The ellipse of insignificance, a refined fragility index for ascertaining robustness of results in dichotomous outcome trials
Figures
![](https://iiif.elifesciences.org/lax:79573%2Felife-79573-fig1-v2.tif/full/617,/0/default.jpg)
Ellipse of insignificance example.
(a) An example ellipse of insignificance for the , , , at a significance level of . All points bounded by the ellipse depict combinations which would not lead to the null being rejected. (b) Relevant vectors for ascertaining misconding thresholds. In this example, the Fewest Experimental/Control Knowingly Uncoded Participants (FECKUP) point is , , and . See text for details.
![](https://iiif.elifesciences.org/lax:79573%2Felife-79573-fig2-v2.tif/full/617,/0/default.jpg)
Application of ellipse of insignificance analysis to existent data.
(a) Ellipses of insignificance analysis for a published study (n = 913) for illustrative example 1 of published data. The shaded region denotes the ellipse of insignificance, the red line shows the Fewest Experimental/Control Knowingly Uncoded Participants (FECKUP) vector (the minimum vector from the origin to the ellipse).
![](https://iiif.elifesciences.org/lax:79573%2Felife-79573-fig3-v2.tif/full/617,/0/default.jpg)
Illustrative example 2.
(a) Ellipses of insignificance analysis for two studies with same statistic. (b) Fewest Experimental/Control Knowingly Uncoded Participants (FECKUP) vectors for both studies. Experiment 1 is given by orange ellipse and red dotted line, Experiment 2 by the blue ellipse and dotted line.
![](https://iiif.elifesciences.org/lax:79573%2Felife-79573-fig4-v2.tif/full/617,/0/default.jpg)
Illustrative example 3.
An ellipse of insignificance (EOI) analysis on the data supplied in the City A/City B screening comparison yields a Fewest Experimental/Control Knowingly Uncoded Participants (FECKUP) vector (in red) of 46.2 subjects, corresponding to a minimum tolerance of 66.5 total subjects after resolving the vector.
As (shown in green) with (shown in blue), but as the sensitivity and specificity of the tests used in City A are known, it can be shown that , exceeding the limits of xi, placing the point within the ellipse and rendering any seeming significance void. Note that only a part of the EOI (denoted by the blue solid shape) is shown for clarity.
Tables
Reported groups and related variables.
Endpoint positive | Endpoint negative | |
---|---|---|
Experimental group | ||
Control group |
Ellipse of insignificance (EOI) derived metrics for published data.
EOI statistic () | Derived value |
---|---|
Experimental group tolerance xi | 6.9 subjects |
Control group tolerance yi | 1.9 subjects |
FECKUP vector length | 1.9 subjects |
Tolerance threshold for error (experimental group) | 0.99% |
Tolerance threshold for error (control group) | 0.89% |
Absolute tolerance threshold for error (all subjects) | 0.22% |
Experimental metrics for similar test statistics.
Significance level | Data | |||
---|---|---|---|---|
Experiment 1 | 17.7% | 18.2% | 8.9% | |
Experiment 2 | 11% | 9.5% | 5.0% | |
Experiment 1 | 16.3% | 17.0% | 8.3% | |
Experiment 2 | 10.4% | 8.6% | 4.6% | |
Experiment 1 | 14.8% | 15.5% | 7.5% | |
Experiment 2 | 9.8% | 7.6% | 4.1% | |
Experiment 1 | 13.5% | 14.3% | 6.9% | |
Experiment 2 | 9.2% | 6.8% | 3.8% |
Results of different analysis.
CIN2 + positive | No CIN2 + detected | Methodology | |
---|---|---|---|
City A (measured) | 113 | 887 | LBC only |
City B (measured) | 24 | 976 | HPV screening/LBC reflex |
True values (both cities) | 20 | 980 | N/A |
Additional files
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MDAR checklist
- https://cdn.elifesciences.org/articles/79573/elife-79573-mdarchecklist1-v2.pdf
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Source code 1
Sample MATLAB/OCTAVE code for rapid implementation of EOI analysis method outlined.
- https://cdn.elifesciences.org/articles/79573/elife-79573-code1-v2.zip