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arXiv · 2504.16912

Definition, Identification, and Estimation of the Direct and Indirect Number Needed to Treat

Valentin Vancak·Arvid Sjölander
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Abstract

The number needed to treat (NNT) is an efficacy and effect size measure commonly used in epidemiological studies and meta-analyses. The NNT was originally defined as the average number of patients needed to be treated to observe one less adverse effect. In this study, we introduce the novel direct and indirect number needed to treat (DNNT and INNT, respectively). The DNNT and the INNT are efficacy measures defined as the average number of patients that needed to be treated to benefit from the treatment's direct and indirect effects, respectively. We start by formally defining these measures using nested potential outcomes. Next, we formulate the conditions for the identification of the DNNT and INNT, as well as for the direct and indirect number needed to expose (DNNE and INNE, respectively) and the direct and indirect exposure impact number (DEIN and IEIN, respectively) in observational studies. Next, we present an estimation method with two analytical examples. A corresponding simulation study follows the examples. The simulation study illustrates that the estimators of the novel indices are consistent, and their analytical confidence intervals meet the nominal coverage rates.

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Valentin Vancak, Arvid Sjölander. 2025-04-23. Definition, Identification, and Estimation of the Direct and Indirect Number Needed to Treat. https://doi.org/10.1515/em-2025-0018

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