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The Risk of Determining Risk with Multivariable Models

John Concato, MD, MS, MPH; Alvan R. Feinstein, MD, MS; and Theodore R. Holford, PhD
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From Yale University School of Medicine, New Haven, Connecticut. Requests for Reprints: John Concato, MD, Medical Service/111, West Haven Veterans Affairs Medical Center, 950 Campbell Avenue, West Haven, CT 06516. Grant Support: Dr. Concato was a Postdoctoral Fellow in the Robert Wood Johnson Clinical Scholars Program, supported by the Department of Veterans Affairs, when this study was conducted.

Copyright ©2004 by the American College of Physicians

Ann Intern Med. 1993;118(3):201-210. doi:10.7326/0003-4819-118-3-199302010-00009
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Purpose: To review the principles of multivariable analysis and to examine the application of multivariable statistical methods in general medical literature.

Data Sources: A computer-assisted search of articles in The Lancet and The New England Journal of Medicine identified 451 publications containing multivariable methods from 1985 through 1989. A random sample of 60 articles that used the two most common methods—logistic regression or proportional hazards analysis—was selected for more intensive review.

Data Extraction: During review of the 60 randomly selected articles, the focus was on generally accepted methodologic guidelines that can prevent problems affecting the accuracy and interpretation of multivariable analytic results.

Results: From 1985 to 1989, the relative frequency of multivariable statistical methods increased annually from about 10% to 18% among all articles in the two journals. In 44 (73%) of 60 articles using logistic or proportional hazards regression, risk estimates were quantified for individual variables (“risk factors”). Violations and omissions of methodologic guidelines in these 44 articles included overfitting of data; no test of conformity of variables to a linear gradient; no mention of pertinent checks for proportional hazards; no report of testing for interactions between independent variables; and unspecified coding or selection of independent variables. These problems would make the reported results potentially inaccurate, misleading, or difficult to interpret.

Conclusions: The findings suggest a need for improvement in the reporting and perhaps conducting of multivariable analyses in medical research.


Grahic Jump Location
Figure 1.
Nonproportional “hazards”.

Crossing of survival curves for groups A and B, violating the assumption of proportional hazards.

Grahic Jump Location




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