Identification of supervised and sparse functional genomic pathways

Fan Zhang; Jeffrey C. Miecznikowski; David L. Tritchler

doi:10.1515/sagmb-2018-0026

Article

Identification of supervised and sparse functional genomic pathways

Fan Zhang , Jeffrey C. Miecznikowski and David L. Tritchler

Published/Copyright: February 29, 2020

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From the journal Statistical Applications in Genetics and Molecular Biology Volume 19 Issue 1

Abstract

Functional pathways involve a series of biological alterations that may result in the occurrence of many diseases including cancer. With the availability of various “omics” technologies it becomes feasible to integrate information from a hierarchy of biological layers to provide a more comprehensive understanding to the disease. In many diseases, it is believed that only a small number of networks, each relatively small in size, drive the disease. Our goal in this study is to develop methods to discover these functional networks across biological layers correlated with the phenotype. We derive a novel Network Summary Matrix (NSM) that highlights potential pathways conforming to least squares regression relationships. An algorithm called Decomposition of Network Summary Matrix via Instability (DNSMI) involving decomposition of NSM using instability regularization is proposed. Simulations and real data analysis from The Cancer Genome Atlas (TCGA) program will be shown to demonstrate the performance of the algorithm.

Keywords: instability; pathway analysis; sparse; supervised network

Acknowledgement

The authors would like to present special thanks to Martin Morgan, PhD, director of R/Bioconductor project, for his assistance with portions of the R coding and for providing access to Roswell Park Comprehensive Cancer Center high-performance computing resources.

Appendix 1: List of algorithms

Algorithm 1

Algorithm 1 DNSMI at δ level for observation matrices YN×1, XN×q and GN×p for a search grid containing h elements on c₁ direction and l elements on c₂ direction.

Generate subsampled YrS (0.5N×1), r = 1, …, R, by drawing 0.5N observations randomly without replacement from Y where “S” indicates subsample. Likewise for XrS (0.5N×q) and GrS (0.5N×p).
Calculate NSM_r matrix for each subsampled (YrS, XrS, GrS).
Given a (c1m,c2n) pair, m=1,2,…,h,n=1,2,…,l.
Calculate Up×R=(u1,…,ur,…,uR),Vq×R=(v1,…,vr,…,vR) where u_r and v_r are sparse solutions from applying PMD using c_1m and c_2n from 3) on NSM_r from 2). Set all nonzero elements in 𝓤 and 𝓥 to 1.
Calculate θu=Pr^(u1is selected⋮up is selected)p×1,θv=Pr^(v1 is selected⋮vq is selected)q×1 by computing row means for 𝓤 and 𝓥.
Calculate
ξ^u(c1m,c2n)=2θu(1−θu)=(ξ1u^(c1m,c2n)⋮ξpu^(c1m,c2n))p×1ξ^v(c1m,c2n)=2θv(1−θv)=(ξ1v^(c1m,c2n)⋮ξqv^(c1m,c2n))q×1
Calculate ξu^(c1m,c2n)=mean(ξ^u(c1m,c2n)), ξv^(c1m,c2n)=mean(ξ^v(c1m,c2n))
Compute ξ^u,v(c1m,c2n)=max(ξu^(c1m,c2n),ξv^(c1m,c2n))
Compute ξ¯^(c1m,c2n)=sup1≤s≤c1m,1≤t≤c2nξ^u,v(s,t)
Select
(c1,c2)=arg⁡max(c1m,c2n)∈E‖(c1mc2n)‖2
where E={(c1m,c2n)∣ξ¯^(c1m,c2n)≤δ over the h × l search grid for a preset δ}.
Apply PMD using the selected (c₁, c₂) from 10) on NSM that is generated from YN×1, XN×q and GN×p. The indices corresponding to nonzero elements in the sparse output u and v represent the A^ and B^, respectively.

end

Algorithm 2

Algorithm 2 Average Mean Squared Error tuned PMD decomposition of NSM (AMSE-PMD).

