The use of an adjusted odds ratio to estimate an adjusted relative risk or prevalence ratio is appropriate for studies of rare outcome but may be misleading when the outcome is common. Such overestimation may inappropriately affect clinical decision-making or policy development [3
]. For example, overestimation of the importance of a risk factor may lead to unintentional errors in the economical analysis of potential intervention programs or treatment, which could be particularly harmful in developing countries.
The ordinary logistic model estimates OR (not RR) and was initially adapted for case-control studies since data from this type of study design can only determine OR [12
]. Moreover, a case-control study is an optimal choice for analyzing rare-event risk factors, for which OR is a close approximation of RR. Thus, ordinary logistic regression is eminently useful for case- control studies mainly because the numeric value of OR mimics RR [12
On the other hand, RR and PR can be directly determined from data based on cohort and cross-sectional studies, respectively, which are practical only for relatively common outcomes. However, in such circumstances OR estimated by ordinary logistic regression will be more discrepant than RR (or PR). This was exemplified in the results of this paper in that ORs progressively overestimated RRs as the outcome frequency increased.
Indeed, OR will always be greater than RR if RR is greater than 1 (adverse event) and OR will also be less than RR if RR less than 1 (protective effect). Therefore, the uncritical application of logistic regression and the misinterpretation of OR as RR can lead to serious errors in determination of both the importance of risk factors and the impact of interventions on clinical practice and public health [13
For these reasons, several strategies for estimating RRs in multivariate analysis have been proposed [7
]. Binomial regression is considered the most adequate choice. However, binomial models often predict probabilities greater than one
and sometimes this regression cannot find possible values and converge in a model. Consequently, other alternative methods have been proposed when binomial regression cannot converge in a model. Cox regression with robust variance using a constant in the time variable seems like a good alternative [7
]. However, these options and other statistical alternatives are only available in sophisticated software that some research groups cannot afford.
This paper presents a strategy for logistic regression that recognizes an entire cohort as controls. As the results show, this method can appropriately estimate RRs or PRs, even in analyses with common outcomes. Moreover, the method proposed in this article could be easily performed using free statistics programs that include only logistic regression for multivariate analysis of dichotomous outcomes.
However, the proposed method is associated with SE inflation, which increases confidence intervals. A simple and practical correction factor cannot be established for this problem because, in a multivariate regression, the standard error for each predictor depends on its correlation with all variables included in the model.
Therefore, since the obtained CIs can be wider than those estimated by other models, investigators must be aware that the risk of Type II error could be higher. For this reason, when an association is not statistically significant with the proposed method, ordinary logistic regression could be used for testing the hypothesis that association measure is different than unity. This is possible since the null hypothesis is mathematically equivalent for both OR and RR, because when RR is equal to 1, OR is also equal to 1.