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

In cross-sectional studies, to quantify the association between a risk factor and a disease (possibly adjusted for confounders), in the framework of the multiplicative model, the more obvious effect measure is a prevalence rate ratio with an associated confidence interval. The validity of this confidence interval requires an unbiased estimator and an appropriate estimate of the variance. In numerous epidemiological studies however, routine use is made of odds ratios and logistic regression. As the odds ratio per se is difficult to understand, prevalence odds ratios are often interpreted as prevalence rate ratios. But this latter approximation is valid only under the rare disease assumption. Moreover, in the logistic regression model, the variance of the estimates is based on the assumption of binomial variability, which is not always supported by the data; in the frequent case of overdispersion, this leads to under-estimation of the type I error rate. Yet, within 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 appropriate to directly estimate adjusted prevalence rate ratios. In case of overdispersion, 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 valid reasons for the systematic choice of odds ratio and of the logistic regression model to estimate prevalence rate ratios, unless the type of study imperatively requires their use.