A simple method for estimating relative risk using logistic regression

Abstract

Background: Odds ratios (OR) significantly overestimate associations between risk factors and common outcomes. The estimation of relative risks (RR) or prevalence ratios (PR) has represented a statistical challenge in multivariate analysis and, furthermore, some researchers do not have access to the available methods.

Objective: To propose and evaluate a new method for estimating RR and PR by logistic regression.

Methods: 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.

Results: 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.

Conclusion: 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.

Figure 1

Inflation Factor of Standard Error (SE) for each predictor according to incidence of outcome.