@bullet @bullet @bullet a Framework That Incorporates Repeated Measurements into the Hazard @bullet a Framework That Incorporates Repeated Measurements into the Hazard

A Framework that Incorporates Repeated Measurements into the Hazard (Under the direction of Michael J. Symons). By allowing covariates to remain constant between consecutive measurements over time. the hazard is able to incorporate repeated measurements in addition to intervening event and baseline information. Within this context. proportionality receives a broader definition. Although an individual's hazard at time t may depend on the values of his most recent measurements. it may also depend on a particular piece-of his covariate information that was measured earlier. A newly defined covariate that describes this "past history" information may then be included into the hazard. Examples are provided. A general parametric representation of the hazard is proposed in which an underlying failure time distribution exists. and the model parameters are expressed as simple functions of the covariates. The multiplicative model is a reduced form of this more general model. and nonproportionality is given interpretability. Nonparametric estimation of the cumulative hazard as a function of covariate strata is used in determining an appropriate parametric form for the underlying hazard. Specifically. Breslow's (1972) piecewise exponential hazard is fitted to each covariate stratum. and the focus is upon the slopes of these cumulative hazard curves. The proposed framework for incorporating repeated measurements into the hazard was appl ied to two data sets: a prospective fol.low-up study of heart diseased patients at Duke University and a iii retrospective follow-up study of chrysotile asbestos textile workers. Measurements were repeated on an individual's congestive heart failure status in the first study. and the workers' annual exposures to chryso-tile asbestos comprised the repeated measurements in the second study. The dose-response effect of a worker's cumulative exposure to chryso-tile asbestos on his hazard of death from lung cancer is of particular interest. The results of the data analyses are presented.