Given matrix NSM, randomly delete 10% of the data elements over the entire matrix, resulting in NSM_i, i=1,2,…,10. Note that for each i, the 10% data are nonoverlapping.
Apply PMD on the 10 NSM_i’s using a given pair (c₁, c₂).
Calculate for each i the mean squared error only of the missing locations in NSM_i to that of NSM.
The AMSE is the average of the 10 means from above step, and each pair of (c₁, c₂) will be associated with one such error.
The optimal (c₁, c₂) will be the one that corresponds to the smallest AMSE over the entire search grid if there is one.
Apply PMD using the selected (c₁, c₂) from 5) on NSM. The indices corresponding to nonzero elements in the sparse output u and v represent the A^ and B^, respectively.

end

Algorithm 3

Algorithm 3 Supervised Sparse Canonical Correlation Analysis with SCCA from Parkhomenko et al. (2009) (sSCCA-P).

Prefilter features in 𝓖 and 𝓧 by Benjamini-Hochberg (BH) procedure for FDR = 0.2, which produce G~ and X~.
Center and standardize the X~ and G~ matrices so that they have zero column means and unit variances.
Calculate sample correlation matrix between X~ and G~ as K.
Given a pair of parameters (ζ_u, ζ_v) each of which ranges from 0 to 2.
Select initial values u⁰ and v⁰ and set i = 0.
Update u:
1. ui+1←Kvi
2. Normalize: ui+1←ui+1‖ui+1‖
3. Apply soft thresholding to obtain sparse solution: uji+1←(|uji+1|−12ζu)+Sign(uji+1) for j=1,…,p
  1. (.)₊ equals to x if x ≥ 0 and 0 if x < 0
  2. Sign(x)={−1if x<0,1if x>0,0if x=0.
4. Normalize: ui+1←ui+1‖ui+1‖
Update v:
1. vi+1←K‘ui+1
2. Normalize: vi+1←vi+1‖vi+1‖
3. Apply soft thresholding to obtain sparse solution: vji+1←(|vji+1|−12ζv)+Sign(vji+1) for j=1,…,q
4. Normalize: vi+1←vi+1‖vi+1‖
i ← i + 1
Repeat steps 6 and 7 until convergence.
The optimal pair of (ζ_u, ζ_v) will be determined by using k-fold cross-validation and will be the one who corresponds to the highest Δ_cor in the search grid where
Δcor=1k∑j=1k|cor(Xjv^−j,Gju^−j)|,
Repeat steps 5–9 using the selected parameters from 10) and the indices corresponding to nonzero elements in the sparse output u and v represent the A^ and B^, respectively.

end

Algorithm 4

Algorithm 4 Supervised Sparse Canonical Correlation Analysis with SCCA from Witten and Tibshirani (2009) (sSCCA-W).

Prefilter features in 𝓖 and 𝓧 by Benjamini-Hochberg (BH) procedure for FDR = 0.2, which produce G~ and X~.
Center and standardize the G~ and X~ matrices so that they have zero column means and unit variances.
Given a pair of parameters (c₁, c₂).
Set w₂ to have L₂ norm 1.
Iterate (a) and (b) until convergence:
1. w1←S(G~TX~w2, Δ1)‖S(G~TX~w2,Δ1)‖2, where Δ₁ = 0 if this results in ‖w1‖1≤c1; otherwise, Δ₁ > 0 is chosen so that ‖w1‖1=c1.
2. w2←S(X~TG~w1, Δ2)‖S(X~TG~w1,Δ2)‖2, where Δ₂ = 0 if this results in ‖w2‖1≤c2; otherwise, Δ₂ > 0 is chosen so that ‖w2‖1=c2.
  S(.) denotes the soft-thresholding operator; that is, S(a, c) = sgn(a)(|a| − c)₊.
Compute z=Cor(X~w1,G~w2).
For i ∈ 1, …, N, N is a large number for permutation purpose.
1. Permute the rows of G~ to obtain the matrix G~i, and compute canonical vectors w1i and w2i using data G~i and X~ and tuning parameter (c₁, c₂).
2. Compute zi=Cor(G~iw1i,X~w2i).
Calculate the p-value p=1N∑i=1NI(zi≥z).
Select the pair of (c₁, c₂) having the smallest p-value over the search grid.
Apply PMD using the selected (c₁, c₂) from 9) on G~TX~. The indices corresponding to nonzero elements in the sparse output u and v represent the A^ and B^, respectively.

