June. 15 2014, Taipei

Symbolic tree for prognosis of Hepato Cellular Carcinoma

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June. 15 2014, Taipei

Taerim Lee(1) Hyosuk Lee(2) Edwin Diday(3)

(1) Korea National Open University [email protected]

(2) Department of Internal Medicine, SNU Hospital (3) University of Paris 9 Dauphine France [email protected]

Symbolic Tree for Prognosis of Hepato Cellular Carcinoma

June. 15 2014, Taipei

mailto:[email protected]


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Outline

1. Review of Literature

2. Motivation

3. Tree structures Classification Model for HCC

4. Symbolic Data Analysis for HCC

5. Remarks


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Motivation

1. To develop the powerful modeling

technique for exploring the functional

form of covariate effects for prognosis of

HCC patients

2. To obtain the tree structured prognostic models for HCC with time covariate

3. To extract new knowledge from a HCC data using Symbolic Data Analysis


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Purposes

1. To identify the effect of prognostic factors of HCC.

2. To quantify the patient characteristics that related to the high risk clinical factor.

3. To explore the functional form of the relationships of the covariates.

4. To extract new knowledge and fit symbolic tree model


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Breiman,L.,Friedman,J.H.,Olshen,R.A.,Stone,C.J.(1984)

developed Classification and regression tree, CART

L. Gorden & R. Olshen (1985) presented tree structured survival analysis in the

CancerTreatment Reports

Ciampi.Thiffault, Nakache & Asselain (1986) proposed a variety of splitting criteria such as

likelihood ratio statistics based on the exponential model or the Cox partial likelihood,

Previous Work


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M.LeBlanc & John Crowley (1992) developed a method for obtaining tree-structured

relative risk estimate using the log-rank statistic for splitting and need between node dissimilarity in a puonning algorithm.

H.Ahn & W.Y. Loh (1994) yields a piece wise-linear Cox proportional hazard

model using curvature detection tests rather than exhaustive serach which evaluate all possible splits in finding splits to reduce computing time.

W.Y. Loh & Y.S shin (1997) derived split selection methods for classification tree

in Statistica Sinica.

Previous Work


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T. R Lee,H.S Moon(1994) Prediction Model of craniofacial growth-dental arch classification of 6 and 7 year old children-, The Journal of Korea Society of Dental Health, vol21,no.3

T. R Lee(1998) Classification Model for High Risk Dental Caries with RBF Neural Networks,, The Journal of Data Science and Classification, vol.2 (2)

T. R Lee et al (2006) Independent Prognostic factors of 861 cases of oral squamous cell carcinoma in korean adults, Oral Oncology, vol.42, p208-217

Previous Work


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Bock, H.H, Diday E (2000) (2000) Analysis of symbolic Data. Analysis of symbolic Data. Exploratory methods for extracting statistical Information Exploratory methods for extracting statistical Information from complex data. Springer Verlag,Heidelbergfrom complex data. Springer Verlag,Heidelberg

Bravo Liatas, M.C C (2000) (2000) Strata decision tree sysmbolic data analysis software , Data analysis, classification and related methods, Springer Verlag, p409-415

T. R Lee(2009) Tree Structured Prognostic Model for Tree Structured Prognostic Model for Hepatocellular Carcinoma, Journal of Korea Health Hepatocellular Carcinoma, Journal of Korea Health Inormation & Statistics, Vol.28 No.1, 2009.Inormation & Statistics, Vol.28 No.1, 2009.

T. R Lee (2011) Survival tree for Hepato Cellular Carcinoma

patient, Journal of Korean Society of Public Health

Information & Statistics

Previous Work


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V. Patel, S.Leethanakul (2001) reported new approaches to the understanding of the reported new approaches to the understanding of the

molecular basis of oral cancer.molecular basis of oral cancer.

