The Ellipse of Insignificance, a refined fragility indexfor ascertaining robustness of results indichotomous outcome trials

  1. David Robert Grimes  Is a corresponding author
  1. Dublin City University, Ireland


There is increasing awareness throughout biomedical science that many results do not withstand the trials of repeat investigation. The growing abundance of medical literature has only increased the urgent need for tools to gauge the robustness and trustworthiness of published science. Dichotomous outcome designs are vital in randomized clinical trials, cohort studies, and observational data for ascertaining differences between experimental and control arms. It has however been shown with tools like the fragility index (FI) that many ostensibly impactful results fail to materialise when even small numbers of patients or subjects in either the control or experimental arms are recoded from event to non-event. Critics of this metric counter that there is no objective means to determine a meaningful FI. As currently used, FI is not multi-dimensional and is computationally expensive. In this work a conceptually similar geometrical approach is introduced, the ellipse of insignificance (EOI). This method yields precise deterministic values for the degree of manipulation or miscoding that can be tolerated simultaneously in both control and experimental arms, allowing for the derivation of objective measures of experimental robustness. More than this, the tool is intimately connected with sensitivity and specificity of the event / non-event tests, and is readily combined with knowledge of test parameters to reject unsound results. The method is outlined here, with illustrative clinical examples.

Data availability

The paper is a modelling study and methodology and contains no data, and code provided in the supplementary material allows reproduction of all methods.

Article and author information

Author details

  1. David Robert Grimes

    Dublin City University, Dublin, Ireland
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-3140-3278


Wellcome Trust (214461/A/18/Z)

  • David Robert Grimes

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Philip Boonstra, University of Michigan, United States

Publication history

  1. Preprint posted: March 28, 2022 (view preprint)
  2. Received: April 19, 2022
  3. Accepted: September 13, 2022
  4. Accepted Manuscript published: September 20, 2022 (version 1)
  5. Version of Record published: October 21, 2022 (version 2)


© 2022, Grimes

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. David Robert Grimes
The Ellipse of Insignificance, a refined fragility indexfor ascertaining robustness of results indichotomous outcome trials
eLife 11:e79573.

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