The Use of Time Dependent Covariates in Modelling Data from an Occupational Cohort Study

In a retrospective cohort study of 768 textile workers, a model‐based approach is used to determine the effect of cumulative exposure to chrysotile asbestos on the hazard of death from lung cancer. Age at death is the outcome variable, and the effects of cumulative exposure, calendar year, and number of years since initial employment are modelled as time dependent covariates. This work quantifies and tests formally the dose‐response effect observed in a standardized mortality ratio analysis by Dement et al. (1982). An extended definition of the proportional hazards model is presented for time dependent covariates defined as step functions of the repeated measurements over time. A complete parametric modelling approach is employed here in addition to the use of Cox's model. Specifically, an underlying failure time distribution is assumed, and the model parameters are expressed as simple linear functions of the covariates. Nonparametric estimation of the cumulative hazard as a function of covariate strata is used to select an appropriate parametric form for the underlying hazard. These procedures are generalized to allow for changing covariate values over time. The Gompertz distribution is chosen for this particular data, and a departure from the proportional hazards model is suggested.