SUGI 28: Estimation of Prevalence Ratios When PROC GENMOD Does Not Converge

When studying a prevalent outcome, it is often of interest to estimate the prevalence ratio instead of the odds ratio. In SAS one can use PROC GENMOD with the binomial distribution and the log link function. Unlike the logistic model, the log-binomial model places restrictions on the parameter space, and the maximum likelihood estimate (MLE) might occur on the boundary of the parameter space, in which case PROC GENMOD will not converge to the correct estimate. We propose a method that uses PROC GENMOD to correctly estimate the MLE. The method consists of expanding the original data set to include a large number of copies of the original data set together with one copy of the original data set with cases and controls reversed. The estimated standard error of the prevalence ratio on the expanded data set is then "adjusted" to obtain the correct estimate of the standard error of the prevalence ratio. We provide a SAS MACRO to implement our new method. In addition we present an exact method for the one independent variable setting. We also provide a SAS MACRO to implement this exact method. The new approximation method yielded estimates which were close to the exact maximum likelihood estimates and to the true parameters. By comparison, the Cox proportional hazard approach did not perform nearly as well as the new method. The exact method can be used easily with single independent variable models, while the approximation method can be used with either single or multiple independent variable models.