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st: Binomial Regression


From   Jay Kaufman <Jay_Kaufman@unc.edu>
To   Stata <statalist@hsphsun2.harvard.edu>
Subject   st: Binomial Regression
Date   Wed, 08 Aug 2007 09:33:20 -0400

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
-----------------------------

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