Billard L, Diday E(2003) looks at the concept of SDA in general, and attempt to looks at the concept of SDA in general, and attempt to

review the methods available to analyze such data.review the methods available to analyze such data. ‘ ‘From the statistics of Data to the Statistics of From the statistics of Data to the Statistics of

knowledge’knowledge’

Mballo C., Diday E.(2005) compare the Kolmogorov Simirnov criterion and Gini compare the Kolmogorov Simirnov criterion and Gini

index for test selection metric for decision tree index for test selection metric for decision tree induction induction

Previous Work


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Tree Structured Classification


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• The tree structured classification modeling

constructs class classification rules based on the information provided in a learning sample of objects with known identities.

L

X2 >b

total

DL D L

X1 >a X 3>c

X4 >d

Tree Model


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By the stepwise Logistic Regression Analysis(LRA), four variables, were used to construct the logistic regression model.

• The Model which involves is as follows ; • Log Likelihood = 611.989, p = 0.0004, • Goodness of fit chi-sq = 569.34, p = 0.02.

Logistic Regression Model


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Schematic comparison of a classification tree and Schematic comparison of a classification tree and logistic regression equation for risk assessment0logistic regression equation for risk assessment0Schematic comparison of a classification tree and Schematic comparison of a classification tree and logistic regression equation for risk assessment0logistic regression equation for risk assessment0


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CART

tree structured prognostic model with effective covariate

: CART uses a decision tree to display how data may be classified or predicted.

: automatically searches for important relationships

and uncovers hidden structure even in highly complex

data.

total

LHH L L

X1 >aX2 >b

X 3>c

X4 >d

H: High riskL: Low risk


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FACT

tree structured prognostic model with effective covariate

: FACT employs statistical hypothesis test to select a

variable for splitting each node and then uses

discriminant analysis to find the split point .

The size of the tree is determined by a set of rules

total

LHL H L

X1 >aX2 >b

X 3>c

X4 >d

H: high riskL: low risk


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QUEST

: QUEST is a new classification tree algorithm derived

from the FACT method. It can be used with

univariate splits or linear combination splits.

Unlike FACT, QUEST uses cross-validation pruning.

It distinguishes from other decision tree classifiers is

that when used with univariate splits the classifier

performs approximately unbiased variable selection.

total

LDL D L

X4+2X1 >aX2 >b

X 3>c

X4 >d

D: deathL: live


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DATA


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H: High Risk groupL: Low Risk group

Classification Tree ModelClassification Tree ModelClassification Tree ModelClassification Tree Model


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1. TAENUM 100.02. AFP 87.73. CHILD 72.3 4. SIZE 59.45. INV 59.06. CLIP 45.5

9446(0)48(1)

CHILD≤5.5CHILD≤5.5

SIZE≤3.85SIZE≤3.85

TAENUM≤1.5TAENUM≤1.5

Fig.4 Tree Structured Model for TACE group of HCC data

109(0)1(1)

CART

107(0)3(1)

33(0)0(1)

4612(0)34(1)

3522(0)13(1)

4915(0)34(1)

AFP≤10.4AFP≤10.400

00

INV≤0.5INV≤0.5

Sensitivity 71.7%

Specificity 85.4%

Total 78.7%188(0)10(1)

1714(0)3(1)

8437(0)47(1)

11

1100

0087(0)1(1)


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RBF Neural Network ClassificationRBF Neural Network Classification

Block diagram representation of nervous system

Stimulus Neural netReceptors ResponseEffectors


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RBF NN ROC curve according to the

Radial Basis Function


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Kernel V16 , V17, V19 66.3 64.2

Classification results


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Survival Tree


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Survival Data

. The response var ; survival time -

The length of time; a patient has

survived after diagnosis

. Censoring is common since the endpoint

may not be observed because of

termination of a study or failure to

follow up


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Cox proportional Hazard Model

. Data (Yi, i, xi)

where Yi is the minimum of failure time Zi

and a censoring time Ci

i = I (Zi Ci) is an indicator of the event

that a failure is observed.

Xi=(X1i …Xpi ) is a p dimensional column

vector of covariates.


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Cox Proportional Hazard Model

Let (t|x) be the hazard rate at time y for

an individual with risk factor X

Cox proportional hazard model;

Where are unknow parameters

0(y) is the baseline hazard rate at

time y.

