Estimating adjusted risk difference (RD) and number needed to treat (NNT) measures in the Cox regression model

Abstract

In medical research, risk difference (RD) and number needed to treat (NNT) measures for survival times have been mainly proposed without consideration of covariates. In this paper, we develop adjusted RD and NNT measures for use in observational studies with survival time outcomes within the framework of the Cox proportional hazards regression model taking the distribution of confounders into account. We consider the typical situation of a cohort study in which the effect of an exposure on a survival time outcome is investigated and important covariates have to be taken into account. The exposure effect described by means of the RD and NNT measures in dependence on whether the effect of allocating an exposure to unexposed persons (number needed to be exposed) or that of removing an exposure from exposed persons (exposure impact number) is considered. Estimation of these adjusted RD and NNT measures is performed by using the average RD approach recently developed for logistic regression. To determine standard errors and confidence intervals for these estimators we use two approaches, the delta method with respect to the regression coefficients of the Cox model and bootstrapping and compare each other. The performance of these estimators is assessed by performing Monte Carlo simulations demonstrating clear advantages of the bootstrap method. The proposed method for point and interval estimation of adjusted RD and NNT measures in the Cox model is illustrated by means of data of the Düsseldorf Obesity Mortality Study (DOMS).