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This work was funded by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant 1 P20 HG003900-01. Information on the Molecular Libraries Roadmap Initiative can be obtained from http://nihroadmap.nih.gov/molecularlibraries/

Jacqueline M. Hughes-Oliver

Department of Statistics

North Carolina State University

[email protected]

*joint with Ke Zhang, GSK and Stan Young, NISS

Analysis of High-Dimensional Structure-Activity Screening

Datasets Using the Optimal Bit String Tree

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2Blackwell-Tapia - November 2008

Outline Background Recursive partitioning OBSTree Simulation study Screening for monoamine oxidase inhibitors Summary

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BackgroundEstimate a function such that

based on

where

Preferably,

},...,1,0{}1,0{: Mf p f

niXMYXY piiii ,,1}1,0{},,1,0{),(

psMf

ffff

ls

l

Ll

l

},,1,0{}1,0{:

),,,,( 1

0|0ˆ0|0ˆ YfYf costs more than

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http://pubchem.ncbi.nlm.nih.gov/

http://eccr.stat.ncsu.edu/

http://www.niss.org/PowerMV/

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AD:Tricyclic:Amitriptyline

N

Background – Structure-Activity Relationship (SAR)

• Willett, Barnard, Downs (1998 JCICS)• Molecular descriptors—Carhart atom pairs

– Atom type—distance—atom type, e.g., C(2,1)-04-C(3,1)– Binary descriptors—few turned on

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TrueFalse

X3=1

Splitting variable chosen to optimize “purity measure”

Search space: size p

Need definitions for:search spacepurity measure, splitting criterionstopping criterion

Recursive Partitioning

TrueFalse

X27=1

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Recursive Partitioning: Rules are complex

0

12

3

17

18 3

9 19

6 3 15

1 16

9 11

6 2

5

8 4

5

12

1

8

13

3

7

0 0

000

0

0

0 0

0

0

00

0

0

0

00

0

• Are all splits necessary for the activity mechanism?• Does an early split impede identification of other mechanisms?

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Need definitions for:• Search space• Purity measure, splitting criterion• Stopping rule

Binary Formal Inference-Based Recursive Modeling (BFIRM)• Cho, Shen, Hermsmeier (2000, JCICS)• Rank predictors according to F-test• Combine important predictors to form splitting variable• Result is better QSAR rules

Recursive Partitioning/Simulated Annealing (RP/SA)• Blower et al. (2002, JCICS)• Best single predictor not necessarily best in combination

Tree Harvesting• Yuan, Chipman, Welch (2006 tech report)• “Trim” bits off each terminal node

Recursive Partitioning: Focus of Study

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Recursive Partitioning: RP/SA• Splitting variables are based on a combination of K predictors• Features are always present:

• Search space of size

• Uses simulated annealing – stochastic optimization• K is held fixed for all splits, and is assumed known

20102

10

500

K

p

1,,1,121

Kjjj XXX

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OBSTree• Splitting variables are based on a combination of K predictors• Combine approaches of BFIRM and RP/SA• Features can be present or absent: chromosome selection

• Search space of size

• Uses simulated annealing + weighted sampling + trimming• “K” can change for all splits, and is assumed unknown• Uses a penalty entropy splitting criterion• Usual stopping criteria applied, including cross validation

2310 102210

5002

K

K

p

1,,1,0,0,14321

Kjjjjj XXXXX

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Pre-OBSTree Setup Remove unary

descriptors Determine Singly

Important group Specify parameters

OBSTree: Flowchart

Descriptor Pool

RP

Singly Important Descriptors

General Descriptors

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OBSTree: Flowchart

Pre-OBSTree Setup Remove unary

descriptors Determine Singly

Important group Specify parameters

Initialize split at next depth: depth=depth+1 a set of K descriptor (X0) using WSS Determine best chromosome x0 of initial X0

SA to determine “optimal” (XA, xA) for split using WSS

Form last terminal node. STOP

depth=d or node size<2min or Ymax=0 or Ybar>M-1

Yes

No

Trim Check 2K-1 subsets of current (XA, xA) Report best trimmed version as (X*, x*)

Form terminal node

X*=x*?

Yes

No

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• Node has N compounds

• Class i has proportion pi in the node, with a total of ni in the node

• Entropy (node impurity):

• Penalty Entropy (penalize unwanted category)

M

iii pp

0

log

Problem:

Entropy=0 (perfect) when a class of junk compounds is identified

form) (general log1

log

compounds)junk (penalize log)1

log1

(1

0

Wiii

Uj

j

M

iii

ppNN

n

ppNN

n

OBSTree: Splitting Criterion

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• Maximum depth d

• The most active compound is junk

• The node size is less than 2j (j is the minimum node size).

