Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression

Abstract

Objective: To assess alternative statistical methods for estimating relative risks and their confidence intervals from multivariable binary regression when outcomes are common.

Study design and setting: We performed simulations on two hypothetical groups of patients in a single-center study, either randomized or cohort, and reanalyzed a published observational study. Outcomes of interest were the bias of relative risk estimates, coverage of 95% confidence intervals, and the Akaike information criterion.

Results: According to simulations, a commonly used method of computing confidence intervals for relative risk substantially overstates statistical significance in typical applications when outcomes are common. Generalized linear models other than logistic regression sometimes failed to converge, or produced estimated risks that exceeded 1.0. Conditional or marginal standardization using logistic regression and bootstrap resampling estimated risks within the [0,1] bounds and relative risks with appropriate confidence intervals.

Conclusion: Especially when outcomes are common, relative risks and confidence intervals are easily computed indirectly from multivariable logistic regression. Log-linear regression models, by contrast, are problematic when outcomes are common.