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SCIENCE CHINA Information Sciences, Volume 62 , Issue 11 : 212205(2019) https://doi.org/10.1007/s11432-019-9866-3

Data-driven group decision making for diagnosis of thyroid nodule

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  • ReceivedJan 2, 2019
  • AcceptedMar 29, 2019
  • PublishedSep 20, 2019

Abstract


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant Nos. 71622003, 71571060, 71690235, 71690230, 71521001).


Supplement

Proofs.


References

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  • Figure 1

    (Color online) MCGDM process for the proposed method.

  • Figure 2

    (Color online) Movement of $\widetilde{C}_{k}^{G_{w},G_{d}}(k~=~1,\ldots,5)$ with random $\lambda_{j}(j~=~1,2,3)$. (a) $\widetilde{t}_{1}$; (b) $\widetilde{t}_{2}$; (c) $\widetilde{t}_{3}$; (d) $\widetilde{t}_{4}$; (e) $\widetilde{t}_{5}$.

  • Figure 3

    (Color online) Comparison between $\widetilde{C}_{k}^{\bar{G}_{w},G_{d}}$ and $\widetilde{C}_{k}^{G_{w},\bar{G}_{d}}(k~=~1,\ldots,5)$. (a) $\widetilde{t}_{1}$; (b) $\widetilde{t}_{2}$; (c) $\widetilde{t}_{3}$; (d) $\widetilde{t}_{4}$; (e) $\widetilde{t}_{5}$.

  • Figure 4

    Comparison between ROC curves from the group-recommended TIRADS categories and that from the overall diagnose for radiologists. (a) $\widetilde{t}_{1}$; (b) $\widetilde{t}_{2}$; (c) $\widetilde{t}_{3}$; (d) $\widetilde{t}_{4}$; (e) $\widetilde{t}_{5}$.

