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Published in: BMC Medical Informatics and Decision Making 1/2014

Open Access 01-12-2014 | Research article

Estimating the optimal threshold for a diagnostic biomarker in case of complex biomarker distributions

Authors: Fabien Subtil, Muriel Rabilloud

Published in: BMC Medical Informatics and Decision Making | Issue 1/2014

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Abstract

Background

Estimating the optimal threshold (and especially the confidence interval) of a quantitative biomarker to be used as a diagnostic test is essential for medical decision-making. This is often done with simple methods that are not always reliable. More advanced methods work well but only for biomarkers with very simple distributions. In fact, biomarker distributions are often complex because of a natural heterogeneity in marker expression and other heterogeneities due to various disease stages, laboratory equipments, etc. Methods are required to estimate a biomarker optimal threshold in case of heterogeneity and complex distributions.

Methods

A previously described Bayesian method developed for normally distributed biomarkers is applied to two flexible distributions; namely, a Student-t and a mixture of Dirichlet processes. Here, numerical studies assess the adequacy of the previous method with both distributions. Two applications are presented: the diagnosis of treatment failure after prostate cancer treated by ultrasound and the early diagnosis of cancers of the upper aerodigestive tract.

Results

Bayesian inference provided reliable credible intervals in terms of bias and coverage probability. The two distributions analysed gave meaningful clinical interpretations in both applications.