end

Appendix 2: Notation dictionary

Latent variable for genes
Latent variable for genes but is independent of Y
Latent variable for genes that is associated with Y but is independent of others
Latent variable for transcripts
Latent variable for transcripts but is independent of Y
Latent variable for transcripts that is associated with Y but is independent of others
Latent variable for outcome
Observation matrices for genes, transcripts and outcome
Filtered observation matrices by supervision criterion
Number of pathway genes
set of indices of g_i’s elements involved in pathway
estimator of 𝒜
Number of pathway transcripts
set of indices of x_i’s elements involved in pathway
estimator of B
Tuning parameter of PMD decomposition method on row direction
Tuning parameter of PMD decomposition method on column direction
Singular value or sparse singular value for Sd-PMD, depending on the context
Number of elements on c₁ direction of search grid
Number of elements on c₂ direction of search grid
Total subjects number or sample size
Number of rows of matrix W, same as number of genes in analysis
Number of columns of matrix W, same as number of transcripts in analysis
Correlation between observation and the corresponding latent variable
Number of subsamples to use IPMDW
Predictability
First left singular vector, sparse or not depends on the context
First right singular vector, sparse or not depends on the context
Importance of the G → X → Y path to the total effect of G on Y
(1−R2)/R2
Preset instability level
Cohen’s Kappa statistic
Instability of ith element of vector u
Instability of jth element of vector v
Mean instability of u vector
Mean instability of v vector
Combined instability from u and v vectors
Supremum instability at (c₁, c₂)
Variance ratio coefficient between noise and y
Total effect of G on Y, τ=βY|G.X+βX|GβY|X.G

Appendix 3: Annotations of DNA methylation sites and transcriptome from DNSMI on UCEC project.

Table 8:

Annotations and significance of 278 DNSMI selected DNA methylation sites from NSM generated from RDT1.