  • Table 1   TIRADS categories applied in the hospital
    Category Finding Cancer risk Recommendation
    TIRADS 3 Probably benign $<$3% Follow-up/FNAB
    TIRADS 4 Suspicious 3%–75%
    TIRADS 4A Low suspicion 3%–24%
    TIRADS 4A-1 Tending towards benign nodule 3%–15% Follow-up/FNAB
    TIRADS 4A-2 Not excluding the possibility of malignant nodule 16%–24% FNAB
    TIRADS 4B Intermediate suspicion 25%–75%
    TIRADS 4B-1 Not excluding the possibility of benign nodule 25%–40% FNAB
    TIRADS 4B-2 Medium possibility of malignant nodule 41%–65% FNAB
    TIRADS 4B-3 Large possibility of malignant nodule 66%–75% FNAB
    TIRADS 4C High suspicion 76%–95% FNAB
    TIRADS 5 Suggestive of malignancy $>$ 95% FNAB
  • Table 2   Details about the eight radiologists
    Radiologist Serving period Diagnostic record
    $D_{1}$ 2013–2018 591
    $D_{2}$ 2011–2018 586
    $D_{3}$ 2012–2018 628
    $D_{4}$ 2015–2018 397
    $D_{5}$ 2013–2017 179
    $D_{6}$ 2011–2016 180
    $D_{7}$ 2017–2018 202
    $D_{8}$ 2018–2018 93
  • Table 3   Weights of the five criteria for the eight radiologists
    Radiologist Learned criterion weight
    $t_{1}$ $w_{i}^{1}~~(i~=~1,\ldots,5)~=~(0.1893,~0.2386,~0.1798,~0.2119,~0.1804)$
    $t_{2}$ $w_{i}^{2}~~(i~=~1,\ldots,5)~=~(0.1901,~0.2412,~0.1778,~0.2164,~0.1745)$
    $t_{3}$ $w_{i}^{3}~~(i~=~1,\ldots,5)~=~(0.2005,~0.2352,~0.188,~0.1938,~0.1825)$
    $\widetilde{t}_{1}$ $\widetilde{w}_{i}^{1}~~(i~=~1,\ldots,5)~=~(0.2002,~0.2287,~0.1745,~0.2115,~0.1851)$
    $\widetilde{t}_{2}$ $\widetilde{w}_{i}^{2}~~(i~=~1,\ldots,5)~=~(0.1928,~0.2238,~0.1852,~0.216,~0.1822)$
    $\widetilde{t}_{3}$ $\widetilde{w}_{i}^{3}~~(i~=~1,\ldots,5)~=~(0.1981,~0.2205,~0.2126,~0.1911,~0.1778)$
    $\widetilde{t}_{4}$ $\widetilde{w}_{i}^{4}~~(i~=~1,\ldots,5)~=~(0.2027,~0.2314,~0.1668,~0.2291,~0.1699)$
    $\widetilde{t}_{5}$ $\widetilde{w}_{i}^{5}~~(i~=~1,\ldots,5)~=~(0.1811,~0.251,~0.1713,~0.2276,~0.169)$
  • Table 4   Distributions of the overall diagnoses on the TIRADS categories for the eight radiologists
    Radiologist Nodule Distributions of overall diagnoses on $T_{c}$
    $t_{1}$ Malignant $d_{1,c}^{m}~~(c~=~1,\ldots,~8)~=~(10,~14,~15,~25,~42,~25,~36,~66)$
    $t_{1}$ Benign $d_{1,c}^{b}~~(c~=~1,\ldots,~8)~=(261,~29,~15,~10,~24,~12,~2,~5)$
    $t_{2}$ Malignant $d_{2,c}^{m}~~(c~=~1,\ldots,~8)~=~(10,~1,~19,~1,~17,~49,~26,~84)$
    $t_{2}$ Benign $d_{2,c}^{b}~~(c~=~1,\ldots,~8)~=~(254,~12,~33,~11,~20,~33,~8,~8)$
    $t_{3}$ Malignant $d_{3,c}^{m}~(c~=~1,\ldots,~8)~=~(5,~1,~18,~0,~32,~76,~17,~18)$
    $t_{3}$ Benign $d_{3,c}^{b}~(c~=~1,\ldots,~8)~=~(155,~18,~23,~7,~13,~10,~2,~2)$
    $\widetilde{t}_{1}$ Malignant $\widetilde{d}_{1,c}^{m}~(c~=~1,\ldots,~8)~=~(17,~1,~21,~2,~36,~71,~52,~42)$
    $\widetilde{t}_{1}$ Benign $\widetilde{d}_{1,c}^{b}~(c~=~1,\ldots,~8)~=~(206,~31,~47,~26,~42,~20,~9,~5)$
    $\widetilde{t}_{2}$ Malignant $\widetilde{d}_{2,c}^{m}~(c~=~1,\ldots,~8)~=~(9,~3,~5,~0,~8,~14,~8,~9)$
    $\widetilde{t}_{2}$ Benign $\widetilde{d}_{2,c}^{b}~(c~=~1,\ldots,~8)~=~(66,~11,~11,~11,~13,~9,~2,~0)$
    $\widetilde{t}_{3}$ Malignant $\widetilde{d}_{3,c}^{m}~(c~=~1,\ldots,~8)~=~(3,~1,~3,~2,~5,~9,~2,~12)$
    $\widetilde{t}_{3}$ Benign $\widetilde{d}_{3,c}^{b}~~(c~=~1,\ldots,~8)~=~(84,~2,~7,~9,~20,~16,~2,~3)$
    $\widetilde{t}_{4}$ Malignant $\widetilde{d}_{4,c}^{m}~(c~=~1,\ldots,~8)~=~(3,~5,~14,~1,~14,~46,~19,~14)$
    $\widetilde{t}_{4}$ Benign $\widetilde{d}_{4,c}^{b}~(c~=~1,\ldots,~8)~=~(60,~7,~12,~1,~1,~4,~1,~0)$
    $\widetilde{t}_{5}$ Malignant $\widetilde{d}_{5,c}^{m}~(c~=~1,\ldots,~8)~=~(3,~2,~2,~2,~11,~27,~10,~2)$
    $\widetilde{t}_{5}$ Benign $\widetilde{d}_{5,c}^{b}~(c~=~1,\ldots,~8)~=~(17,~7,~4,~1,~3,~2,~0,~0)$
  • Table 5   Diagnostic capabilities of radiologists $\widetilde{t}_{k}~(k~=~1,\ldots,~5)$ in different situations
    Condition Diagnostic capabilities of five radiologists
    Group's weights and group's distributions $\widetilde{C}_{k}^{G_{w},G_{d}}~(k~=~1,\ldots,5)~=~(0.8088,~0.7712,~0.8104,~0.7793,~0.7721)$
    Group's weights and radiologists' distributions $\widetilde{C}_{k}^{G_{w},R_{d}}~(k~=~1,\ldots,5)~=(0.7566,~0.7469,~0.8104,~0.6821,~0.6577)$
    Radiologists' weights and group's distributions$\widetilde{C}_{k}^{R_{w},G_{d}}~(k~=~1,\ldots,5)~=(0.8012,~0.7712,~0.805,~0.7698,~0.7721)$
    Radiologists' weights and radiologists' distributions $\widetilde{C}_{k}^{R_{w},R_{d}}~(k~=~1,\ldots,5)~=~(0.7514,~0.7469,~0.805,~0.6745,~0.6577)$
    Radiologists' overall diagnoses $\widetilde{C}_{k}^{R_{0}}~(k~=~1,\ldots,5)~=(0.7505,~0.7317,~0.7451,~0.7445,~0.7025)$
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