Latency models for analyses of protracted exposures.

The effect of an increment of exposure on disease risk may vary with time-since-exposure. If the pattern of temporal variation is simple (eg, a peak and then a decline in excess risk of disease) then this may be modeled efficiently via a parametric latency function. Estimation of the parameters for such a model can be difficult because the parameters are not a function of a simple summary of the exposure history. Typically, such parameters are estimated via an iterative search that requires calculating a different time-weighted exposure for each combination of the latency function parameters. This article describes a simple approach to fitting logistic regression models that include a parametric latency function. This approach is illustrated using data from a study of the association between radon exposure and lung cancer mortality among underground uranium miners. This approach should facilitate fitting models to assess variation with time since exposure in the effect of a protracted environmental or occupational exposure.