Prediction of Sickle Cell Anemia Patient’s Response to Hydroxyurea Treatment Using ARTMAP Network Hongyu Xu, Faramarz Valafar, Marko Vuskovic Department.

Prediction of Sickle Cell Anemia Patient’s Response to Hydroxyurea Treatment Using ARTMAP Network

Hongyu Xu, Faramarz Valafar, Marko Vuskovic

Department of Computer ScienceSan Diego State UniversitySan Diego, CA 92182-7720

METMBS 2003

Las Vegas, June 24, 2003

The full paper and these slides are available at:

http://medusa.sdsu.edu/Robotics/Neuromuscular Control/Neuromuscular.htm

2

Contents

• Sickle cell anemia• Data and data preprocessing• Linear dependency of features• Feature selection• Data labeling• MART clustering algorithm• MART classification algorithm• Results• Conclusion

3

Sickle Cell Anemia

• Sickle cell anima is a genetic disorder, caused by single point mutation in the beta globin gene that changes from CCTGAGG to CCTGTGG.

• The molecules of sickle cell hemoglobin adhere to each other and distort red blood cells (RBC) into sickle shape . They stick in narrow blood vessels, blocking the flow of blood.

• Sickle cell patients experience severe painful crises. Many sickle cell patients die before the age of 20.

• In the United States, about 1 in 500 African Americans develops sickle cell anima [5]. In Africa, about 1 in 100 individuals develop the disease.

• In 1983, a drug called hydroxyurea (HU) was first used on sickle cell patients.

• The patients who responded to HU treatment positively experienced less pain and their life span were prolonged, but HU can also be quite toxic.

4

Patient Features1 Age Age of patient (in days) 2 Sex Male/Female 3 NAGG Globin gene number 4 SBAN # of BAN haplotypes 5 SBEN # of BEN haplotypes 6 SCAM # of CAM haplotypes 7 SSEN # of SEN haplotypes 8 TotalTx 9 WGT Weight of patient

10 %HbF Fetal hemoglobin, as % of total hemoglobin

11 HbF Fetal Hemoglobin, absolute value

12 Hb Total hemoglobin concentration

13 RBC Red blood cell count

14 RDW % Variation in the size of red cells

15 PCV Packed cell volume 16 Retic Reticulocytes 17 MCV Mean cell volume 18 MCH Mean cell hemoglobin 19 WBC White cell count

20 Polys Polymorph nuclear leukocytes

21 Plats Platelet count 22 Bili Bilirubin concentration

23 SNRBC Nucleated RBC seen in peripheral blood

24 %fHbF Max. percentage of HbF 25 fHbF Maximum value of HbF

Note: The data used in this research is obtained from University of Georgia, Structural Genomics Group. Dr. Homayoun Valafar was responsible for the data collection and preprocessing.

5

Excerpt from patient’s data

Age 1.1940 1.2966 0.9639 0.7705 1.0031 1.0165 1.2163 0.9955 . . . Sex 0.0001 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0001 . . .

NAGG 0.0003 0.0003 0.0004 0.0003 0.0004 0.0004 0.0004 0.0004 . . . SBAN 0.0002 0.0001 0.0002 0.0001 0.0001 0.0003 0.0002 0.0002 . . . SBEN 0.0002 0.0003 0.0002 0.0003 0.0003 0.0001 0.0002 0.0001 . . . SCAM 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 . . . SSEN 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 . . . TTx 0.0093 0.0014 0.0024 0.0009 0.0029 0.0019 0.0075 0.0024 . . . WGT 0.0049 0.0079 0.0059 0.0060 0.0060 0.0061 0.0060 0.0059 . . . HbF 0.0001 0.0006 0.0004 0.0004 0.0007 0.0002 0.0010 0.0004 . . . Hb 0.0007 0.0008 0.0009 0.0008 0.0010 0.0009 0.0010 0.0009 . . . RBC 0.0002 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 0.0003 . . . RDW 0.0022 0.0019 0.0021 0.0022 0.0025 0.0025 0.0022 0.0017 . . . PCV 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 . . . Retic 0.0288 0.0326 0.0271 0.0121 0.0285 0.0367 0.0590 0.0877 . . . MCV 0.0094 0.0086 0.0091 0.0081 0.0089 0.0091 0.0099 0.0093 . . . MCH 0.0031 0.0030 0.0030 0.0027 0.0029 0.0031 0.0034 0.0032 . . . WBC 0.0018 0.0010 0.0011 0.0011 0.0010 0.0018 0.0012 0.0015 . . . Polys 0.0010 0.0006 0.0006 0.0008 0.0006 0.0012 0.0006 0.0011 . . . Plats 0.0576 0.0842 0.0432 0.0454 0.0590 0.0478 0.0270 0.0247 . . . Bili 0.0004 0.0006 0.0003 0.0002 0.0002 0.0004 0.0003 0.0004 . . . SNBRC 0.0001 0.0002 0.0001 0.0009 0.0001 0.0001 0.0003 0.0006 . . . Class 0.0002 0.0002 0.0002 0.0002 0.0001 0.0001 0.0002 0.0001 . . .

