A simple method for estimating relative risk using logistic regression

A provisional database was designed in which events were duplicated but identified as non-events. After, a logistic regression was performed and effect measures were calculated, which were considered RR estimations. This method was compared with binomial regression, Cox regression with robust variance and ordinary logistic regression in analyses with three outcomes of different frequencies.ORs estimated by ordinary logistic regression progressively overestimated RRs as the outcome frequency increased. RRs estimated by Cox regression and the method proposed in this article were similar to those estimated by binomial regression for every outcome. However, confidence intervals were wider with the proposed method.This simple tool could be useful for calculating the effect of risk factors and the impact of health interventions in developing countries when other statistical strategies are not available.The odds ratio (OR) is commonly used to assess associations between exposure and outcome and can be estimated by logistic regression, which is widely available in statistics software. OR has been considered an approximation to the prevalence ratio (PR) in cross-sectional studies or the risk ratio (RR, which is mathematically equivalent to PR) in cohort studies or clinical trials. This is acceptable when the outcome is relatively rare (< 10%). However, since many health outcomes are common, the interpretation of OR as RR is questionable because OR overstates RR, sometimes dramatically [1-3]. Moreover, the OR has been considered an "unintelligible" effect measure in some contexts [3].Binomial regression has been recommended for the estimation of RRs (and PRs) in multivariate analysis [4]. However, sometimes this statistical method cannot estimate RR because convergence problems are frequent. Therefore, the Cox regression with robust variance has been recommended as a suitable method for estimating RRs [5,6].However, these statistical methods (binomial and Cox regression) are