Composite Element Reference	Chromosome	Gene symbol	p-value^a	Estimate^b	Correlation^{^c}
cg00282704	chr10	CASC10\|MIR1915	0.002	−10.236	−0.18
cg00363811	chr10	BTRC	0.021	−11.686	−0.14
cg00451513	chr10	ASCC1	0.022	12.044	0.14
cg00520540	chr10	CDNF\|HSPA14	0.028	−11.545	−0.13
cg00766678	chr10	NPM3	0.036	−11.231	−0.13
cg00997424	chr10	PI4K2A\|RP11-548K23.11	0.029	−9.053	−0.13
cg01068136	chr10	DCLRE1A\|NHLRC2	0.001	−11.327	−0.2
cg01087392	chr10	GBF1	0.036	−9.99	−0.13
cg01237870	chr10	MCM10	0.004	−18.268	−0.18
cg02016328	chr10	RAB18	0.035	−15.245	−0.13
cg02024446	chr10	C10orf111\|RPP38	0.035	−10.933	−0.13
cg02156071	chr10	FAM204A	0.015	−12.841	−0.15
cg02180545	chr10	C10orf2\|MRPL43	0.017	−9.124	−0.14
cg02452627	chr10	ZNF438	0.01	−11.107	−0.16
cg02550110	chr10	DDX50	0.019	−12.005	−0.14
cg02733266	chr10	GSTO1	0.005	−11.123	−0.17
cg02878913	chr10	SH3PXD2A	0	−23.138	−0.27
cg02956254	chr10	RP11-298J20.4	0.04	−11.503	−0.13
cg03539850	chr10	PANK1\|RP11-80H5.2	0.018	−13.527	−0.14
cg03576467	chr10	DNAJC9-AS1\|MRPS16	0.033	−15.373	−0.13
		RP11-152N13.5
cg03727700	chr10	DCLRE1A\|NHLRC2	0.006	−9.508	−0.17
cg03801898	chr10	ADD3\|ADD3-AS1	0.048	−8.146	−0.12
cg04036272	chr10	CCDC6	0.032	−10.619	−0.13
cg04126427	chr10	EIF3A	0.002	−12.379	−0.18
cg04290666	chr10	WNT8B	0.016	12.09	0.15
cg04446777	chr10	BTRC	0.024	−11.41	−0.14
cg04683551	chr10	CDNF\|HSPA14	0.02	24.485	0.14
cg04959674	chr10	MMS19\|UBTD1	0.018	−13.782	−0.14
cg05505307	chr10	MCM10	0.049	−12.503	−0.12
cg06206603	chr10	RP11-574K11.24\|SEC24C	0.014	−10.294	−0.15
cg07203258	chr10	DDX50	0.04	−8.986	−0.13
cg07217563	chr10	WDR37	0.012	−12.144	−0.15
cg07895186	chr10	EMX2\|EMX2OS	0.021	23.769	0.14
cg08069263	chr10	MXI1	0.032	−12.995	−0.13
cg08096168	chr10	CCDC6	0.045	−8.923	−0.12
cg08299755	chr10	ZFYVE27	0.025	−13.161	−0.14
cg09152955	chr10	NPM3	0.026	−10.445	−0.14
cg09269103	chr10	NFKB2	0.004	−10.915	−0.18
cg09333812	chr10	ARHGAP19\|ARHGAP19-SLIT1	0.044	−12.06	−0.12
cg09478103	chr10	CAP1P2\|ZNF485	0.007	−15.592	−0.17
cg09655100	chr10	TCF7L2	0.003	−11.73	−0.18
cg09747456	chr10	PANK1\|RP11-80H5.2	0.027	−11.051	−0.14
		RP11-80H5.5
cg09886360	chr10	CSGALNACT2\|RP11-351D16.3	0.014	−10.535	−0.15
cg10325336	chr10	RP11-574K11.24\|SEC24C	0.021	−10.008	−0.14
cg10708548	chr10	ARID5B	0.014	−9.667	−0.15
cg10739686	chr10	KAT6B	0.05	−9.895	−0.12
cg10800082	chr10	PDCD4\|PDCD4-AS1	0.023	−11.631	−0.14
cg10878076	chr10	NDUFB8\|RP11-411B6.6	0.015	9.511	0.15
cg10905918	chr10	RPS24	0.027	−14.052	−0.13
cg11223711	chr10	EIF3A	0.012	−11.642	−0.15
cg11423178	chr10	HNRNPH3\|PBLD	0.04	−12.218	−0.13
cg11499984	chr10	BLOC1S2	0.006	−13.085	−0.17
cg11996395	chr10	NOLC1	0.033	−10.888	−0.13
cg12198729	chr10	BTRC	0.011	−12.527	−0.15
cg12226046	chr10	PANK1\|RP11-80H5.2	0.012	−11.05	−0.15