1.0e+004 *

6

Data Preprocessing

• Normalization• Log transformation• Treatment of incomplete features

7

Patient Data (after log transform)Age 9.3877 9.4702 9.1737 8.9498 9.2135 9.2268 9.4062 9.2059 . . . Sex 0.6931 0.6931 1.0986 1.0986 1.0986 1.0986 1.0986 0.6931 . . . NAGG 1.3863 1.3863 1.6094 1.3863 1.6094 1.6094 1.6094 1.6094 . . . SBAN 1.0986 0.6931 1.0986 0.6931 0.6931 1.3863 1.0986 1.0986 . . . SBEN 1.0986 1.3863 1.0986 1.3863 1.3863 0.6931 1.0986 0.6931 . . . SCAM 0.6931 0.6931 0.6931 0.6931 0.6931 0.6931 0.6931 0.6931 . . . SSEN 0.6931 0.6931 0.6931 0.6931 0.6931 0.6931 0.6931 1.0986 . . . TTx 4.5433 2.7081 3.2189 2.3026 3.4012 2.9957 4.3307 3.2189 . . . WGT 3.9080 4.3820 4.0983 4.1076 4.1109 4.1239 4.1109 4.0882 . . . HbF 0.7419 1.8871 1.5476 1.6292 2.0919 0.9555 2.3514 1.5261 . . . Hb 2.0669 2.1633 2.3224 2.2192 2.3795 2.3321 2.3609 2.2824 . . . RBC 1.1725 1.2782 1.4061 1.4110 1.4793 1.3813 1.3376 1.3191 . . . RDW 3.1369 2.9857 3.1046 3.1224 3.2542 3.2619 3.1369 2.9014 . . . PCV 0.1906 0.2013 0.2476 0.2231 0.2631 0.2414 0.2453 0.2263 . . . Retic 5.6650 5.7909 5.6058 4.8032 5.6549 5.9067 6.3820 6.7774 . . . MCV 4.5570 4.4648 4.5250 4.4018 4.4976 4.5250 4.6052 4.5433 . . . MCH 3.4626 3.4243 3.4275 3.3142 3.3945 3.4689 3.5610 3.4995 . . . WBC 2.9444 2.3702 2.5096 2.5014 2.4423 2.9178 2.5337 2.8034 . . . Polys 2.3721 1.8764 1.9459 2.1668 1.9125 2.5703 1.9502 2.4723 . . . Plats 6.3578 6.7370 6.0707 6.1203 6.3818 6.1717 5.6021 5.5134 . . . Bili 1.6094 1.9459 1.4110 1.0986 0.9555 1.6487 1.2809 1.6292 . . . SNBRC 0.6931 1.0986 0.6931 2.3026 0.6931 0.6931 1.3863 1.9459 . . . Class 2.0000 2.0000 2.0000 2.0000 1.0000 1.0000 2.0000 1.0000 . . .

(1) (1) (1)1 2(2) (2) (2)1 2

1 2

( ) ( ) ( )1 2

D

DD

N N ND

x x x

x x x

x x x

X ξ ξ ξ

(1)

1ξ 2ξ Dξ

Columns iξ , jξ and kξ , are linearly dependent if

i i j j k ka a a ξ ξ ξ 0 (2) or

1

,D

i ii

a

ξ Xa 0 (3)

where

1 2[ , ,..., ] , 0, , ,TD ma a a a m i j k a

Linear Dependency of Features

Equation Xa 0 is equivalent to

1, or

1T

N

X Xa 0 Sa 0

(4)

where S = cov(X) (suppose X has zero means without loss of generality) Condition (4) is fulfilled if

( )eigenvectora S for which

( ) 0eigenvalue S

Linear Dependency of Features (Cont.)

