A deterministic mathematical model has been developed for quantitative reconstruction of historical exposure. The model takes into account the causal variables actually responsible for changes in exposure and the interdependence between mean exposures in consecutive time periods. The effects of causal variables are described by step functions. In contrast, statistical modeling, a popular alternative strategy, often employs ad hoc exploratory variables, presumes independence among exposure levels, and invokes linearity or curvilinearity. Changes in exposure-modifying variables used in the deterministic model are identified from plant records. Available industrial hygiene sampling data are employed to estimate model parameters by the method of weighted least squares. The resulting general solution permits reconstruction of past exposure levels for the entire time period of interest, e.g., in a retrospective epidemiologic study. The method is illustrated by using formaldehyde exposure data from the coremaking area of a foundry. Mean exposures estimated by the model are found to predict available data well. Using the same data set, the deterministic method is compared with three typical statistical models. The strengths and limitations of the deterministic approach are discussed.
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Yu et al. (1990) studied this question.