Cargando…
The statistical properties of RCTs and a proposal for shrinkage
We abstract the concept of a randomized controlled trial as a triple [Formula: see text] , where [Formula: see text] is the primary efficacy parameter, b the estimate, and s the standard error ([Formula: see text]). If the parameter [Formula: see text] is either a difference of means, a log odds rat...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
John Wiley and Sons Inc.
2021
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9290572/ https://www.ncbi.nlm.nih.gov/pubmed/34425632 http://dx.doi.org/10.1002/sim.9173 |
_version_ | 1784748932562157568 |
---|---|
author | van Zwet, Erik Schwab, Simon Senn, Stephen |
author_facet | van Zwet, Erik Schwab, Simon Senn, Stephen |
author_sort | van Zwet, Erik |
collection | PubMed |
description | We abstract the concept of a randomized controlled trial as a triple [Formula: see text] , where [Formula: see text] is the primary efficacy parameter, b the estimate, and s the standard error ([Formula: see text]). If the parameter [Formula: see text] is either a difference of means, a log odds ratio or a log hazard ratio, then it is reasonable to assume that b is unbiased and normally distributed. This then allows us to estimate the joint distribution of the z‐value [Formula: see text] and the signal‐to‐noise ratio [Formula: see text] from a sample of pairs [Formula: see text]. We have collected 23 551 such pairs from the Cochrane database. We note that there are many statistical quantities that depend on [Formula: see text] only through the pair [Formula: see text]. We start by determining the estimated distribution of the achieved power. In particular, we estimate the median achieved power to be only 13%. We also consider the exaggeration ratio which is the factor by which the magnitude of [Formula: see text] is overestimated. We find that if the estimate is just significant at the 5% level, we would expect it to overestimate the true effect by a factor of 1.7. This exaggeration is sometimes referred to as the winner's curse and it is undoubtedly to a considerable extent responsible for disappointing replication results. For this reason, we believe it is important to shrink the unbiased estimator, and we propose a method for doing so. We show that our shrinkage estimator successfully addresses the exaggeration. As an example, we re‐analyze the ANDROMEDA‐SHOCK trial. |
format | Online Article Text |
id | pubmed-9290572 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | John Wiley and Sons Inc. |
record_format | MEDLINE/PubMed |
spelling | pubmed-92905722022-07-20 The statistical properties of RCTs and a proposal for shrinkage van Zwet, Erik Schwab, Simon Senn, Stephen Stat Med Research Articles We abstract the concept of a randomized controlled trial as a triple [Formula: see text] , where [Formula: see text] is the primary efficacy parameter, b the estimate, and s the standard error ([Formula: see text]). If the parameter [Formula: see text] is either a difference of means, a log odds ratio or a log hazard ratio, then it is reasonable to assume that b is unbiased and normally distributed. This then allows us to estimate the joint distribution of the z‐value [Formula: see text] and the signal‐to‐noise ratio [Formula: see text] from a sample of pairs [Formula: see text]. We have collected 23 551 such pairs from the Cochrane database. We note that there are many statistical quantities that depend on [Formula: see text] only through the pair [Formula: see text]. We start by determining the estimated distribution of the achieved power. In particular, we estimate the median achieved power to be only 13%. We also consider the exaggeration ratio which is the factor by which the magnitude of [Formula: see text] is overestimated. We find that if the estimate is just significant at the 5% level, we would expect it to overestimate the true effect by a factor of 1.7. This exaggeration is sometimes referred to as the winner's curse and it is undoubtedly to a considerable extent responsible for disappointing replication results. For this reason, we believe it is important to shrink the unbiased estimator, and we propose a method for doing so. We show that our shrinkage estimator successfully addresses the exaggeration. As an example, we re‐analyze the ANDROMEDA‐SHOCK trial. John Wiley and Sons Inc. 2021-08-23 2021-11-30 /pmc/articles/PMC9290572/ /pubmed/34425632 http://dx.doi.org/10.1002/sim.9173 Text en © 2021 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 van Zwet, Erik Schwab, Simon Senn, Stephen The statistical properties of RCTs and a proposal for shrinkage |
title | The statistical properties of RCTs and a proposal for shrinkage |
title_full | The statistical properties of RCTs and a proposal for shrinkage |
title_fullStr | The statistical properties of RCTs and a proposal for shrinkage |
title_full_unstemmed | The statistical properties of RCTs and a proposal for shrinkage |
title_short | The statistical properties of RCTs and a proposal for shrinkage |
title_sort | statistical properties of rcts and a proposal for shrinkage |
topic | Research Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9290572/ https://www.ncbi.nlm.nih.gov/pubmed/34425632 http://dx.doi.org/10.1002/sim.9173 |
work_keys_str_mv | AT vanzweterik thestatisticalpropertiesofrctsandaproposalforshrinkage AT schwabsimon thestatisticalpropertiesofrctsandaproposalforshrinkage AT sennstephen thestatisticalpropertiesofrctsandaproposalforshrinkage AT vanzweterik statisticalpropertiesofrctsandaproposalforshrinkage AT schwabsimon statisticalpropertiesofrctsandaproposalforshrinkage AT sennstephen statisticalpropertiesofrctsandaproposalforshrinkage |