Article Abstract

Estimate risk difference and number needed to treat in survival analysis

Authors: Zhongheng Zhang, Federico Ambrogi, Alex F. Bokov, Hongqiu Gu, Edwin de Beurs, Khaled Eskaf


The hazard ratio (HR) is a measure of instantaneous relative risk of an increase in one unit of the covariate of interest, which is widely reported in clinical researches involving time-to-event data. However, the measure fails to capture absolute risk reduction. Other measures such as number needed to treat (NNT) and risk difference (RD) provide another perspective on the effectiveness of an intervention, and can facilitate clinical decision making. The article aims to provide a step-by-step tutorial on how to compute RD and NNT in survival analysis with R. For simplicity, only one measure (RD or NNT) needs to be illustrated, because the other measure is a reverse of the illustrated one (NNT=1/RD). An artificial dataset is composed by using the survsim package. RD and NNT are estimated with Austin method after fitting a Cox-proportional hazard regression model. The confidence intervals can be estimated using bootstrap method. Alternatively, if the standard errors (SEs) of the survival probabilities of the treated and control group are given, confidence intervals can be estimated using algebraic calculations. The pseudo-value model provides another method to estimate RD and NNT. Details of R code and its output are shown and explained in the main text.