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Abstract
Background: It is known that the consequence of adjusting for balanced covariates in logistic regression is on one hand a loss of precision but on the other hand an increased efficiency in testing for a treatment effect. The reason for the latter is that the downward bias induced by omitting the covariate is avoided. However, these results are based upon investigations of the regression coefficients and the corresponding odds ratios (ORs). Objectives: This study investigates the effect of adjusting for balanced covariates in logistic regression when the risk difference (RD) and its inverse, the number needed to treat (NNT), are used as effect measures. Methods: RDs and NNTs with adjustment for covariates are estimated by using an adaptation of the average risk difference (ARD) approach (Stat. Med. 2007, 26: 5586-5595). Precision and relative bias of the estimates and coverage probabilities of the corresponding confidence intervals are investigated by means of a simulation study. Results: In contrast to the results for ORs, estimation of RDs and NNTs with adjustment for balanced covariates does not lead to a loss of precision. The standard errors of the adjusted estimates are reduced by about 20% if the covariate has a strong effect and large variance. Thus, the adjustment leads to a gain in precision. No relevant bias and coverage probabilities close to the nominal level were found for both the crude and the adjusted estimation of RDs. Conclusions: In addition to increased power for testing treatment effects, an adjustment for balanced covariates leads to reduced standard errors and shorter confidence intervals if the treatment effect is presented in terms of RDs and NNTs. In meta-analyses of clinical trials, in which the application of an absolute effect measure is appropriate, it is preferable to use adjusted risk differences to estimate the pooled treatment effect.