Conclusions

Reliable methods can be used to estimate a biomarker optimal threshold, even in case of complex distributions.
Appendix
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Literature
1.
go back to reference Subtil F, Rabilloud M: Robust non-linear mixed modelling of longitudinal PSA levels after prostate cancer treatment. Stat Med. 2010, 29: 573-587.PubMed Subtil F, Rabilloud M: Robust non-linear mixed modelling of longitudinal PSA levels after prostate cancer treatment. Stat Med. 2010, 29: 573-587.PubMed
2.
go back to reference Li A, Bozdag S, Kotliarov Y, Fine HA: GliomaPredict: a clinically useful tool for assigning glioma patients to specific molecular subtypes. BMC Med Inform Decis Mak. 2010, 10: 38-10.1186/1472-6947-10-38.CrossRefPubMedPubMedCentral Li A, Bozdag S, Kotliarov Y, Fine HA: GliomaPredict: a clinically useful tool for assigning glioma patients to specific molecular subtypes. BMC Med Inform Decis Mak. 2010, 10: 38-10.1186/1472-6947-10-38.CrossRefPubMedPubMedCentral
3.
go back to reference Exarchos KP, Goletsis Y, Fotiadis DI: A multiscale and multiparametric approach for modeling the progression of oral cancer. BMC Med Inform Decis Mak. 2012, 12: 136-10.1186/1472-6947-12-136.CrossRefPubMedPubMedCentral Exarchos KP, Goletsis Y, Fotiadis DI: A multiscale and multiparametric approach for modeling the progression of oral cancer. BMC Med Inform Decis Mak. 2012, 12: 136-10.1186/1472-6947-12-136.CrossRefPubMedPubMedCentral
4.
go back to reference Pepe MS: The statistical evaluation of medical tests for classification and prediction. 2003, New York: Oxford University Press Pepe MS: The statistical evaluation of medical tests for classification and prediction. 2003, New York: Oxford University Press
5.
go back to reference Fluss R, Faraggi D, Reiser B: Estimation of the Youden Index and its associated cutoff point. Biom J. 2005, 47: 458-472. 10.1002/bimj.200410135.CrossRefPubMed Fluss R, Faraggi D, Reiser B: Estimation of the Youden Index and its associated cutoff point. Biom J. 2005, 47: 458-472. 10.1002/bimj.200410135.CrossRefPubMed
6.
go back to reference Schisterman EF, Perkins N: Confidence intervals for the Youden index and corresponding optimal cut-point. Commun Stat: Simul Comput. 2007, 36: 549-563. 10.1080/03610910701212181.CrossRef Schisterman EF, Perkins N: Confidence intervals for the Youden index and corresponding optimal cut-point. Commun Stat: Simul Comput. 2007, 36: 549-563. 10.1080/03610910701212181.CrossRef
7.
go back to reference Leeflang MMG, Moons KGM, Reitsma JB, Zwinderman AH: Bias in sensitivity and specificity caused by data-driven selection of optimal cutoff values: mechanisms, magnitude, and solutions. Clin Chem. 2008, 54: 729-737. 10.1373/clinchem.2007.096032.CrossRefPubMed Leeflang MMG, Moons KGM, Reitsma JB, Zwinderman AH: Bias in sensitivity and specificity caused by data-driven selection of optimal cutoff values: mechanisms, magnitude, and solutions. Clin Chem. 2008, 54: 729-737. 10.1373/clinchem.2007.096032.CrossRefPubMed
8.
go back to reference Ruopp MD, Perkins NJ, Whitcomb BW, Schisterman EF: Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection. Biom J. 2008, 50: 419-430. 10.1002/bimj.200710415.CrossRefPubMedPubMedCentral Ruopp MD, Perkins NJ, Whitcomb BW, Schisterman EF: Youden Index and optimal cut-point estimated from observations affected by a lower limit of detection. Biom J. 2008, 50: 419-430. 10.1002/bimj.200710415.CrossRefPubMedPubMedCentral
9.
go back to reference Subtil F, Rabilloud M: A Bayesian method to estimate the optimal threshold of a longitudinal biomarker. Biom J. 2010, 52: 333-347. 10.1002/bimj.200900242.CrossRefPubMed Subtil F, Rabilloud M: A Bayesian method to estimate the optimal threshold of a longitudinal biomarker. Biom J. 2010, 52: 333-347. 10.1002/bimj.200900242.CrossRefPubMed
10.
go back to reference Jund J, Rabilloud M, Wallon M, Ecochard R: Methods to estimate the optimal threshold for normally or log-normally distributed biological tests. Med Dec Making. 2005, 25: 406-415. 10.1177/0272989X05276855.CrossRef Jund J, Rabilloud M, Wallon M, Ecochard R: Methods to estimate the optimal threshold for normally or log-normally distributed biological tests. Med Dec Making. 2005, 25: 406-415. 10.1177/0272989X05276855.CrossRef
11.
go back to reference Cantor SB, Sun CC, Tortolero-Luna G, Richards-Kortum R, Follen M: A comparison of C/B ratios from studies using receiver operating characteristic curve analysis. J Clin Epidemiol. 1999, 52: 885-892. 10.1016/S0895-4356(99)00075-X.CrossRefPubMed Cantor SB, Sun CC, Tortolero-Luna G, Richards-Kortum R, Follen M: A comparison of C/B ratios from studies using receiver operating characteristic curve analysis. J Clin Epidemiol. 1999, 52: 885-892. 10.1016/S0895-4356(99)00075-X.CrossRefPubMed
12.
go back to reference Gilks WR, Richardson S, Spiegelhalter DJ: Markov Chain Monte Carlo in practice. 1996, London: Chapman & Hall Gilks WR, Richardson S, Spiegelhalter DJ: Markov Chain Monte Carlo in practice. 1996, London: Chapman & Hall
13.
14.
go back to reference Gelman A, Carlin JB, Stern HS, Rubin DB: Bayesian data analysis. 2004, London: Chapman & Hall/CRC, 2 Gelman A, Carlin JB, Stern HS, Rubin DB: Bayesian data analysis. 2004, London: Chapman & Hall/CRC, 2
