Relative risks and confidence intervals were easily computed indirectly from multivariable logistic regression.
OBJECTIVE
To assess alternative statistical methods for estimating relative risks and their confidence intervals from multivariable binary regression when outcomes are common.


METHODS
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.


CONCLUSIONS
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.
Localio
A Russell
AR
Division of Biostatistics, Department of Biostatistics and Epidemiology, Center for Clinical Epidemiology and Biostatistics, University of Pennsylvania School of Medicine, Philadelphia, PA 19104-6021, USA. rlocalio@mail.med.upenn.edu
Margolis
David J
DJ
Berlin
Jesse A
JA
D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D006801:Humans; D016015:Logistic Models; D015999:Multivariate Analysis; D016017:Odds Ratio; D016032:Randomized Controlled Trials as Topic; D018570:Risk Assessment / Q000379:methods*; D012984:Software