A simulation study of regression approaches for estimating risk ratios in the presence of multiple confounders

Risk ratio is a popular effect measure in epidemiological research. Although previous research has suggested that logistic regression may provide biased odds ratio estimates when the number of events is small and there are multiple confounders, the performance of risk ratio estimation has yet to be examined in the presence of multiple confounders.

We conducted a simulation study to evaluate the statistical performance of three regression approaches for estimating risk ratios: (1) risk ratio interpretation of logistic regression coefficients, (2) modified Poisson regression, and (3) regression standardization using logistic regression. We simulated 270 scenarios with systematically varied sample size, the number of binary confounders, exposure proportion, risk ratio, and outcome proportion. Performance evaluation was based on convergence proportion, bias, standard error estimation, and confidence interval coverage.

With a sample size of 2500 and an outcome proportion of 1%, both logistic regression and modified Poisson regression at times failed to converge, and the three approaches were comparably biased. As the outcome proportion or sample size increased, modified Poisson regression and regression standardization yielded unbiased risk ratio estimates with appropriate confidence intervals irrespective of the number of confounders. The risk ratio interpretation of logistic regression coefficients, by contrast, became substantially biased as the outcome proportion increased.

Regression approaches for estimating risk ratios should be cautiously used when the number of events is small. With an adequate number of events, risk ratios are validly estimated by modified Poisson regression and regression standardization, irrespective of the number of confounders.