Assessing the effect of intensity when exposure varies over time.

In epidemiologic studies, analysis of the relationship between exposure intensity and risk is complicated by the fact that exposures often take place over extended periods, during which intensities can vary substantially. To relate exposure to outcome, it is necessary to combine information about duration, intensity and timing into a summary measure of exposure. If the aim of the exposure-response analysis is to estimate the risk associated with differing exposure intensities, the results depend on the manner in which one incorporates intensity into the summary exposure metric. Most metrics used to summarize exposure, such as the cumulative exposure index, are time-weighted summations of intensity. They are thus based on the assumption that for any fixed time point, the effect of a unit of exposure is proportional to its intensity. This paper describes an approach for constructing and fitting summary measures of exposure that one can use to incorporate alternative assumptions about the effect of exposure intensity, as well as effects relating to the timing of exposure. Data from a study of lung cancer mortality in asbestos miners and millers serve to illustrate the method. Exposure metrics based on various functions of intensity and time of exposure are constructed and fitted to the data using conditional logistic regression. The results demonstrate how the choice of a function for quantification of exposure can affect the exposure-response analysis and the risk estimates it yields.