Using tensor product splines in modeling exposure–time–response relationships: Application to the Colorado Plateau Uranium Miners cohort

An adequate depiction of exposure–time–response relationships is important in assessing public health implications of an occupational or environmental exposure. Recent advances have focused on flexible modeling of the overall shape of latency. Methods are needed to allow for varying shapes of latency under different exposure profiles. A tensor product spline model is proposed for describing exposure–response relationships for protracted time‐dependent occupational exposure histories in epidemiologic studies. The methods use flexible multi‐dimensional techniques to jointly model age, latency and exposure–response effects. In analyzing data from the Colorado Plateau Uranium Miners cohort, a model that allows for varying exposure‐dependent latency shapes is found to be superior to models that only allowed for an overall latency curve. Specifically, the model suggests that, at low exposure levels risk increased at short latencies followed by a slow decline for longer latency periods. On the other hand, risk was higher but did not change much by latency for higher exposure levels. The proposed methodology has the advantage of allowing for latency functions that vary by exposure levels and, conversely, exposure–response relationships that are influenced by the latency structure. Copyright © 2008 John Wiley & Sons, Ltd.