cg12563239	chr10	ANKRD26	0.02	−10.82	−0.14
cg13800022	chr10	ITGB1\|RP11-462L8.1	0.014	−16.688	−0.15
cg13830636	chr10	RP11-574K11.24\|SEC24C	0.014	−10.169	−0.15
cg13962355	chr10	BTRC	0.03	−11.111	−0.13
cg14039939	chr10	LRRC27\|STK32C	0.001	12.222	0.21
cg14052593	chr10	BMS1P4\|DUSP8P5	0.018	−13.196	−0.14
		\|GLUD1P3\|RP11-464F9.1
cg14461522	chr10	NPM3	0.006	−14.121	−0.17
cg14562081	chr10	TCF7L2	0.008	−10.501	−0.16
cg14700647	chr10	ASAH2B	0.031	−11.586	−0.13
cg15322766	chr10	POLR3A	0.035	−10.921	−0.13
cg15384821	chr10	EGR2	0.049	−11.094	−0.12
cg15523443	chr10	POLR3A	0.012	−12.58	−0.15
cg15831653	chr10	DNAJC1	0.001	−17.937	−0.2
cg15939466	chr10	VTI1A\|ZDHHC6	0.004	−11.788	−0.17
cg15952994	chr10	VTI1A\|ZDHHC6	0.021	−11.298	−0.14
cg16754967	chr10	RSU1	0.002	−11.832	−0.18
cg17555499	chr10	CHCHD1	0.015	−10.032	−0.15
cg18493566	chr10	C10orf76	0.032	−12.277	−0.13
cg18510056	chr10	ZNF503-AS2	0.013	−8.904	−0.15
cg18762013	chr10	ZNF33A	0.022	−8.76	−0.14
cg18913254	chr10	ANXA7	0.01	−11.69	−0.16
cg18928584	chr10	CUEDC2	0.04	−11.02	−0.13
cg19014323	chr10	HNRNPF	0.033	−9.228	−0.13
cg19032306	chr10	CPEB3\|MARCH5	0.008	−10.692	−0.16
cg19040518	chr10	NDST2\|RP11-574K11.31	0.018	−12.549	−0.14
cg19138900	chr10	KLF6	0.038	−7.942	−0.13
cg20444320	chr10	STAM\|STAM-AS1	0.014	−11.784	−0.15
cg21374208	chr10	DNAJC1	0.017	−14.929	−0.15
cg21949958	chr10	BUB3	0.027	−9.949	−0.14
cg23087635	chr10	INPP5A	0.004	−17.151	−0.18
cg23319797	chr10	RAB18	0.049	−12.962	−0.12
cg23751407	chr10	RP11-95I16.2	0.028	−9.458	−0.13
cg23936098	chr10	NOLC1	0.007	−15.037	−0.16
cg23991622	chr10	VIM\|VIM-AS1	0.016	−12.909	−0.15
cg24166097	chr10	NPM3	0.032	−10.913	−0.13
cg24573310	chr10	CISD1	0.042	−10.687	−0.12
cg25089494	chr10	C10orf131\|ENTPD1-AS1	0.045	−10.352	−0.12
		RP11-248J23.7
cg25355065	chr10	ARL3\|SFXN2	0.048	−10.477	−0.12
cg25648639	chr10	ARHGAP12	0.015	−12.949	−0.15
cg26002628	chr10	ARID5B	0.015	−9.416	−0.15
cg26306372	chr10	VIM\|VIM-AS1	0.043	−11.096	−0.12
cg26625369	chr10	CDC123\|NUDT5	0.037	−11.197	−0.13
cg26881277	chr10	PDCD4\|PDCD4-AS1	0.003	−12.846	−0.18
cg26964061	chr10	MXI1	0.004	−13.658	−0.18
cg27255678	chr10	LZTS2	0.05	−12.631	−0.12
cg27510901	chr10	DNAJC1	0.046	−11.448	−0.12
cg00440043	chr10	ZEB1\|ZEB1-AS1	0.062	−9.479	−0.11
cg00588577	chr10	CCAR1	0.161	−9.448	−0.09
cg00879184	chr10	MLLT10	0.16	−6.801	−0.09
cg01021053	chr10	ZWINT	0.292	−6.844	−0.06
cg01042749	chr10	FAM178A\|RP11-179B2.2	0.105	−9.749	−0.1
cg01154046	chr10	VIM\|VIM-AS1	0.099	−10.199	−0.1
cg01367750	chr10	ACBD5\|RP11-85G18.6	0.084	−7.675	−0.11
cg01431972	chr10	ZNF503-AS2	0.053	−10.168	−0.12
cg02150674	chr10	PHYH	0.091	−7.866	−0.1
cg02351056	chr10	METTL10\|RP11-12J10.3	0.159	−8.332	−0.09
