American Journal of Epidemiology Advance Access originally published online on June 29, 2005
American Journal of Epidemiology 2005 162(3):199-200; doi:10.1093/aje/kwi188
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INVITED EDITORIAL NOTE |
Easy SAS Calculations for Risk or Prevalence Ratios and Differences
American Journal of Epidemiology Departments of Epidemiology and Biostatistics Harvard School of Public Health Boston, MA 02115
Department of Epidemiology Harvard School of Public Health Boston, MA 02115
We would like to make the readership aware that risk or prevalence ratios and differences, when they are the parameter of interest, can be directly calculated by using SAS software (SAS Institute, Inc., Cary, North Carolina). There is no longer any good justification for fitting logistic regression models and estimating odds ratios when the odds ratio is not a good approximation of the risk or prevalence ratio. Instead, SAS PROC GENMOD's log-binomial regression (1
) capability can be used for estimation and inference about the parameter of interest. Here is an example of the code required to analyze the breast cancer survival data discussed by Greenland (2):
- proc genmod descending;
- model death=receptor stage2 stage3/dist=bin link=log;
- estimate ‘RR receptor low vs. high’ receptor 1/exp;
- estimate ‘RR stage2 vs stage1’ stage2 1/exp;
- estimate ‘RR stage 3 vs stage1’ stage3 1/exp;
- model death=receptor stage2 stage3/dist=bin link=log;
There are times when the log-binomial model fails to converge. It is well known that the log-binomial model is less numerically stable than the logistic model. When this is the case, the analyst may use SAS PROC GENMOD's Poisson regression capability with the robust variance (3, 4), as follows:
- proc genmod;
- class id;
- model death=receptor stage2 stage3/dist=poisson link=log;
- repeated subject=id/type=ind;
- estimate ‘RR receptor low vs. high’ receptor 1/exp;
- estimate ‘RR stage2 vs stage1’ stage2 1/exp;
- estimate ‘RR stage 3 vs stage1’ stage3 1/exp;
- class id;
By replacing link=log with link=identity in the MODEL statement, multivariate-adjusted risk (prevalence) differences are obtained as follows:
- proc genmod descending;
- model death=receptor stage2 stage3/dist=bin link=identity;
- model death=receptor stage2 stage3/dist=bin link=identity;
- proc genmod;
- class id;
- model death=receptor stage2 stage3/dist=poisson link=identity;
- repeated subject=id/type=ind;
- class id;
A well-documented, user-friendly SAS macro, %RELRISK8, has been developed that automates this computational and analytic approach. The modified Poisson estimates are used to start the iterations to obtain the log-binomial maximum likelihood estimates. These are the final estimates if convergence of the binomial likelihood is not obtained. The macro can be downloaded from the first author's website (http://www.hsph.harvard.edu/faculty/spiegelman/relrisk8.html).
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ACKNOWLEDGMENTS |
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Conflict of interest: none declared.
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References |
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 TOP References |
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- Wacholder S. Binomial regression in GLIM: estimating risk ratios and risk differences. Am J Epidemiol 1986;123:174–84.
[Abstract/Free Full Text] - Greenland S. Model-based estimation of relative risks and other epidemiologic measures in studies of common outcomes and in case-control studies. Am J Epidemiol 2004;160:301–5.
[Abstract/Free Full Text] - Huber PJ. The behavior of maximum likelihood estimates under non-standard conditions. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Vol 1. Berkeley, CA: University of California Press, 1967:221–33.
- Zou G. A modified Poisson regression approach to prospective studies with binary data. Am J Epidemiol 2004;159:702–6.
[Abstract/Free Full Text]
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T. Neogi and Y. Zhang Re: "easy sas calculations for risk or prevalence ratios and differences". Am. J. Epidemiol., June 15, 2006; 163(12): 1157 - 1157. [Full Text] [PDF]
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M. R. Petersen and J. A. Deddens Re: "easy sas calculations for risk or prevalence ratios and differences". Am. J. Epidemiol., June 15, 2006; 163(12): 1158 - 1159. [Full Text] [PDF]
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D. Spiegelman and E. Hertzmark THE AUTHORS REPLY Am. J. Epidemiol., June 15, 2006; 163(12): 1159 - 1161. [Full Text] [PDF]
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L. Tian and K. Liu Re: "easy sas calculations for risk or prevalence ratios and differences". Am. J. Epidemiol., June 15, 2006; 163(12): 1157 - 1158. [Full Text] [PDF]
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