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

The number needed to treat (NNT) is an efficacy index commonly used in randomized clinical trials. The NNT is the average number of treated patients for each undesirable patient outcome, for example, death, prevented by the treatment. We introduce a systematic theoretically-based framework to model and estimate the conditional and the harmonic mean NNT in the presence of explanatory variables, in various models with dichotomous and nondichotomous outcomes. The conditional NNT is illustrated in a series of four primary examples; logistic regression, linear regression, Kaplan-Meier estimation, and Cox regression models. Also, we establish and prove mathematically the exact relationship between the conditional and the harmonic mean NNT in the presence of explanatory variables. We introduce four different methods to calculate asymptotically-correct confidence intervals for both indices. Finally, we implemented a simulation study to provide numerical demonstrations of the aforementioned theoretical results and the four examples. Numerical analysis showed that the parametric estimators of the NNT with nonparametric bootstrap-based confidence intervals outperformed other examined combinations in most settings. An R package and a web application have been developed and made available online to calculate the conditional and the harmonic mean NNTs with their corresponding confidence intervals.

Automated summary

This study introduces a theoretically-based framework to estimate the conditional and harmonic mean NNT in the presence of explanatory variables. The effectiveness of the framework is demonstrated through several examples and numerical simulations. The results show that parameter estimators with nonparametric bootstrap-based confidence intervals perform better in most cases.