cg02622557	chr10	EIF3A	0.204	−6.689	−0.08
cg02952711	chr10	LRRC27\|STK32C	0.232	−8.554	−0.07
cg03020000	chr10	ARID5B	0.179	−8.616	−0.08
cg03141879	chr10	PITRM1\|RP11-298E9.7	0.203	6.307	0.08
cg03211233	chr10	SIRT1	0.273	−7.445	−0.07
cg03361817	chr10	ARID5B	0.178	−8.511	−0.08
cg03524461	chr10	MLLT10	0.092	−9.21	−0.1
cg03588299	chr10	DIP2C	0.276	6.334	0.07
cg03714691	chr10	WDR37	0.149	6.397	0.09
cg03922645	chr10	MEIG1	0.298	−5.658	−0.06
cg03941040	chr10	TFAM	0.468	−5.432	−0.04
cg04167018	chr10	ECD\|FAM149B1	0.109	−10.809	−0.1
cg04179819	chr10	TAF3	0.14	13.568	0.09
cg04534276	chr10	PPP3CB\|PPP3CB-AS1	0.07	−10.027	−0.11
cg04622176	chr10	MCMBP\|SEC23IP	0.25	−8.036	−0.07
cg04646451	chr10	DDX50	0.29	−6.457	−0.06
cg04733624	chr10	ADK	0.074	17.371	0.11
cg04749667	chr10	ECD\|FAM149B1	0.064	−9.771	−0.11
cg05088677	chr10	CASC10\|MIR1915	0.243	−6.805	−0.07
cg05313070	chr10	ARHGAP12	0.213	−6.889	−0.08
cg05420251	chr10	OLMALINC	0.053	−10.755	−0.12
cg06583105	chr10	PPRC1	0.414	−5.95	−0.05
cg06649808	chr10	RP11-574K11.24\|SEC24C	0.133	−8.762	−0.09
cg06782748	chr10	CREM\|RP11-297A16.2	0.313	−5.926	−0.06
cg07030336	chr10	VTI1A\|ZDHHC6	0.311	−4.968	−0.06
cg07301505	chr10	PI4K2A\|RP11-548K23.11	0.102	−7.745	−0.1
cg07636870	chr10	ACTR1A\|SUFU	0.273	−5.608	−0.07
cg07679896	chr10	RP11-298J20.4	0.084	−10.818	−0.11
cg07855525	chr10	TAF3	0.162	−8.624	−0.09
cg07900823	chr10	NUTM2B-AS1\|RP11-182L21.6	0.141	10.984	0.09
cg08395899	chr10	UPF2	0.233	−7.141	−0.07
cg08616269	chr10	CCAR1	0.116	−10.837	−0.1
cg08668510	chr10	IDI1\|WDR37	0.112	−8.677	−0.1
cg08797625	chr10	CAMK2G	0.286	−5.494	−0.07
cg08799865	chr10	NT5C2	0.136	−8.556	−0.09
cg08905519	chr10	FAM208B	0.09	−12.262	−0.1
cg09219177	chr10	ACBD5\|RP11-85G18.6	0.149	−8.413	−0.09
cg09391093	chr10	RP11-393J16.4\|ZNF25	0.077	−9.92	−0.11
cg09526975	chr10	SEPHS1	0.13	−8.258	−0.09
cg09563120	chr10	RP11-108L7.15	0.07	−8.55	−0.11
cg09688285	chr10	XPNPEP1	0.199	−8.006	−0.08
cg09933375	chr10	CCAR1	0.136	−8.499	−0.09
cg10295800	chr10	TFAM	0.146	−8.161	−0.09
cg10436918	chr10	VTI1A\|ZDHHC6	0.271	−7.126	−0.07
cg10526556	chr10	SEPHS1	0.338	−6.629	−0.06
cg10609984	chr10	RP11-393J16.4\|ZNF25	0.202	−6.433	−0.08
cg10831391	chr10	PFKP	0.064	17.827	0.11
cg10894697	chr10	CASP7	0.192	−7.271	−0.08
cg10928925	chr10	ZCCHC24	0.062	−10.162	−0.11
cg11271505	chr10	ZSWIM8	0.132	−8.726	−0.09
cg11420031	chr10	VPS26A	0.126	−9.04	−0.09
cg11460820	chr10	RPS24	0.065	−11.18	−0.11
cg11504511	chr10	ZMIZ1\|ZMIZ1-AS1	0.094	−9.122	−0.1
cg11655691	chr10	MICU1	0.146	−8.186	−0.09
cg11660725	chr10	ANKRD26	0.179	−7.058	−0.08
cg11814667	chr10	PDCD11\|USMG5	0.077	−11.843	−0.11
cg11977348	chr10	SMC3	0.076	−11.558	−0.11
cg12143181	chr10	LIPA	0.057	−8.017	−0.12
cg12144272	chr10	ZMIZ1\|ZMIZ1-AS1	0.066	−9.189	−0.11