• 5-fold cross-validation, e.g., choose depth d if– # correct classifications levels off at depth d

– Accept H0: d+1 = 0 for d+1 = sensitivity between depths d and d+1

OBSTree: Stopping Criteria

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• 1000 compounds, 500 binary descriptors• Four active groups (20 compounds per group) – 8% active

Activity Mechanisms Potency Descriptor Sets and Chromosomes

I 3 1 2 3 4 5

1 0 1 0 1

II 3 5 6 7 8 9

0 1 1 1 1

III 2 3 11 12 13 17

1 1 1 1 1

IV 1 15 16 17 18 19

1 1 0 1 1

Simulation Study

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Simulation Study: Standard RP Tree

0

12

3

17

18 3

9 19

6 3 15

1 16

9 11

6 2

5

8 4

5

12

1

8

13

3

7

0 0

000

0

0

0 0

0

0

00

0

0

0

00

0

5 compounds of 3 + 5 compounds of 0 7 compounds of 3

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Simulation Study: Sample OBSTree

0

1,2,3,4,5/1,0,1,0,1

3

1

3

2

15,16,17,18,19/1,1,0,1,1

5,6,7,8,9/0,1,1,1,1

3,11,12,13,17/1,1,1,1,1

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Simulation Study: 5-fold Cross-validation Actual Accuracy

0 1 2 3

Prediction 0 918 0 0 5 99.5%

1 0 20 0 0 100%

2 0 0 20 0 100%

3 2 0 0 35 94.6%

Hit 99.7% 100% 100% 87.5% Overall Accuracy: 99.3%

OBSTree

RP

Actual Accuracy

0 1 2 3

Prediction 0 910 1 0 34 96.3%

1 3 19 0 0 86.4%

2 0 0 20 0 100%

3 7 0 0 6 46.2%

Hit 98.9% 95% 100% 15% Overall Accuracy: 93.5%

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Simulation Study: Sensitivity Analysis• K, descriptor set size

– K >7 perfectly found all mechanisms– K =7 perfectly found all but one mechanism

• Basic tree parameters– Min node size is 5

• SA parameters– Initial temperature– Minimum temperature– Temperature reduction rate– # transitions at a given temperature– # failures to accept new point before increasing transition counter– Sampling weights in WSS

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Screening to Identify MAO Inhibitors• Neuronal MAO deactivates neurotransmitters

• Pargyline, an MAO inhibitor, was used to treat depression• MAO inhibitors no longer used due to toxicity & interactions• Abbott Laboratories dataset of MAO inhibitors

Brown & Martin (1996 JCICS), 1646 chemically diverse compounds 1380 binary 2D atom-pair descriptors Response variable – 0, 1, 2, 3 (ordered data) [1358/114/86/88] Category 3 has 2 well-known mechanisms - Rusinko et al. (1999 JCICS)

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0/1/0/6

1/0/1/26

32,572,844

184,721,879

0/0/0/33

0/0/0/15

1, 579,1184,809/1,1,1,0

81,177,579,183/1,1,1,0

2/0/0/32

2/0/5/24

9/2/1/2

704

1184

65

81

OBSTreeOBSTree RP/SA

RP

959/85/55/18 99/1/0/0

183

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MAO: Activity Mechanism I • “Irreversible binding to flavin cofactor of MAO”• Pargyline-like compounds• Typical features of pargyline-like compounds

A triple bondA tertiary nitrogenAn aromatic ring

• 1st terminal node of OBSTree

• Highest active terminal node of RP

• 1st terminal node of RP/SA

81 7042/0/0/32

1 1

81 183 177 5790/0/0/33

1 0 1 1

184 721 8790/1/0/6

1 1 1

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MAO: Activity Mechanism I

• Compound 1: Pargyline, y=3, has 579 & 81 & 177 but not 183• Compound 2: y=0, has feature 183 so violates OBSTree• Compound 3: y=0, falls in active node from RP• Compound 4: y=0, falls in active node from RP and RP/SA

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HO

O

N

N

) C(1,0)-3-C(1,0)579: C(2,1)-3-C(3,1) 1:C(1,0)-3-C(1,0)

1184:N(2,0)-2-N(2,0)

MAO: Activity Mechanism II• “Binding to active site"• –N-N-C(=O)- is a hydrazine feature that can be hydrolyzed to

bind protein (MAO) as a nonselective, irreversible inhibitor

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Absent Descriptor (809: C(3,1)-4-Br)

O N

N

Br

O N

N

BrC(3,1)-4-Br

Activity=3 Activity=2

C(3,1)-4-Br

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Summary• OBSTree: new RP algorithm for obtaining simplified output

– Model presence and absence of molecular features– Combination size is data-driven, varies over splits– Penalty entropy splitting criterion for one-sided purity– Weighted sampling during optimization allows prior information

• Simpler verification of QSAR• Standard RP and RP/SA are special cases of OBSTree

• Output is not deterministic• As with any RP output, care should be taken when

interpreting the results– Can miss highly correlated but important predictors– Different trees provide similar partitions of the data– Because of hard thresholding, predictions are highly variable

• Computationally intensive!

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Acknowledgements

• Atina Brooks, North Carolina State University• Jiajun Liu, Merck• Haojun Ouyang, North Carolina State University• Abbott Laboratories• Jack Liu, OmicSoft• Jun Feng, NIH• GoldenHelix

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