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

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.