cg12276298	chr10	ECD\|FAM149B1	0.234	−7.105	−0.07
cg12294817	chr10	METTL10\|RP11-12J10.3	0.124	−7.881	−0.09
cg12536451	chr10	ZFYVE27	0.057	−12.562	−0.12
cg12580870	chr10	CCAR1	0.169	−7.792	−0.08
cg12823012	chr10	CCAR1	0.156	−8.948	−0.09
cg12832988	chr10	CDNF\|HSPA14	0.085	−8.824	−0.11
cg13188511	chr10	CUL2	0.292	−6.597	−0.06
cg13320518	chr10	VTI1A\|ZDHHC6	0.143	−7.643	−0.09
cg13509954	chr10	MTPAP	0.477	−4.996	−0.04
cg13708259	chr10	C10orf2\|MRPL43	0.325	−5.19	−0.06
cg13763308	chr10	ADK\|AP3M1	0.111	−11.26	−0.1
cg13799287	chr10	WAC\|WAC-AS1	0.253	−9.547	−0.07
cg13817732	chr10	BLOC1S2	0.319	−5.838	−0.06
cg14193565	chr10	INPP5F	0.05	−11.468	−0.12
cg14409890	chr10	PCGF6	0.156	−9.557	−0.09
cg14434255	chr10	ENTPD7	0.244	−6.679	−0.07
cg14440794	chr10	FAM171A1	0.051	12.832	0.12
cg14631462	chr10	ZEB1\|ZEB1-AS1	0.191	−6.402	−0.08
cg14694828	chr10	ZMYND11	0.074	−9.632	−0.11
cg14825384	chr10	CASP7	0.41	−6.934	−0.05
cg14924826	chr10	BBIP1\|SHOC2	0.144	−7.789	−0.09
cg15055039	chr10	BAG3	0.423	−5.22	−0.05
cg15169471	chr10	LINC00863\|NUTM2A-AS1	0.395	−6.242	−0.05
cg15172601	chr10	CDK1	0.064	−12.138	−0.11
cg15317221	chr10	ABI1	0.094	−7.683	−0.1
cg15317837	chr10	GTPBP4\|RP11-363N22.3	0.454	−5.371	−0.05
cg15363487	chr10	VIM\|VIM-AS1	0.256	9.5	0.07
cg15433901	chr10	NMT2	0.121	−8.11	−0.09
cg15462502	chr10	BMS1	0.29	−7.432	−0.06
cg15563952	chr10	DHTKD1	0.188	−8.475	−0.08
cg15825287	chr10	NRBF2	0.21	−7.643	−0.08
cg15834928	chr10	LRRC27\|STK32C	0.346	−5.805	−0.06
cg15872329	chr10	BLOC1S2	0.084	−9.828	−0.11
cg16124546	chr10	ECD\|FAM149B1	0.181	−9.093	−0.08
cg16139770	chr10	ARID5B	0.261	−8.344	−0.07
cg16423650	chr10	DNMBP	0.188	−8.155	−0.08
cg16584947	chr10	LARP4B	0.057	−9.119	−0.12
cg16742925	chr10	PDCD11\|USMG5	0.337	−6.308	−0.06
cg16905311	chr10	ARL5B\|NSUN6	0.235	−7.037	−0.07
cg17012863	chr10	LIPA	0.069	−13.118	−0.11
cg17122475	chr10	DIP2C	0.057	−15.102	−0.12
cg17465063	chr10	MXI1	0.402	−5.149	−0.05
cg17586365	chr10	CDC123\|NUDT5	0.103	−8.543	−0.1
cg17629447	chr10	CHUK\|RP11-316M21.6	0.34	−7.511	−0.06
cg17710288	chr10	NPM3	0.068	−10.053	−0.11
cg17982459	chr10	SFR1	0.141	−9.884	−0.09
cg18035301	chr10	MAP3K8	0.257	−6.526	−0.07
cg18221224	chr10	ACBD5	0.12	−8.052	−0.1
cg18375586	chr10	FAM171A1	0.25	−7.871	−0.07
cg18409845	chr10	CPEB3\|MARCH5	0.054	−7.817	−0.12
cg18691055	chr10	MKI67	0.275	−5.129	−0.07
cg18803045	chr10	PDCD4\|PDCD4-AS1	0.173	−6.725	−0.08
cg18827378	chr10	CDK1	0.095	−8.558	−0.1
cg19038917	chr10	GSTO1	0.124	−7.03	−0.09
cg19210816	chr10	EIF3A	0.075	−8.966	−0.11
cg19391892	chr10	DDX50	0.156	−6.993	−0.09
cg19402405	chr10	EGR2	0.304	−5.531	−0.06
cg19535032	chr10	KIF5B\|Y_RNA	0.106	−8.799	−0.1
cg19559179	chr10	C10orf76	0.055	−12.012	−0.12
cg19577016	chr10	ANAPC16\|ASCC1	0.164	−8.853	−0.09
