Transcript ppt
Fuzzy Receiver Operating
Characteristic Curve: An
Option to Evaluate Diagnostic Tests
Source : IEEE Transactions on Information Technology in Biomedicine
Accepted for future publication Volume PP, Issue 99, 2006
Author : Castanho J. P. ; Barros C. ; Yamakami Akebo ; Vendite L. .
Present : Hsi-Chi Chen
Date
: 1/11/2007
Outline
Introduction
ROC
Fuzzy ROC analysis
Example
Experiment results
Conclusions
Introduction
The traditional ROC analysis requires that the possible test
results be classified in two categories: Positive, if the disease
state in question is present, or Negative, if it is absent.
This paper utilizes the fuzzy sets theory (sets with imprecise
boundaries) to deal with uncertainties inherent in diagnostic
tests.
Gold standard ：Diseased and Nondiseased
Traditional ROC analysis
ROC
Traditional ROC analysis
黃金標準：有病 D+、沒病 D檢驗
：陽性 T+、陰性 T-
效度指標
敏感度 sensitivity ：有病者驗為陽性
特異度 specificity ：沒病者驗為陰性
Traditional ROC analysis
關係
真陽 TP＋假陰 FN =全部有病者(TPF, true positive fraction)
真陰 TN＋假陽 FP =全部沒病者(TNF, true negative fraction)
FPF=1-TNF
FNF=1-TPF
D+
D-
Test (+)
True Positive
False Positive
Test (-)
False Negative True Negative
Fuzzy Set
Fuzzy rule-based system (FRBS)
模糊化介面 (Fuzzification Interface)：負責將crisp input data 轉換成Fuzzy
set，做為模糊推論的輸入資料。
模糊推論引擎 (Fuzzy Infernece Engine)：將輸入的模糊語意資料，根據知識
庫的規則來做推 論，產生一些相關的Fuzzy output。
解模糊介面 (Defuzzification Interface)：負責將Fuzzy output轉換成相對應的
明確資料，做 為系統的正式輸出。
FRBS-資料庫
資料庫 (Data Base)：包含一些語意規則以及定義這些語意的隸屬函
數 (membership functions) 行成的集合。每一個語意變數對應一個問
題範圍的模糊分段，典型的模糊分段有七個三角形的模糊隸屬函數
(triangular-shaped fuzzy membership functions)。
FRBS-規則庫 (Rule Base)
規則庫 (Rule Base)：包含有一些語意規則及一些運算符號，對於一個輸入可能會有
多條規則同時被驅動。
若有兩個輸入的語意變數 X1 與 X2，一個輸出變數 Y。X1，X2 與 Y 所對應的語意是
{small, medium, large}, {short, medium, long}, {bad, medium, good}。則對應的語意規則
有下列五條：
R1: IF X1 is small and X2 is short THEN Y is bad
R2: IF X1 is small and X2 is medium THEN Y is bad
R3: IF X1 is medium and X2 is short THEN Y is medium
R4: IF X1 is large and X2 is medium THEN Y is medium
R5: IF X1 is large and X2 is long THEN Y is good
FRBS-推論系統
推論系統使用 generalized modus ponens，將 input domain X 的模糊集合 U =
U1 x U2 x ... x Un
與 output domain Y 的模糊集合 V = V1 x V2 x ... x Vn
EXAMPLE - Prostate Cancer
Using the rule base and the Mamdani inference method,
center of gravity defuzzification process(重心法)
To include the possibility of the cancer being in each stage in the evaluation
of the system, we use the fuzzy ROC methodology.
EXAMPLE - Prostate Cancer
If a patient has
serum PSA level equal：3.2 ng/mL,
clinical stage classified：T2a
Gleason score： 5
the output of FRBS：0.3711
This value corresponds to degree 0.73 in Confined set
It means that the test strongly indicates, although not
absolutely, the patient has prostate-confined cancer.
EXAMPLE - Confined set
Negative：we consider the cancer to be confined in the prostate
Positive,：the tumor has an extension beyond the prostate (capsular and/or
seminal vesicles and/or lymph nodes involvement).
EXAMPLE – Fuzzy Gold standard
In this case, the gold standard determines the frequency in which the
individuals who have a certain test result present prostate-confined or
nonconfined cancer.
Experiment results
Conclusions
Why Fuzzy ROC?
1. Values close to the cut-off point
2. Increase the number of categories from 5 or 6
3. The main benefit：avoid loss of information and to model
vague concepts
FRBS outcome is given in possibilistic terms and the gold
standard in frequency terms, so the use of fuzzy ROC analysis
is appropriate because it avoids abandoning so much
information.