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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
John Wiley and Sons Inc.
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9540555/ https://www.ncbi.nlm.nih.gov/pubmed/35472818 http://dx.doi.org/10.1002/sim.9418 |
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author | Vancak, Valentin Goldberg, Yair Levine, Stephen Z. |
author_facet | Vancak, Valentin Goldberg, Yair Levine, Stephen Z. |
author_sort | Vancak, Valentin |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-9540555 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | John Wiley and Sons Inc. |
record_format | MEDLINE/PubMed |
spelling | pubmed-95405552022-10-14 The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application Vancak, Valentin Goldberg, Yair Levine, Stephen Z. Stat Med Research Articles 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. John Wiley and Sons Inc. 2022-04-26 2022-07-30 /pmc/articles/PMC9540555/ /pubmed/35472818 http://dx.doi.org/10.1002/sim.9418 Text en © 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd. https://creativecommons.org/licenses/by-nc-nd/4.0/This is an open access article under the terms of the http://creativecommons.org/licenses/by-nc-nd/4.0/ (https://creativecommons.org/licenses/by-nc-nd/4.0/) License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifications or adaptations are made. |
spellingShingle | Research Articles Vancak, Valentin Goldberg, Yair Levine, Stephen Z. The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title | The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title_full | The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title_fullStr | The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title_full_unstemmed | The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title_short | The number needed to treat adjusted for explanatory variables in regression and survival analysis: Theory and application |
title_sort | number needed to treat adjusted for explanatory variables in regression and survival analysis: theory and application |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9540555/ https://www.ncbi.nlm.nih.gov/pubmed/35472818 http://dx.doi.org/10.1002/sim.9418 |
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