Systematic analysis of the number needed to treat

Abstract

The number needed to treat is often used to measure the efficacy of a binary outcome in randomized clinical trials. There are three different available measures of the number needed to treat. Two of these measures, Furukawa and Leucht’s and Kraemer and Kupfer’s, focus on converting Cohen’s δ index into the number needed to treat, while Laupacis et al.’s measure deals primarily with the number needed to treat’s estimation rather than with a reformulation. Mathematical and numerical analysis of numbers needed to treat and their estimators was conducted. Three novel number needed to treat estimators were introduced to supplement the numbers needed to treat introduced by Laupacis, Furukawa and Leucht, and Kraemer and Kupfer. The analysis showed that Laupacis et al.’s number needed to treat is intrinsically different from Kraemer and Kupfer’s number needed to treat, and that Furukawa and Leucht’s estimator is appropriate to use only for normally distributed outcomes with equal standard deviations. Based on the numerical analysis, the novel numbers needed to treat outperformed the existing ones under correct model specifications. Asymptotic analysis was used to test three different types of confidence intervals to supplement the numbers needed to treat. An R-package to calculate these numbers needed to treat and their confidence intervals has been developed and made available for users online.

Preventive small-quantity lipid-based nutrient supplements reduce severe wasting and severe stunting among young children: an individual participant data meta-analysis of randomized controlled trials

“…For descriptive purposes, we calculated the number needed to avert a single case of severe wasting ("number needed to treat", NNT) following the standard approach (41). The equation requires an assumed population prevalence of severe wasting among the untreated, and then the prevalence of severe wasting among the treated is estimated as the prevalence among the untreated multiplied by the prevalence ratio reduction for severe wasting.…”

The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application

“…A comprehensive review of the NNT's statistical limitations can be found in Hutton 10 . Recently Vancak et al 14 resolved the pitfall of singularity at 0 by introducing a modification to the original definition of the NNT. The modified NNT is $$$$ NNT\equiv g\left({p}_s\right)=\left\{\begin{array}{cc}1/{p}_s,& {p}_s>0,\\ {}\infty, & {p}_s\le 0.\end{array}\right.$$…”

“…Dichotomization often relies on the definition of the minimal clinically important difference (MCID) 19 that is denoted by $$$ \tau $$$. Therefore, for nondichotomous outcomes, without loss of generality, we define the beneficial outcome as $$$ I=I\left\{Y>\tau \right\} $$$, where $$$ I=1 $$$ if the beneficial outcome occurs, and 0 otherwise 14 . Fourth, the NNT does not account for time‐dependent outcomes and thus can be misleading 11,12 .…”

“…A comprehensive review of the NNT's statistical limitations can be found in Hutton. 10 Recently Vancak et al 14 resolved the pitfall of singularity at 0 by introducing a modification to the original definition of the NNT. The modified NNT is…”

“…Therefore, for nondichotomous outcomes, without loss of generality, we define the beneficial outcome as I = I{Y > 𝜏}, where I = 1 if the beneficial outcome occurs, and 0 otherwise. 14 Fourth, the NNT does not account for time-dependent outcomes and thus can be misleading. 11,12 Fifth, the interpretation and the definition of the NNT are debatable since different clinical scenarios may result in the same NNT.…”