Fitting latency models using B-splines in EPICURE for DOS

Disease latency refers to the interval between an increment of exposure and a subsequent change in an individual’s risk. This implies that the risk from a certain exposure history does not depend on cumulative exposure alone, but on the timing of exposure. It can be expected that risk varies over time in a smooth way, and this variation can be described by a latency curve. We explain how to apply a spline function model to data on exposure history and disease. Splines are piecewise polynomial functions [1]. Theoretically, latency patterns could be described by estimating separate risk parameters for exposures received in each year prior to current age. However, the number of parameters would be large, and all the parameters could not be estimated due to limited data and possibly correlations between exposures in subsequent time intervals. The large number of parameters that would have to be estimated in such a nonparametric approach can be reduced by the use of spline functions. The use of cubic splines is a mild restriction because of their flexibility in approximating smooth functions. The model that includes risk with total cumulative exposure, which corresponds to a constant latency curve, is nested in the spline model. This method has been applied in occupational lung cancer epidemiologic studies where the exposures were asbestos [2] and radon [3]. Other approaches to analyze latency in epidemiologic studies include simple exploratory techniques [4, 5] or the bilinear model developed by Langholz et al. [6]. We briefly describe the spline function model and explain the use of EPICURE code to fit this model.