Modeling nonlinear effects in longitudinal survival data: implications for the physiological dynamics of biological systems.
Despite the wealth of longitudinal data on the health dynamics of human populations, information on covariates (risk factors) changes in those studies has not been systematically and fully exploited. In this work we use the 46-year follow-up of the Framingham Heart Study to analyze dynamics of these risk factors in survival models that go far beyond the standard linear dynamic formulation. We focus on improving the inferences about the physiology of human aging processes and its plasticity and on modeling state trajectories for individuals 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 found that problems with the dynamics are a consequence of the intrinsic nonlinear nature of these models. We show that evolution of the risk factors measured in the Framingham study is more complicated for females than for males (i.e., female health status is more sensitive to nonlinear interactions among risk factors). We suggest that this is due to the rapid rate of decline of estrogen production after menopause.
Kulminski
A
A
Duke University, Center for Demographic Studies, 2117 Campus Drive, Box 90408, Durham, NC 27708-0408, USA. kam@cds.duke.edu
Akushevich
I
I
Manton
K
K
D000375:Aging / Q000502:physiology; D005260:Female; D005500:Follow-Up Studies; D006306:Health Surveys; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D012307:Risk Factors; D013534:Survival; D013598:Systems Theory