)exp()()|(1

0

P

kkkXyxt

p ,, 21


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STUDI

Survival Tree with Unbiased Detection of Interaction

: STUDI is a tree-structured regression modeling tool.

It is easy to interpret predict survival value for new case.

Missing values can easily be handled and time dependent

covariates can be incorporated.

total

LSL S L

X1 >aX2 >b

X 3>c

X4 >d

S: short term surviveL: long term survive


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Split Covariate SelectionSplit Covariate Selection

1. Fit a model to n and f covariates in the node. 2. Obtain the modified Cox-Snell residuals. 3. Perform a curvature test for each of n-s-and c-covariates.

4. Perform a interaction test for each pair of n- s-and c-covariates. 5. Select the covariate which has the smallest p-value.


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Survival Tree with Unbiased Detection of

Interaction

Cho & Loh(2001)

- STUDI is tree structured regression modeling tool.

- It is easy to interpret predict survival value for new case.

- Missing value can easily be handled and time dependent covariates can be incorporated.

STUDI


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Let the survival function for a covariate Xi

be

where is the cumulative baseline hazard rate.

Then median survival time for an individual i is defined as and the cost at a node t be is defined as

STUDI

)}exp()(exp{)|( 0 ii XyxXyS

)(0 y

}5.0)(|inf{~ ySyy

n

1iii |yy|R(t)


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Modified Cox-Snell(MCS) residuals;

for

where is the estimator of the cumulative baseline hazard function.

ni ,,1

0

)1(693.0)ˆexp()(ˆMCS 0 iii XY

Tree Structured Survival Model

STUDI


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Fig 4. Scatter plot of Box plot of the MCS Residuals


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Fig.11 Tree Structured Survival Model with SNP and Clinical Data

of HCC using imputed 252 missing data


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Fig. 6 Tree structured Survival model for OSCC

28

5

21

88

121110 13

4 6 7

3 141Radio ≤ 0.00E+00

Radio ≤ 5.92E+03

Pstage=1,2,3

Age ≤ 5.20E+01

15

2.42E+02

73

25txmethod=1,2,5

48

t=1,4

size ≤ 1.60E+01

25

109.40E+01

151.80E+01

size ≤ 1.04E+01

Age ≤ 5.80E+01

15

19

181

44Site

=10,2,3,4,5,6,7,9

20 21

40 41 45

9190

180

2322 28

1514

296

6.30E+01

size ≤ 6.77E+00

401.06E+02

96.30E+01

67.30E+01

Site=10,2,3,5,6,7,9

12 62.60E+01

63.30E+01

66.50E+01

18

size ≤ 1.00E+00

24 241.00E+01

131.57E+02

88.70E+01

77.50E+01

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SDA

1. To generalize data mining and statistics to

higher level units described by symbolic

data

2. To extract new knowledge from a database

by using a standard data table 3. Working on higher level units called concepts

necessary described by more complex data

extending data mining to knowledge mining

(Symbolic Data Analysis)


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From data mining to knowledge mining

1. A SDA needs two level of units

The first level : individual

The second level : concepts

2. A Concept is described by using the description

of class of individuals of its extent

3. The description of a concept must express the

variation of the individuals of its extent

4. Output of SDA provide new symbolic objects

associated with new categories, categories of

concepts


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SDA steps

1. Related database : composed of several more or less

linked data

2. Define a set of categories based on the categorical

variable from a quary to be given related database

3. The class of individuals which defines the extent of

category

4. Generalize process is applied to the subset of

individuals belonging to the extent of each concept

5. Define a symbolic data table

6. Symbolic Data Analysis


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The main step for a SDAThe main step for a SDA The main step for a SDAThe main step for a SDA

Put the Data in a relational Data Base

Define a Context by Giving the Units & Classes

Build a Symbolic Data Table

Apply SDA tools: Decision tree, Clustering, Graphical visualization


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SDA Advantage

Aggregated data representation Confidentiality preservation Data volume reduction

Symbolic Object

= intention(symbolic description + recognition function of the extension)

