Smoothing in survival models: an application to workers exposed to metalworking fluids

BACKGROUND In occupational epidemiology it is typically assumed that the relation between exposure, possibly transformed, and the risk of an adverse health outcome is linear in the parameters. Alternatively, exposure is transformed into a categorical variable. METHODS We used nonparametric regression to examine the linearity assumption for prostate and brain cancer mortality in a cohort of 46,400 autoworkers exposed to metalworking fluids. Using a nested case-control sample, we fit Cox proportional hazards models with penalized splines, in which we allowed the risk to be a smooth function of exposure to each of three types of metalworking fluids. Two dose metrics in addition to cumulative exposure were considered. RESULTS The shape of the dose-response curve for soluble metalworking fluids and each cancer was approximately piecewise linear, with a small increase in risk at lower exposures followed by a larger increase at exposures above a critical point. CONCLUSIONS This example illustrates that the penalized spline methodology can be easily applied to cohort studies to estimate smooth exposure-response curves.