10

0.00000000000000

0.00256150340499

0.01333767987431

0.02706030811732

0.24557311804605

0.35250509014528

0.35928764793261

0.42623565749994

0.50573961196044

( ) eigenvalue S

0.58261174912046

0.64043036275371

0.71088964216252

0.94270671457188

1.01103697465426

1.05724628013530

1.19139596505584

1.30377846956195

1.60639276715028

1.85530156051614

2.01212049592360

2.63302188860452

4.52076651280861

1

0.00000000000000

0.00000000000000

0.00000000000000

0.62565943239141

0.62048464459037

0.23181406284457

0.41208169184607

0.00000000000000

0.00000000000000

0.00000000000000

0.00000000000003( )

0.000000eigenvector S

00000000

0.00000000000000

0.00000000000003

0.00000000000000

0.00000000000002

0.00000000000002

0.00000000000000

0.00000000000000

0.00000000000000

0.00000000000000

0.00000000000000

SBAN

SBEN

SCAM

SSEN

11

0.00000000000000

0.00256150340499

0.01333767987431

0.02706030811732

0.24557311804605

0.35250509014528

0.35928764793261

0.42623565749994

0.50573961196044

( ) eigenvalue S

0.58261174912046

0.64043036275371

0.71088964216252

0.94270671457188

1.01103697465426

1.05724628013530

1.19139596505584

1.30377846956195

1.60639276715028

1.85530156051614

2.01212049592360

2.63302188860452

4.52076651280861

0.00256126489588

0.01332903873712

0.02701549513325

0.16384841398602

0.25413974178433

0.35323111291620

0.37258676969163

0.42642124431095

0.51885189369743

0.58642282297788

( ) 0.70543828114eigenvalue S 615

0.71850896886954

0.94469163213133

1.02193628486286

1.14660867183184

1.27633481113233

1.59635080902170

1.82624383380192

1.98186706263660

2.54312053824721

4.52049130818781

Beforeremoval:

After removal:

12

Feature Selection

Not all features carry enough information. Need to select the more important ones, to reduce the dimension of the feature space.

1 1 ( )

( )

T

TM M

z

z

v x x

v x x

Observation: If elements corresponding to a certain index, , of all

iv (1 i M ) are very small, then x x will contribute very little to the new pattern z . In that case the feature value x carries very little information and the feature type can be dropped from analysis.

13

Feature Selection (Cont.)

Steps for feature selection:

1. Calculate the eigenvalues and eigenvectors ofX . 2. Compute the relative eigenvalues. 3. Select m most important eigenvectors. 4. Scale the selected m eigenvectors with their relative

eigenvalues. 5. Sum up the magnitudes of the corresponding elements of

scaled eigenvectors. 6. Sort and select features.

Note: This method works well in some cases, but not always, like PCA.

14

Data Labeling

For supervised training and classification data have to be labeled. Here are used two approaches:

Double-rule: If the final HbF is increased at least two times over the initial value of HbF, the patient is labeled as a responder

15

Data Labeling (Cont.)

15 percent rule: If the final %HbF is over 15% while initial value of %HbF is under 15% , the patient is labeled as a responder.

16

Representation of Patient’s Data in Reduced Feature Space

Plot along three most significant dimensions

(o : non-responders, + : responders)

Double rule

17

Representation of Patient’s Data in Reduced Feature Space (Cont.)

