Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity
The burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the <inline-form...
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| Format: | Article |
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MDPI AG
2021-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2826 |
| _version_ | 1827678114580267008 |
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| author | Manuel Franco Juana-María Vivo |
| author_facet | Manuel Franco Juana-María Vivo |
| author_sort | Manuel Franco |
| collection | DOAJ |
| description | The burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>) indexes exhibit limitations to analysing genomic data. Among other issues, the inability to differentiate between biomarkers whose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curves cross each other with the same <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula> value, the inappropriate expression of non-concave <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curves, and the lack of a convenient interpretation, restrict their use in practice. Here, we have proposed the fitted partial area index (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>), which is computable through an algorithm valid for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curve shape, as an alternative performance summary for the evaluation of highly sensitive biomarkers. The proposed approach is based on fitter upper and lower bounds of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula> in a high-sensitivity region. Through variance estimates, simulations, and case studies for diagnosing leukaemia, and ovarian and colon cancers, we have proven the usefulness of the proposed metric in terms of restoring the interpretation and improving diagnostic accuracy. It is robust and feasible even when the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curve shows hooks, and solves performance ties between competitive biomarkers. |
| first_indexed | 2024-03-10T05:57:05Z |
| format | Article |
| id | doaj.art-ac7ba9ebfd6949f59103c075332c5fa3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:05Z |
| publishDate | 2021-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ac7ba9ebfd6949f59103c075332c5fa32023-11-22T21:19:24ZengMDPI AGMathematics2227-73902021-11-01921282610.3390/math9212826Evaluating the Performances of Biomarkers over a Restricted Domain of High SensitivityManuel Franco0Juana-María Vivo1Department of Statistics and Operations Research, University of Murcia, CEIR Campus Mare Nostrum, 30100 Murcia, SpainDepartment of Statistics and Operations Research, University of Murcia, CEIR Campus Mare Nostrum, 30100 Murcia, SpainThe burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>) indexes exhibit limitations to analysing genomic data. Among other issues, the inability to differentiate between biomarkers whose <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curves cross each other with the same <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula> value, the inappropriate expression of non-concave <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curves, and the lack of a convenient interpretation, restrict their use in practice. Here, we have proposed the fitted partial area index (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula>), which is computable through an algorithm valid for any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curve shape, as an alternative performance summary for the evaluation of highly sensitive biomarkers. The proposed approach is based on fitter upper and lower bounds of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mi>A</mi><mi>U</mi><mi>C</mi></mrow></semantics></math></inline-formula> in a high-sensitivity region. Through variance estimates, simulations, and case studies for diagnosing leukaemia, and ovarian and colon cancers, we have proven the usefulness of the proposed metric in terms of restoring the interpretation and improving diagnostic accuracy. It is robust and feasible even when the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>O</mi><mi>C</mi></mrow></semantics></math></inline-formula> curve shows hooks, and solves performance ties between competitive biomarkers.https://www.mdpi.com/2227-7390/9/21/2826<i>ROC</i> partial areascaled partial area indexhigh sensitivitynegative diagnostic likelihood ratiovariance of <i>FpAUC</i>biomarker performance |
| spellingShingle | Manuel Franco Juana-María Vivo Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity Mathematics <i>ROC</i> partial area scaled partial area index high sensitivity negative diagnostic likelihood ratio variance of <i>FpAUC</i> biomarker performance |
| title | Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity |
| title_full | Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity |
| title_fullStr | Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity |
| title_full_unstemmed | Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity |
| title_short | Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity |
| title_sort | evaluating the performances of biomarkers over a restricted domain of high sensitivity |
| topic | <i>ROC</i> partial area scaled partial area index high sensitivity negative diagnostic likelihood ratio variance of <i>FpAUC</i> biomarker performance |
| url | https://www.mdpi.com/2227-7390/9/21/2826 |
| work_keys_str_mv | AT manuelfranco evaluatingtheperformancesofbiomarkersoverarestricteddomainofhighsensitivity AT juanamariavivo evaluatingtheperformancesofbiomarkersoverarestricteddomainofhighsensitivity |