hypotheses about the relation of physiological change and mortality, and use longitudinal data to generalize assumptions about physiological change. This model is applied to (a) a 34-year follow-up of risk factors and mortality and (b) a 9.5-year follow-up of function and mortality from longitudinal surveys of the U.S. elderly population.