Definition, identification, and estimation of the direct and indirect number needed to treat

Objectives: The number needed to treat (NNT) is a widely used efficacy and effect-size measure in epidemiology and meta-analysis, originally defined as the average number of patients who need be treated to obtain one additional beneficial outcome. In this study, we introduce novel direct and indirect formulations of the NNT, the number needed to be exposed (NNE) and the exposure impact number (EIN) - quantifying the average number needed to treat (expose) to achieve benefit via the treatment's direct and indirect effects in the respective treatment group. Methods: Using nested potential outcomes, we formally define the direct effect NNT, NNE, and EIN (DNNT, DNNE, and DEIN, respectively) and the indirect effect NNT, NNE, and EIN (INNT, INNE, and IEIN, respectively). We then derive their identification conditions in observational studies. We introduce an estimation method and illustrate it with two analytical examples. Results: The identification results provide explicit conditions under which the novel direct and indirect indices are estimable in observational studies. Simulation studies demonstrate that the proposed estimators are consistent and that the associated analytic confidence intervals attain their nominal coverage rates. Two analytical examples clarify implementation and interpretation. Conclusions: We formalize novel path-dependent efficacy measures - DNNT, INNT, DNNE, INNE, DEIN, and IEIN - and derive their identification conditions for observational studies. We also introduce an estimation method and demonstrate its efficiency and accuracy using theoretical results and a simulation study. The widespread use of NNT and NNE, together with the need for path-dependent reporting, supports the utility of the proposed indices. These indices can help disentangle direct and indirect benefits and guide the choice among intervention strategies in public health, clinical practice, and other policy decision-making contexts.