In this project we develop models for the analysis of the Danish Twins disability data and for analyzing the positively restricted spectra of the joint disability failure time distributions of the insect experiments. In addition, we will examine the dynamic equilibrium of disability and mortality in a multivariate stochastic diffusion process generalized for convexly bounded state spaces. These developments are further evolution of methods, model and analytic procedures we have successfully applied to other longitudinal data sets containing long-term follow-up of a rich state space for human populations (e.g., Framingham; 1982, 1984, 1989 NLTCS). In none of those studies did we deal explicitly with genetic variation though the models were constructed in a general enough way so that the mathematical representation (and statistical estimation of parameters) of genetic effects only required the availability of appropriate genetic data. There are a total of four aims to be covered. 1) Aid in the design and implementation of the longitudinal Danish Twin Study; calculation of variance optimized design; development of appropriate sample weights; analyses and evaluation of left and right censoring effects. 2) Analysis of the data from the Danish Twin Study of ascertain the genetic contributions to a multivariate functional status stochastic process which interacts with mortality. 3) Development of spectral analysis techniques for the two sets of insect data which are constrained to the positive quadrant for joint disability state transition/mortality processes. 4) Evaluation of dynamic equations of disability and mortality in determining the shape of mortality at late ages.
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