Logistic regression vs other generalized linear models to estimate prevalence rate ratios

In cross-sectional studies, to quantify the association between a risk fact or and a disease (possibly adjusted for confounders), in the framework of r ite multiplicative model, the more obvious effect measure is a prevalence r ate ratio with an associated confidence interval. The validity of this conf idence interval requires an unbiased estimator and an appropriate estimate of the variance. In numerous epidemiological studies however, routine use i s made of odds ratios and logistic regression. As the odds ratio per se is difficult to understand prevalence odds ratios are often interpreted as pre valence rate ratios. But this latter approximation is valid only under the rare disease assumption. Moreover, in the logistic regression model, the va riance of the estimates is based on the assumption of binomial variability, which is not always supported by the data, in the frequent case of overdis persion, this leads to under-estimation of the type I error rate. Yet, with in the generalized linear model, it is easy to choose a link function other than the logit. For example, the log link (log-binomial model) is appropri ate to directly estimate adjusted prevalence rate ratios. In case of overdi spersion, it is also possible to achieve a better fit of the model, either by choosing another distribution in the exponential family or by estimating a dispersion parameter for the binomial distribution. Thus, there are no v alid reasons for the systematic choice of odds ratio and of the logistic re gression model to estimate prevalence rate ratios, unless the type of study imperatively requires their use.