Dose‐response analyses using restricted cubic spline functions in public health research

Abstract

Taking into account a continuous exposure in regression models by using categorization, when non-linear dose-response associations are expected, have been widely criticized. As one alternative, restricted cubic spline (RCS) functions are powerful tools (i) to characterize a dose-response association between a continuous exposure and an outcome, (ii) to visually and/or statistically check the assumption of linearity of the association, and (iii) to minimize residual confounding when adjusting for a continuous exposure. Because their implementation with SAS® software is limited, we developed and present here an SAS macro that (i) creates an RCS function of continuous exposures, (ii) displays graphs showing the dose-response association with 95 per cent confidence interval between one main continuous exposure and an outcome when performing linear, logistic, or Cox models, as well as linear and logistic-generalized estimating equations, and (iii) provides statistical tests for overall and non-linear associations. We illustrate the SAS macro using the third National Health and Nutrition Examination Survey data to investigate adjusted dose-response associations (with different models) between calcium intake and bone mineral density (linear regression), folate intake and hyperhomocysteinemia (logistic regression), and serum high-density lipoprotein cholesterol and cardiovascular mortality (Cox model).