st: Binomial Regression

[Jay Kaufman <Jay_Kaufman@unc.edu>]

Apropos the recent discussion on this list, this article was just
published in The Journal of Clinical Epidemiology.  It contains an
appendix with Stata code for running the proposed model based on
"marginal standardization".  Unlike Stata routines like -mfx-, this
does not require fixing covariates to a single value in order to
obtain the risk ratio from logistic regression, and this is perhaps
the intended advantage.  - JK

Journal of Clinical Epidemiology
Volume 60, Issue 9, September 2007, Pages 874-882 	

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

A. Russell Localio a, David J. Margolis b, c and Jesse A. Berlin d
a Division of Biostatistics, Department of Biostatistics and Epidemiology, Center for Clinical 
Epidemiology and Biostatistics, Centers for Education and Research on Therapeutics, University of 
Pennsylvania School of Medicine, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA
b Division of Epidemiology, Department of Biostatistics and Epidemiology, Center for Clinical 
Epidemiology and Biostatistics, Centers for Education and Research on Therapeutics, University of 
Pennsylvania School of Medicine, 423 Guardian Drive, Philadelphia, PA 19104-6021, USA
c Department of Dermatology, University of Pennsylvania School of Medicine, 423 Guardian Drive, 
Philadelphia, PA 19104-6021, USA
d Statistical Science, Biometrics and Clinical Informatics (BCI), J&J Pharmaceutical Research and 
Development, LLC, 1125 Trenton-Harbourton Road, P.O. Box 200, Titusville, NJ 08560, USA

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.

Keywords: Logistic regression; Relative risk; Bootstrap; Simulations; Standardization; Odds ratio

--
Jay S. Kaufman, Ph.D
Associate Professor
-----------------------------
email: Jay_Kaufman@unc.edu
-----------------------------
Department of Epidemiology
UNC School of Public Health
2104C McGavran-Greenberg Hall
Pittsboro Street, CB#7435
Chapel Hill, NC 27599-7435
phone:  919-966-7435
fax:    919-966-2089
-----------------------------

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/