Recent developments in the analysis of longitudinal data have addressed one of the two aspects:
(i) the relationship between a repeatedly measured covariate and time or other covariates (covariate tracking model), and
(ii) the relationship between the time-dependent covariate and the probability of disease development (disease risk model).This talk address both of these issues in a single analysis by modeling a continuous covariate over time and simultaneously relating the covariate to disease risk. For the covariate tracking model a random components model with normal errors is assumed. A proportional hazards model for disease risk is used. To obtain parameter estimates, a Bayesian perspective is taken, i.e. all inferences of the unknown parameters of interest are obtained from the marginal posterior distribution of unobserved quantities (parameters and missing data) given only the observed data. MCMC methods are utilized for model fitting, which has several advantages. For instance, estimates of variability, and in fact the entire marginal or joint posterior distributions, of all model parameters are obtained without complex derivations or simplifying assumptions. Thus, the variance estimates for the disease risk parameters correctly reflect the uncertainty inherent in the covariate tracking model parameters, and, conversely, the variance estimates of the covariate tracking model parameters reflect the uncertainty in the parameters of the disease risk model. A simulation study and real-data set are used for illustration.
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