+ extension(individuals represented by the concept)

Eg. [ sex~(man(0.8), woman(0.2))]^[region~{city, rural}]^ Salary~[1.2, 3.1]


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Symbolic ObjectSymbolic Object Symbolic ObjectSymbolic Object


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SDASchematic expression


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SDA Input Symbolic DataInput Symbolic Data Input Symbolic DataInput Symbolic Data

concepts

Description of individual

Column symbolic variable


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Symbolic Data Table


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Symbolic Data variable


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Input Symbolic Data 2D Zoom VisualizationInput Symbolic Data 2D Zoom VisualizationInput Symbolic Data 2D Zoom VisualizationInput Symbolic Data 2D Zoom Visualization


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3D Zoom Stars3D Zoom Stars3D Zoom Stars3D Zoom Stars


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2D and 3D Doom Stars2D and 3D Doom Stars2D and 3D Doom Stars2D and 3D Doom Stars


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Fig5. SDA results according to new defined

concept of metastasis & prognosis


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Symbolic Tree


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Clustering Tree


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Table 1. Patients Baseline characteristics of HCC


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Table 2 Cox proportional hazards model for metastasis-free survival


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Fig1. Survival curve of metastasis free HCC


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Fig2. Survival curve of metastasis free HCC patient according to AJCC statge


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Fig3. Survival curve of metastasis free HCC patient according to the histologic response


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Fig.11 Tree Structured Survival Model with SNP and Clinical Data

of HCC using imputed 252 missing data


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individuals free of HCC and liver cirrhosis but bCL (2x0xbCL), individuals free

of HCC and diagnosis3 and liver cirrhosis (3x1xbCL), individuals with

diagnosis4 and liver cirrhosis and acute HCC (4x1xaHCC), and individuals with

diagnosis 6 and acute HCC and free of liver cirrhosis (6x0xaHCC).

Fig.5 Characterization of the classes according to the evolution of HCC.


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groups the 12 clinical variables and 3 gene data with the lowest frequency of

degradation (3x1xbCL), against Partition HCC class that contains the larger

variance with the highest frequency of degradation (4x1xaHCC).

Fig.5 Comparison of the Partition free of HCC class.


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Fig.6 The most discriminating variables to influence HCC prognosis.


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INPUT: the symbolic data table with three concepts OUTPUT: a symbolic data table with three rows associated to

the three concepts:The first column represents the frequencies of missing data "."

the others represent the frequencies of LC = 0 and the last row the frequencies of LC = 1

Fig.6 The most discriminating variables to influence HCC prognosis.


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Fig.7 Maps of the distribution in the categories of "Encephalothy",

"Ascites", on the first factorial plane.

Data with the lowest frequency of degradation (3x1xbCL),

against Partition HCC class that contains the larger variance

with the highest frequency of degradation (4x1xaHCC).


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Fig.8 Correlation circle between the first more discriminating symbolic

variables and some of their bins

The plane and symbolic variables in the smallest square which contains the first quadrant of the circle of correlation. The Figure 8 shows the distribution of the categories of the weight. From the representation of the weight on the left, it can be seen that the class (3x1xbCL), i. e. individuals with HCC at baseline and at the end of the study, are the lightest individuals, and from the representation of the encephalothy on the right, we can see that the class 3x1xbC of degradation has greater ascites well.


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Fig.9 Correlation circle the whole gene variable and bins of clinical variables


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INPUT : Patient data table

OUTPUT : Decision tree and rules

Notice that Symbolic TREE is better adapted

working on concepts than on individuals.

Symbolic Tree for HCC


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Fig.10 Symbolic Tree for HCC


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Table 3 List of the most characteristic bins of 3x1xbCL and 4x1xaHCC


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RemarksRemarksRemarksRemarks

1. The application of tree structured classification

gave easy interpretable method with small number

predictor variables.

2. The application of SDA results in more detail

information and symbolic description of classes.

3. SDA gave more practical information with

visualization graph and diagram.

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Q & A

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Thank you !谢谢 !

June. 15 2014, Taipei

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