Estimating relative risks for common outcome using PROC NLP

In cross-sectional or cohort studies with binary outcomes, it is biologically interpretable and of interest to estimate the relative risk or prevalence ratio, especially when the response rates are not rare. Several methods have been used to estimate the relative risk, among which the log-binomial models yield the maximum likelihood estimate (MLE) of the parameters. Because of restrictions on the parameter space, the log-binomial models often run into convergence problems. Some remedies, e.g., the Poisson and Cox regressions, have been proposed. However, these methods may give out-of-bound predicted response probabilities. In this paper, a new computation method using the SAS Nonlinear Programming (NLP) procedure is proposed to find the MLEs. The proposed NLP method was compared to the COPY method, a modified method to fit the log-binomial model. Issues in the implementation are discussed. For illustration, both methods were applied to data on the prevalence of microalbuminuria (micro-protein leakage into urine) for kidney disease patients from the Diabetes Control and Complications Trial. The sample SAS macro for calculating relative risk is provided in the appendix.