15.
go back to reference Lunn DJ, Thomas A, Best N, Spiegelhalter D: WinBUGS - a Bayesian modelling framework: Concepts, structure, and extensibility. Stat Comput. 2000, 10: 325-337. 10.1023/A:1008929526011.CrossRef Lunn DJ, Thomas A, Best N, Spiegelhalter D: WinBUGS - a Bayesian modelling framework: Concepts, structure, and extensibility. Stat Comput. 2000, 10: 325-337. 10.1023/A:1008929526011.CrossRef
16.
go back to reference Escobar MD: Estimating normal means with a Dirichlet process prior. J Am Stat Assoc. 1994, 89: 268-277. 10.1080/01621459.1994.10476468.CrossRef Escobar MD: Estimating normal means with a Dirichlet process prior. J Am Stat Assoc. 1994, 89: 268-277. 10.1080/01621459.1994.10476468.CrossRef
17.
go back to reference Escobar MD, West M: Bayesian density estimation and inference using mixtures. J Am Stat Assoc. 1995, 90: 577-588. 10.1080/01621459.1995.10476550.CrossRef Escobar MD, West M: Bayesian density estimation and inference using mixtures. J Am Stat Assoc. 1995, 90: 577-588. 10.1080/01621459.1995.10476550.CrossRef
18.
go back to reference Colonna M, Hedelin G, Esteve J, Grosclaude P, Launoy G, Buemi A, Arveux P, Tretarre B, Chaplain G, Lesec'h JM, Raverdy N, Carli PM, Menegoz F, Faivre J: National cancer prevalence estimation in France. Int J Can. 2000, 87: 301-304. 10.1002/1097-0215(20000715)87:2<301::AID-IJC24>3.0.CO;2-Y.CrossRef Colonna M, Hedelin G, Esteve J, Grosclaude P, Launoy G, Buemi A, Arveux P, Tretarre B, Chaplain G, Lesec'h JM, Raverdy N, Carli PM, Menegoz F, Faivre J: National cancer prevalence estimation in France. Int J Can. 2000, 87: 301-304. 10.1002/1097-0215(20000715)87:2<301::AID-IJC24>3.0.CO;2-Y.CrossRef
19.
go back to reference Lange KL, Little RJA, Taylor JMG: Robust statistical modeling using the t distribution. J Am Stat Assoc. 1989, 84: 881-896. Lange KL, Little RJA, Taylor JMG: Robust statistical modeling using the t distribution. J Am Stat Assoc. 1989, 84: 881-896.
20.
go back to reference R Development Core Team: R: a language and environment for statistical computing. 2009, Vienna: R Foundation for Statistical Computing R Development Core Team: R: a language and environment for statistical computing. 2009, Vienna: R Foundation for Statistical Computing
21.
go back to reference Rücker G, Schumacher M: Summary ROC curve based on a weighted Youden index for selecting an optimal cutpoint in meta-analysis of diagnostic accuracy. Stat Med. 2010, 29: 3069-3078. 10.1002/sim.3937.CrossRefPubMed Rücker G, Schumacher M: Summary ROC curve based on a weighted Youden index for selecting an optimal cutpoint in meta-analysis of diagnostic accuracy. Stat Med. 2010, 29: 3069-3078. 10.1002/sim.3937.CrossRefPubMed
22.
go back to reference Lavine M: Some aspects of Polya tree distributions for statistical modelling. Ann Stat. 1992, 20: 1222-1235. 10.1214/aos/1176348767.CrossRef Lavine M: Some aspects of Polya tree distributions for statistical modelling. Ann Stat. 1992, 20: 1222-1235. 10.1214/aos/1176348767.CrossRef
23.
go back to reference Kleinman KP, Ibrahim JG: A semiparametric Bayesian approach to the random effects model. Biometrics. 1998, 54: 921-938. 10.2307/2533846.CrossRefPubMed Kleinman KP, Ibrahim JG: A semiparametric Bayesian approach to the random effects model. Biometrics. 1998, 54: 921-938. 10.2307/2533846.CrossRefPubMed
24.
go back to reference Ohlssen DI, Sharples LD, Spiegelhalter DJ: Flexible random-effects models using Bayesian semi-parametric models: applications to institutional comparisons. Stat Med. 2007, 26: 2088-2112. 10.1002/sim.2666.CrossRefPubMed Ohlssen DI, Sharples LD, Spiegelhalter DJ: Flexible random-effects models using Bayesian semi-parametric models: applications to institutional comparisons. Stat Med. 2007, 26: 2088-2112. 10.1002/sim.2666.CrossRefPubMed
25.
go back to reference Lee KJ, Thompson SG: Flexible parametric models for random-effects distributions. Stat Med. 2008, 27: 418-434. 10.1002/sim.2897.CrossRefPubMed Lee KJ, Thompson SG: Flexible parametric models for random-effects distributions. Stat Med. 2008, 27: 418-434. 10.1002/sim.2897.CrossRefPubMed
26.
go back to reference Perkins NJ, Schisterman EF: The Youden Index and the optimal cut-point corrected for measurement error. Biom J. 2005, 47: 428-441. 10.1002/bimj.200410133.CrossRefPubMed Perkins NJ, Schisterman EF: The Youden Index and the optimal cut-point corrected for measurement error. Biom J. 2005, 47: 428-441. 10.1002/bimj.200410133.CrossRefPubMed
27.
go back to reference Schisterman EF, Faraggi D, Reiser B, Hu J: Youden Index and the optimal threshold for markers with mass at zero. Stat Med. 2008, 27: 297-315. 10.1002/sim.2993.CrossRefPubMedPubMedCentral Schisterman EF, Faraggi D, Reiser B, Hu J: Youden Index and the optimal threshold for markers with mass at zero. Stat Med. 2008, 27: 297-315. 10.1002/sim.2993.CrossRefPubMedPubMedCentral
Metadata
Title
Estimating the optimal threshold for a diagnostic biomarker in case of complex biomarker distributions
Authors
Fabien Subtil
Muriel Rabilloud
Publication date
01-12-2014
Publisher
BioMed Central
Published in
BMC Medical Informatics and Decision Making / Issue 1/2014
Electronic ISSN: 1472-6947
DOI
https://doi.org/10.1186/1472-6947-14-53

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