(o : non-responders, + : sponders)

15% rule

18

Approaches in Pattern Recognition

Bayes’ Classifier

Bayes’ Classifier

Neural networks

Neural networks

Single layer

Perceptrons

Single layer

Perceptrons

Probability density estimation

Parzen window

Multilayer Perceptro

ns

Multilayer Perceptro

ns

K-nearest neighbor

Mixture model

Feed forward

Feed forward

ART ART

Recurrent

Recurrent

Basis functions

Maximum liklihood

Bayesian inference

Pattern recognition

Pattern recognition

MART MART

K-mean

SOM

Mixture model

Radial Basis

Function

Radial Basis

Function

19

ART Networks

Grossberg, 1976Unsupervised ART Learning

Fuzzy ARTCarpenter, Grossberg, etal,1991

ARTMAP

Carpenter, Grossberg, etal,1991

Fuzzy ARTMAP

Carpenter, Grossberg, etal,1991

Gaussian ARTMAP

Williamson,1992

ART1, ART2Carpenter &

Grossberg, 1987

Supervised ART Learning

Simplified ART

Baraldi and Alpaydin, 1998

Simplified ARTMAP

Kasuba, 1993

Mahalanobis distance based

ARTMAP

Vuskovic & Du, 2001

Vuskovic, Xu & Du, 2002

20

MART clustering Algorithm

C = {}, L= {}, W= {}, M=0, N= {}; % Initialize network resources while (X not empty) % Learning loop { get x; % Get a labeled pattern from X

new = true; % Set flag “new node needed”

if ( ( )label Cx ) % If the category hasn’t been seen so far

: ( )C C label x ; % add new category to C else { loop j = 1,m

{ if ( ( ) ( )Jlabel labelw x ) % For templates with the same label as x

( , , , )jt T j x w Q ; % computer activation function }

argmin ;j

j mJ t

% Find the closest template for x

if ( Jt )

{ ( , , ) : ( , , )J J J J J JN U Nw Q w Q ; % update the template new = false % Set flag " no new node needed” }

} NEWNODE(new); }

21

MART clustering Algorithm (Cont.)

macro routine: NEWNODE(new) if new == true % If the flag of “new node needed” set {

: 1m m ; % Increment the count of templates : 1m mN N ; % Increase the size of the new template

m w x ; % Initialize the new template with the pattern

: mW W w ; % Add new template to the template set

0: Q Q Q ; % Add new 0Q to the Q template

( );mL label x % Recode the label of the new template in L }

22

MART Functions

Activation fun. : ( ) ( )( , , , )T

j j j jt T j= = - -x wQ x w Q x w

Mahalanobis distance from x to jw

Match function: j jm t match function is the same as activation function

Resonance: 2; ( , )jm d p resonance happens when jt less than vigilance

Update fun. : ( ): 1j jb b= - +w w x learning rule of template j

2

:T

j jj j j

jTb

b

æ ö÷ç ÷= -ç ÷ç ÷÷ç +è ø

ggQ Q learning rule of inverse covariance matrix of

template j

where:

1 21

1 1 1, ,

1 2 jjN

, ( )j j j g Q x w

23

MART Classification Algorithm

12 1

2/ 2

( | )(2 )

jtj

D

Qp j e

x

The trained network is a Gaussian mixture model. Each class maps to one or more clusters. The class probability is proportional to the sum of posterior probabilities of individual clusters of the same class. The prediction is class that yields the maximum class probability.

Class conditional pdf of x given

cluster j

Prior probability of cluster j

1

( ) jj M

ii

NP L

N

( )

arg max ( | ) arg max ( | ) ( )k k j k

class P k p j P j

x x

Posterior probability

24

Results

15% Rule Double Rule

# of Features 19 8 19 3

Accuracy of Predicting Responders

84.4% (38/45)

68.89% (31/45)

100% (63/63)

96.82% (61/63)

Accuracy of Predicting Non-Responders 45.16%

(14/31) 67.74% (21/31)

5% (1/18)

77.77% (14/18)

Global Hit Rate 68.42% 68.42% 79.01% 92.59%

# of Output Nodes 3.50 4.20 3.32 2.06

(These results were obtained using leave-one-out approach. Each time a pattern is left out for testing, the rest is used for training. The procedure is repeated until all patterns have been tested. The results are averaged over the entire data set)

25

Conclusion

• MART has shown superior performance in various benchmarks, which has inspired us to apply MART to sickle cell anemia patients data.

• MART achieved 96.82% accuracy for predicting responders to HU treatment and give 92.59% global accuracy.

• Removal of linear dependency of features has improved the numerical stability of the algorithms.

• Reduction of the feature space from 23 to only 3 features has considerably improved the performance (decreased the numerical complexity and even increased the accuracy)

• In the future we plan to explore other labeling methods.

• We also plan to investigate more data preprocessing methods, which include both linear and nonlinear transformations.