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American Journal of Epidemiology Advance Access originally published online on September 12, 2007
American Journal of Epidemiology 2007 166(11):1337-1344; doi:10.1093/aje/kwm223
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American Journal of Epidemiology © The Author 2007. Published by the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

ORIGINAL CONTRIBUTIONS

A Modified Least-Squares Regression Approach to the Estimation of Risk Difference

Yin Bun Cheung

From the MRC Tropical Epidemiology Group, Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, London, United Kingdom

Correspondence to Dr. Yin Bun Cheung, Department of Epidemiology and Population Health, London School of Hygiene and Tropical Medicine, Keppel Street, London WC1E 7HT, United Kingdom (e-mail: cheungyb{at}graduate.hku.hk).

Received for publication December 11, 2006. Accepted for publication July 6, 2007.

Risk ratio and risk difference are parameters of interest in many medical studies. The risk ratio has a property that the value for the outcome Y = 0 is not the inverse of the risk ratio for the outcome Y = 1. This property makes risk ratios inappropriate in some situations. Estimation of risk difference often encounters the problem that the binomial regression model fails to converge. Recently discussed alternatives may have the same problem of nonconvergence or are difficult to implement. Here the author proposes a modified least-squares regression approach— unweighted least-squares regression with a Huber-White robust standard error—for estimation of risk differences. Four versions of the robust standard error are considered. The binomial, ordinary least-squares, and modified least-squares estimators are compared analytically in a simple situation of one exposure variable. Multivariable regression analyses are simulated to demonstrate the usefulness of the approach. For sample sizes of approximately 200 or less, a small-sample version of the robust standard error is recommended. The method is illustrated with data from a patient survey in which the binomial regression fails to converge in the analyses of four out of five outcome variables.

binomial model; least-squares analysis; regression analysis; risk; robustness; variance-covariance matrix; variance heterogeneity

Abbreviations: ECOG, Eastern Cooperative Oncology Group; EQ-5D, EuroQol 5-Dimension; MLE, maximum likelihood estimation; MLS, modified least-squares; OLS, ordinary least-squares


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