Life Tables with Covariates: Dynamic Model for Nonlinear Analysis of Longitudinal Data

ABSTRACT

Life table models based on nonlinear dynamics of risk factors are developed using stochastic differential Equations for individual changes and on the resulting Fokker-Planck equation to describe population changes. Central to the model is a microsimulation strategy developed as a numerical procedure to represent a mortality effect when analytic approaches are not applicable. The model is applied to the Framingham Heart Study 46-year follow-up data. Life table functions and projections of risk factors are calculated to demonstrate the nonlinear effects on observable quantities over time. A set of statistically significant nonlinear contributions to covariate dynamics is identified. Their synergistic effect on dynamics and use of them as “new” risk factors are discussed. An important advantage of this approach is the ability to study the effects of health interventions at the individual level. This is illustrated in several examples.

Keywords:

• stochastic differential Equations
• quadratic hazard
• life table
• risk factors
• Fokker-Planck equation
• longitudinal data

Acknowledgments

This research was supported by grant P01 AG17937-05 from the National Institutes of Health/National Institute on Aging. The Framingham Heart Study (FHS) is conducted and supported by the NHLBI in collaboration with the FHS Study Investigators. This paper was prepared using a limited access dataset obtained by the NHLBI and does not necessarily reflect the opinions or views of the FHS Study or the NHLBI.