Abstract
Risk differences and associated confidence intervals are frequently the basis for statistical testing in clinical trials. The analysis is often complicated by the presence of measured baseline covariates related to response that may be used to improve the precision of the treatment comparison by covariate adjustment in the statistical analysis. We use a clinical trial example and supporting simulations to show that logistic regression can be used to estimate the risk difference and compare its performance to common weighted-difference methods. We also examine when a useful improvement in precision can result from covariate adjustment, the use of a continuous rather than categorized covariate, and the consequences of including an unpredictive covariate.
Similar content being viewed by others
References
Greenland S, Holland P. Estimating standardized risk differences from odds ratios. Biometrics. 1991;47:319–322.
O’Gorman T, Woolson R, Jones M. A comparison of two methods of estimating a common risk difference in a stratified analysis of a multicenter clinical trial. Control Clin Trials. 1994;15:135–153.
Lipsitz S, Laird N, Molenberghs G. Tests for homogeneity of the risk difference when data are sparse. Biometrics. 1998;54:148–160.
Kim B, Carter R, Rao P, Ariet M, Resnick M. Standardized risk and description of results from multivariable modeling of a binary response. Biometric J. 2006;48:54–66.
Grizzle J. A note on stratifying versus complete random assignment in clinical trials. Control Clin Trials. 1982;3:365–368.
Agresti A. Categorical Data Analysis. New York: Wiley; 1990.
Radhakrishna S. Combination of results from several 2 × 2 contingency tables. Biometrics. 1965;21:86–98.
Robins J, Breslow N, Greenland S. Estimators of the Mantel-Haenszel variance consistent in both sparse data and large-strata limiting models. Biometrics. 1986;42:311–323.
Sato T. On the variance estimator for the Mantel-Haenszel risk difference. Biometrics. 1989;45: 1323–1324.
Greenland S, Robins J. Estimation of a common effect parameter from sparse follow-up data. Biometrics. 1985;41:55–68.
Mehrotra D, Railkar R. Minimum risk weights for comparing treatments in stratified binomial trials. Stat Med. 2000;19:811–825.
Grizzle J, Starmer C, Koch G. Analysis of categorical data by linear models. Biometrics. 1969;35: 817–819.
Boehning D, Sarol J. Estimating risk difference in multicenter studies under baseline-risk heterogeneity. Biometrics. 2000;56:304–308.
Kuhnert R, Böhning D. The failure of meta-analytic asymptotics for the seemingly efficient estimator of the common risk difference. Stat Papers. 2005;46:541–554.
Flanders WD, Rhodes PH. Large sample confidence intervals for regression standardized risks, risk ratios, and risk differences. J Chron Dis. 1987; 40:697–704.
Freedman D. Randomization does not justify logistic regression. Stat Sci. 2008;23:237–249.
Lane P, Nelder J. Analysis of covariance and standardization as instances of prediction. Biometrics. 1982;38:613–621.
Greenland S. Estimating standardized parameters from generalized linear models. Stat Med. 1991;10:1069–1074.
Gulick RM, Lalezari J, Goodrich J, et al. Maraviroc for previously treated patients with R5 HIV-1 infection. N Engl J Med. 2008;359:1429–1441.
Hézode C, Forestier N, Dusheiko G, et al. Telaprevir and peginterferon with or without ribavirin for chronic HCV infection. N Engl J Med. 2009;360:1839–1850.
Hoeffding W. On the distribution of the number of successes in independent trials. Ann Math Stat. 1956;27:713–721.
Robinson LD, Jewell NP. Some surprising results about covariate adjustment in logistic regression models. Int Stat Rev. 1991;58:227–240.
Fleiss J. The Design and Analysis of Clinical Experiments. New York: Wiley; 1986.
Cochran W. Some methods for strengthening the common chi-squared tests. Biometrics. 1954;10: 417–451.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ge, M., Durham, L.K., Meyer, R.D. et al. Covariate-Adjusted Difference in Proportions from Clinical Trials Using Logistic Regression and Weighted Risk Differences. Ther Innov Regul Sci 45, 481–493 (2011). https://doi.org/10.1177/009286151104500409
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1177/009286151104500409