Prevalence threshold (ϕe) and the geometry of screening curves.
The relationship between a screening tests' positive predictive value, ρ, and its target prevalence, ϕ, is proportional-though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity a and specificity b b...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2020-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0240215 |
| _version_ | 1819113961845424128 |
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| author | Jacques Balayla |
| author_facet | Jacques Balayla |
| author_sort | Jacques Balayla |
| collection | DOAJ |
| description | The relationship between a screening tests' positive predictive value, ρ, and its target prevalence, ϕ, is proportional-though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity a and specificity b beyond which the rate of change of a test's ρ drops precipitously relative to ϕ. Herein, we show the mathematical model exploring this phenomenon and define the prevalence threshold (ϕe) point where this change occurs as: [Formula: see text] where ε = a + b. From the prevalence threshold we deduce a more generalized relationship between prevalence and positive predictive value as a function of ε, which represents a fundamental theorem of screening, herein defined as: [Formula: see text] Understanding the concepts described in this work can help contextualize the validity of screening tests in real time, and help guide the interpretation of different clinical scenarios in which screening is undertaken. |
| first_indexed | 2024-12-22T04:37:44Z |
| format | Article |
| id | doaj.art-1113ae3e61e448a18fef01a3715fe237 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-12-22T04:37:44Z |
| publishDate | 2020-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-1113ae3e61e448a18fef01a3715fe2372022-12-21T18:38:49ZengPublic Library of Science (PLoS)PLoS ONE1932-62032020-01-011510e024021510.1371/journal.pone.0240215Prevalence threshold (ϕe) and the geometry of screening curves.Jacques BalaylaThe relationship between a screening tests' positive predictive value, ρ, and its target prevalence, ϕ, is proportional-though not linear in all but a special case. In consequence, there is a point of local extrema of curvature defined only as a function of the sensitivity a and specificity b beyond which the rate of change of a test's ρ drops precipitously relative to ϕ. Herein, we show the mathematical model exploring this phenomenon and define the prevalence threshold (ϕe) point where this change occurs as: [Formula: see text] where ε = a + b. From the prevalence threshold we deduce a more generalized relationship between prevalence and positive predictive value as a function of ε, which represents a fundamental theorem of screening, herein defined as: [Formula: see text] Understanding the concepts described in this work can help contextualize the validity of screening tests in real time, and help guide the interpretation of different clinical scenarios in which screening is undertaken.https://doi.org/10.1371/journal.pone.0240215 |
| spellingShingle | Jacques Balayla Prevalence threshold (ϕe) and the geometry of screening curves. PLoS ONE |
| title | Prevalence threshold (ϕe) and the geometry of screening curves. |
| title_full | Prevalence threshold (ϕe) and the geometry of screening curves. |
| title_fullStr | Prevalence threshold (ϕe) and the geometry of screening curves. |
| title_full_unstemmed | Prevalence threshold (ϕe) and the geometry of screening curves. |
| title_short | Prevalence threshold (ϕe) and the geometry of screening curves. |
| title_sort | prevalence threshold ϕe and the geometry of screening curves |
| url | https://doi.org/10.1371/journal.pone.0240215 |
| work_keys_str_mv | AT jacquesbalayla prevalencethresholdpheandthegeometryofscreeningcurves |