ObjectivesTo estimate the uncertainty of a deep learning (DL)-based prostate segmentation algorithm through conformal prediction (CP) and to assess its effect on the calculation of the prostate volume (PV) in patients at risk of prostate cancer (PC).MethodsThree-hundred seventy-seven multi-center 3-Tesla axial T2-weighted exams from biopsied males (66.64 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 7.47 years) at risk of PC were retrospectively included in the study. Assessment of PV based on PI-RADS 2.1 ellipsoid formula (PVref\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{ref}}$$\\end{document}) was available for included patients. Prostate segmentations were obtained from a DL model and used to calculate the PV (PVDL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{DL}}$$\\end{document}). CP was applied at a confidence level of 85% to flag unreliable pixel segmentations of the DL model. Subsequently, the PV (PVCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{CP}}$$\\end{document}) was calculated when disregarding uncertain pixel segmentations. Agreement between PVDL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{DL}}$$\\end{document} and PVCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{CP}}$$\\end{document} was evaluated against the reference standard PVref\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{ref}}$$\\end{document}. Intraclass correlation coefficient (ICC) and Bland–Altman plots were used to assess the agreement. The relative volume difference (RVD) was used to evaluate the PV calculation accuracy, and the Wilcoxon Signed-Rank Test was used to assess statistical differences. A p-value < 0.05 was considered statistically significant.ResultsConformal prediction significantly reduced RVD when compared to the DL algorithm (RVD = − 2.81 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 8.85 and RVD = −8.01 ±\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm$$\\end{document} 11.50). PVCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{CP}}$$\\end{document} showed a significantly larger agreement than PVDL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{DL}}$$\\end{document} when using the reference standard PVref\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{ref}}$$\\end{document} (mean difference (95% limits of agreement) PVCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{CP}}$$\\end{document}: 1.27 mL (− 13.64; 16.17 mL) PVDL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{DL}}$$\\end{document}: 6.07 mL (− 14.29; 26.42 mL)), with an excellent ICC (PVCP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{\\rm{PV}}}}_{{CP}}$$\\end{document}: 0.97 (95% CI: 0.97 to 0.98)).ConclusionUncertainty quantification through CP increases the accuracy and reliability of DL-based PV assessment in patients at risk of PC.Critical relevance statementConformal prediction can flag uncertain pixel predictions of DL-based prostate MRI segmentation at a desired confidence level, increasing the reliability and safety of prostate volume assessment in patients at risk of prostate cancer.Key PointsConformal prediction can flag uncertain pixel predictions of prostate segmentations at a user-defined confidence level.Deep learning with conformal prediction shows high accuracy in prostate volumetric assessment.Agreement between automatic and ellipsoid-derived volume was significantly larger with conformal prediction.Graphical
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