Re: "Easy SAS calculations for risk or prevalence ratios and differences".

We applaud Drs. Spiegelman and Hertzmark’s idea of using SAS procedure PROC GENMOD to estimate the risk ratio or difference (1). However, we have reservations about 1) the claim that there is no good justification for fitting the logistic regression and estimating the odds ratio when the odds ratio is not a good approximation of the risk ratio, and 2) using Poisson regression (PROC GENMOD) to estimate the risk ratio when the log-binomial model fails to converge. In our opinion, the choice of models (e.g., logistic vs. logbinomial regression) is dictated by the data; that is, only that model supported by the data should be used. In this regard, the popularity of the logistic regression model lies in its ability to fit a wide range of data well, rather than the fact that the odds ratio sometimes is an approximation of the risk ratio. In addition, the odds ratio given by the logistic regression model is a good summary of the association in its own right. Furthermore, the failure of convergence in the log-binomial regression is not only a numerical problem but also an indication that the data do not support the model. We use a simple example from Hosmer and Lemeshow (2) to illustrate our point. The data set consists of 100 participants aged 20–69 years and their coronary heart disease status (presence vs. absence). The goal is to study the relation between the prevalence of coronary heart disease and age. Since the average prevalence in the cohort was 43 percent, the risk ratio and odds ratio were not similar. The simple log-binomial model fails to converge. If we use Poisson regression to estimate the risk ratio (prevalence ratio) in the log-binomial model, the estimated risk ratio for a 10year increase is 1.72. As shown in figure 1, we compared the resulting model-based prevalence of coronary heart disease with its nonparametric counterpart, estimated from a model assuming only that the prevalence varies smoothly with age. Since nonparametric fitting requires no specific parametric model, the estimated prevalence may serve as the ‘‘true’’ prevalence. The prevalence estimated by the log-binomial model approximates the ‘‘true’’ prevalence well for age 60 years but poorly for age >60 years (figure 1). For eight participants older than age 60 years, the average prevalence estimated by using the log-binomial model is 102 percent (meaningless); the observed prevalence is 87.5 percent. In this case, the log-binomial regression model fails to converge because of poor fitting of the data. By forcing