Evaluating the effects of observed and unobserved diffusion processes in survival analysis of longitudinal data

Abstract

In biostatistical, epidemiological and demographic studies of human survival it is often necessary to consider the dynamics of physiological processes and their influences on observed mortality rates. The parameters of a stochastic covariate process can be estimated using a conditional Gaussian strategy based on the mortality model presented in M.A. Woodbury and K.G. Manton, A random walk model of human mortality and aging. Theor. Popul. Biol. 11 , 37–48 (1977) and A.I. Yashin, K.G. Manton, and J.W. Vaupel, Mortality and aging in a heterogeneous population: A stochastic process model with observed and unobserved variables. Theor. Popul. Biol. , in press. (1985). The utility of this approach for modeling survival in a longitudinally followed population is discussed—especially in the context of conducing coordinated analyses of multiple similarly constituted databases. Furthermore, the conditional Gaussian approach offers several substantive and computational advantages over the Cameron- Martin approach R.H. Cameron and W.T. Martin, The Wiener measure of Hilbert neighborhoods in the space of real continuous functions. J. Math. Phys. 23 , 195–209.