A method to improve predictivity of Net-Cox

using Mutual Information based network

Abstract

Cancer genes

Gene co-expression Network

NetCox(Network-constrained Cox regression)

Predict Survivability

1g

2g

3g

Dataset

Correlation between gene pairs

Abstract

CNA

mRNA

METH

TCGA data

10,022 genes

340 patients

Censored : 0

Observed : 1

Clinical outcome

M.I. based Network

NetCox(Network-constrained Cox regression)

Predict Survivability

3g

1g

2g

𝐼(𝑔𝑖 , 𝑔𝑗 ; 𝑌)Mutual Information between gene pairs and clinical outcome of patients

M.I. based network

gene pair clinical outcome of patients

Joint entropy of X, YEntropy of X

Mutual information of X, Y

Mutual information of two genes and

clinical outcome of patient

0, 0.1, 0.2, …, 0.7

Threshold from permutation strategy

1g

2g

3g

NetCox (Network-constrained Cox regression)

Network information1e-4, 1e-3, 1e-2, 1e-1

0.1, 0.3, 0.5, 0.7, 0.9, 1

L2-Cox

The importance of network

information increases

Regression coefficients

Prognostic index

Profile data

Which

parameter is

the best?

Predict Survivability

Cross validation for optimal parameters

profileG

10022

10022

network

profileX

Data

340 patients

10022 genes

1

1

0

1

…

340 patients

Clinical outcome

uncensored

(deceased)

censored

(living)

Test set Training set

5-fold cross validation

Sort in ascending order

by survival time of patients

test

profileX

NetCox training

'XPI

Evaluation

40%

40%

High-risk

group

low-risk

group

PIrank the

patients • Log-rank test • Time dependent ROC

𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑐, 𝑡 𝑓 𝑋 = Pr 𝑓 𝑋 > 𝑐|𝛿 𝑡 = 1 ,𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 𝑐, 𝑡 𝑓 𝑋 = Pr 𝑓 𝑋 ≤ 𝑐|𝛿 𝑡 = 0

• 𝑓 𝑋 = 𝑋′ 𝛽• 𝑐 ∶ 𝑐𝑢𝑡𝑜𝑓𝑓 𝑝𝑜𝑖𝑛𝑡• 𝑡 ∶ 𝑡𝑖𝑚𝑒• 𝛿 𝑡 : 𝑒𝑣𝑒𝑛𝑡 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡

The area under the ROC curve for any time t

-> how well PI classifies the patients into

high or low risk group

−log(𝑝𝑣𝑎𝑙𝑢𝑒)

Evaluate whether the patients

are assigned to the right group.

Results - Time-dependent ROC & log-rank test

Results

Mutual

InformationCorrelation

Functional

LinkageL2-Cox

CNA 0.6276 0.6265 0.6192 0.6229

mRNA 0.6427 0.6481 0.6366 0.6418

METH 0.5876 0.5845 0.5855 0.5663

Mutual

InformationCorrelation

Functional

LinkageL2-Cox

CNA 1.4068 1.4335 1.0968 1.2020

mRNA 1.8107 2.0748 1.2346 1.5018

METH 0.9714 0.8576 0.7596 0.7407

(a) Best Performance Comparison with time AUC

(b) Best Performance Comparison with log-rank test

Results

Results

Genomic

ProfileTest lambda alpha theta threshold

No. of gene pairs

above thresholdPercentage

CNAlog-rank

1E-030.3 0.4 0.0930 66,754 0.13%

AUC 0.7 0.3 0.0863 179,963 0.36%

mRNAlog-rank

1E-04 0.1 0.6 0.1221 6,487 0.01%AUC

METHlog-rank

1E-040.1 0.3 0.1017 32,282 0.06%

AUC 0.3 0.5 0.1173 3,641 0.01%

Results – CNA network

Results – mRNA network

Results – Methylation network

Results

Results

Profile Category ID description count p-value corr p-value

CNA BP 42335 cuticle development 2 1.91E-06 2.53E-03

CNA MF 16174 NAD(P)H oxidase activity 2 2.26E-05 5.13E-03

meth BP 97479 synaptic vesicle localization 4 1.86E-05 5.82E-03

meth BP 48489 synaptic vesicle transport 4 1.74E-05 5.82E-03

mRNA BP 6915 apoptotic process 16 1.55E-07 1.81E-04

mRNA BP 30162 regulation of proteolysis 10 1.04E-06 3.87E-04

P-value < 0.01