Estimating adjusted NNTs in randomised controlled trials with binary outcomes: A simulation study

The number needed to treat (NNT) is a popular measure to describe the absolute effect of a new treatment compared with a standard treatment or placebo in randomised controlled trials (RCTs) with binary outcome. For applications in epidemiology, the average risk difference (ARD) approach based upon logistic regression was proposed to estimate NNT measures with adjustment for covariates. In the context of cohort studies, averaging is performed separately over the unexposed and the exposed persons to account for possible different exposure effects in the two groups or over the entire sample. In this paper, we apply the ARD approach to estimate adjusted NNTs in RCT settings with balanced covariates where it is adequate to average over the whole sample. It is known that the consequence of adjusting for balanced covariates in logistic regression is on one hand a loss of precision and on the other hand an increased efficiency in testing for treatment effects. However, these results are based upon the investigation of regression coefficients and corresponding odds ratios. By means of simulations we show that the estimation of risk differences and NNTs with adjustment for balanced covariates leads to a gain in precision. A considerable gain in precision is obtained in the case of strong covariate predictors with large variance. Therefore, it is preferable to adjust for balanced covariates in RCTs when the treatment effect is expressed in terms of risk differences and NNTs and the covariate represents a strong predictor.