Longitudinal Survival Data and Problems of Nonlinear Dynamics

Aliaksandr Kulminski, Duke University

Due to considerable investment and effort in collecting epidemiologic and demographic data tracking individual's health status over long time periods the problem of adequately modeling this data becomes actual. Conventional methods of treating such data are based on linear paradigm when only linear combination of risk factors at given time period is assumed to contribute into future health state. In this work we use the 46-year follow-up of the Framingham Heart Study to analyze dynamics of the risk factors in survival models focusing on modeling state trajectories for individuals and considering the effect of nonlinear interactions among covariates. We find that using standard statistical methods to construct models describing the age dependence of health status might give rise to surprising results with highly "diluted" dynamics, but with significantly improved statistical criteria. It is shown that problems with the dynamics are a consequence of the intrinsic nonlinear nature of these models.