American Journal of Epidemiology
ª The Author 2010. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of
Public Health. All rights reserved. For permissions, please e-mail: email@example.com.
Vol. 171, No. 5
Advance Access publication:
February 4, 2010
Practice of Epidemiology
Estimating Model-Adjusted Risks, Risk Differences, and Risk Ratios From
Complex Survey Data
Gayle S. Bieler*, G. Gordon Brown, Rick L. Williams, and Donna J. Brogan
* Correspondence to Gayle S. Bieler, RTI International, P.O. Box 12194, Research Triangle Park, NC 27709-2194 (e-mail:
Initially submitted March 31, 2009; accepted for publication December 9, 2009.
There is increasing interest in estimating and drawing inferences about risk or prevalence ratios and differences
instead of odds ratios in the regression setting. Recent publications have shown how the GENMOD procedure in
SAS (SAS Institute Inc., Cary, North Carolina) can be used to estimate these parameters in non-population-based
studies. In this paper, the authors show how model-adjusted risks, risk differences, and risk ratio estimates can be
obtained directly from logistic regression models in the complex sample survey setting to yield population-based
inferences. Complex sample survey designs typically involve some combination of weighting, stratification,
multistage sampling, clustering, and perhaps finite population adjustments. Point estimates of model-adjusted
risks, risk differences, and risk ratios are obtained from average marginal predictions in the fitted logistic regression
model. The model can contain both continuous and categorical covariates, as well as interaction terms. The
authors use the SUDAAN software package (Research Triangle Institute, Research Triangle Park, North Carolina)
to obtain point estimates, standard errors (via linearization or a replication method), confidence intervals, and
P values for the parameters and contrasts of interest. Data from the 2006 National Health Interview Survey are
used to illustrate these concepts.
health surveys; logistic regression; logistic risk; odds ratio; prevalence; risk; risk ratio; survey analysis
Abbreviations: CRN, cost-related nonadherence; NHIS, National Health Interview Survey.
There is increasing interest in the public health community
in estimating and drawing inferences about risk ratios and
risk differences instead of odds ratios in the binary-response
regression setting (e.g., see Greenland (1, 2)). Spiegelman
and Hertzmark (3) have recently shown how the GENMOD
procedure in SAS (SAS Institute Inc., Cary, North Carolina)
can be used to estimate these parameters, using the log-
binomial regression model for the risk ratio and the binomial
regression model for the risk difference. Zou (4) has recom-
mended the modified Poisson model with a Huber (5) robust
variance estimate when maximum likelihood estimation of
(6), noting that there are situations when even the modified
Poisson model can fail to converge, has shown that risk dif-
ferences can instead be reliably estimated via an ordinary
least-squares linear regression model with a binary response
variable and a robust variance estimate. Although there is no
risk of nonconvergencewith Cheung’s modified least-squares
regression method, it has the drawback that estimates of the
are not bounded by 0 and 1.
population-based studies. Complex sample surveys are de-
signed to yield population-based estimates and inferences,
and they typically involve some combination of sample
weighting, stratification, multistage sampling, clustering, and
perhaps finite population adjustments. Many public-use data
files contain information from national public health surveys
Health and Nutrition Examination Survey and the National
Health Interview Survey (NHIS). Special statistical methods
are needed to account for these complex sample designs in
order to obtain unbiased estimates of population parameters,
618Am J Epidemiol 2010;171:618–623
by guest on September 13, 2015
1. 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(4):
2. Greenland S. Interpretation and choice of effect measures in
epidemiologic analyses. Am J Epidemiol. 1987;125(5):
3. Spiegelman D, Hertzmark E. Easy SAS calculations for risk or
4. Zou G. A modified Poisson regression approach to prospective
studies with binary data. Am J Epidemiol. 2004;159(7):
5. Huber PJ. The behavior of maximum likelihood estimates
under non-standard conditions. In: Proceedings of the Fifth
Berkeley Symposium on Mathematical Statistics and Proba-
bility. Vol 1. Berkeley, CA: University of California Press;
6. Cheung YB. A modified least-squares regression approach to
the estimation of risk difference. Am J Epidemiol. 2007;
7. Brogan D. Software for sample survey data: misuse of stan-
dard packages. In: Armitage P, Colton T, eds. Encyclopedia of
Biostatistics. 2nd ed. Chichester, United Kingdom: John Wiley
& Sons Ltd; 2005:5057–5064.
8. Brogan D. Sampling error estimation for survey data. (Chapter
XXI and annex). In: Yansaneh IS, Kalton G, eds. Household
Sample Surveys in Developing and Transition Countries.
(Studies in methods, series F, no. 96). New York, NY: United
Nations; 2005: 447–490. (http://unstats.un.org/unsd/HHsurveys/
Annex_CD-Rom.pdf). (Accessed March 1, 2009).
9. Wolter KM. Introduction to Variance Estimation. 2nd ed. New
York, NY: Springer-Verlag; 2007.
10. Graubard BI, Korn EL. Predictive margins with survey data.
11. Korn E, Graubard B. Analysis of Health Surveys. New York,
NY: John Wiley and Sons, Inc; 1999.
12. National Center for Health Statistics, Centers for Disease
Control and Prevention. National Health Interview Survey
(NHIS). 2006 Data Release [data file and documentation].
Hyattsville, MD: National Center for Health Statistics; 2007.
(Accessed June 11, 2008).
13. Research Triangle Institute. SUDAAN Language Manual,
Release 10.0. Research Triangle Park, NC: Research Triangle
14. Briesacher BA, Gurwitz JH, Soumerai SB. Patients at-risk for
cost-related medication nonadherence: a review of the litera-
ture. J Gen Intern Med. 2007;22(6):864–871.
15. Madden JM, Graves AJ, Zhang F, et al. Cost-related medica-
tion nonadherence and spending on basic needs following
implementation of Medicare Part D. JAMA. 2008;299(16):
16. Piette JD, Heisler M, Krein S, et al. The role of patient-
physician trust in moderating medication nonadherence due to
cost pressures. Arch Intern Med. 2005;165(15):1749–1755.
17. Bambauer KZ, Safran DG, Ross-Degnan D, et al. De-
pression and cost-related medication nonadherence in
Medicare beneficiaries. Arch Gen Psychiatry. 2007;64(5):
18. Piette JD, Heisler M, Wagner TH. Cost-related medication
underuse among chronically ill adults: the treatments people
forgo, how often, and who is at risk. Am J Public Health.
19. Soumerai SB, Pierre-Jacques M, Zhang F, et al. Cost-related
medication nonadherence among elderly and disabled
Medicare beneficiaries: a national survey 1 year before the
Medicare drug benefit. Arch Intern Med. 2006;166(17):
Risk Ratios and Differences With Survey Data623
Am J Epidemiol 2010;171:618–623
by guest on September 13, 2015