cg19603966	chr10	DNAJC1	0.336	−6.415	−0.06
cg19716967	chr10	FAM204A	0.203	−7.977	−0.08
cg19839763	chr10	ITPRIP	0.161	−6.85	−0.09
cg19874323	chr10	ARL5B\|NSUN6	0.051	−9.793	−0.12
cg20203089	chr10	NFKB2	0.058	−8.164	−0.12
cg20264529	chr10	MTPAP	0.065	−11.269	−0.11
cg20318353	chr10	ABI1	0.06	−10.792	−0.11
cg20355062	chr10	KLF6	0.158	−9.552	−0.09
cg20475000	chr10	PDCD11\|USMG5	0.087	−9.876	−0.1
cg20489345	chr10	CASP7	0.072	−11.237	−0.11
cg20778294	chr10	PPRC1	0.112	−11.411	−0.1
cg21201659	chr10	MCMBP\|SEC23IP	0.137	−10.717	−0.09
cg22553140	chr10	PRDX3	0.353	−6.281	−0.06
cg22593633	chr10	ZMYND11	0.165	−7.13	−0.08
cg22635723	chr10	ADD3\|ADD3-AS1	0.069	−7.749	−0.11
cg22664157	chr10	PWWP2B	0.377	−6.383	−0.05
cg22860891	chr10	RBM17	0.288	−6.565	−0.06
cg23026419	chr10	ITPRIP	0.128	−6.523	−0.09
cg23087130	chr10	ABI1	0.152	−9.211	−0.09
cg23635883	chr10	MASTL\|YME1L1	0.143	−8.063	−0.09
cg23638686	chr10	INPP5A	0.096	−13.741	−0.1
cg23654971	chr10	GBF1	0.184	−8.348	−0.08
cg24182333	chr10	PSAP	0.165	−9.404	−0.08
cg24201716	chr10	CCDC186\|MIR2110	0.344	−6.744	−0.06
cg24293903	chr10	ENTPD7	0.29	−7.636	−0.06
cg24315770	chr10	PDCD11\|USMG5	0.169	−8.374	−0.08
cg24807448	chr10	SMC3	0.432	−5.864	−0.05
cg24826355	chr10	KIF5B\|Y_RNA	0.219	−8.398	−0.08
cg24980609	chr10	DPCD\|POLL	0.228	−7.428	−0.07
cg25243854	chr10	BCCIP\|UROS	0.075	−13.147	−0.11
cg25713684	chr10	TAF5	0.08	−9.639	−0.11
cg25822326	chr10	NET1	0.16	−8.127	−0.09
cg26022877	chr10	ACADSB\|IKZF5	0.08	−9.874	−0.11
cg26075202	chr10	SIRT1	0.407	−6.149	−0.05
cg26097210	chr10	HNRNPH3\|PBLD	0.111	−8.36	−0.1
cg26213561	chr10	CASC10\|MIR1915	0.336	−6.234	−0.06
cg26273962	chr10	SORBS1	0.112	−10.027	−0.1
cg26358059	chr10	GSTO1	0.348	−5.792	−0.06
cg26485946	chr10	IDI1\|WDR37	0.116	−8.325	−0.1
cg26538046	chr10	WDR11\|WDR11-AS1	0.207	−7.981	−0.08
cg26538214	chr10	KLF6	0.16	−9.496	−0.09
cg27350398	chr10	PITRM1	0.366	−5.73	−0.06
cg27352063	chr10	PPIF	0.287	10.936	0.07
cg27445265	chr10	BCCIP\|UROS	0.103	−9.767	−0.1
cg27503573	chr10	PAOX	0.391	−5.837	−0.05
cg27521563	chr10	ADRB1	0.35	−5.867	−0.06
cg27523141	chr10	ZNF37BP	0.055	−8.999	−0.12
cg27636376	chr10	C10orf111\|RPP38	0.381	−7.108	−0.05

^aSimple linear regression using percent tumor invasion as response variable.
^bSimple linear regression coefficient estimate using percent tumor invasion as response variable.
^cCorrelation with percent tumor invasion.

Table 9:

Annotations and significance of 39 DNSMI selected Transcriptome elements from NSM generated from RDT1.

Ensemble Gene ID	Chromosome	Gene name	p-value^a	p-value^b	Estimate^c	Correlation^d
ENSG00000057608	chr10	GDI2	0.002	0.445	5e-06	0.19
ENSG00000095787	chr10	WAC	0.037	0.175	−7.4e-05	0.13
ENSG00000099194	chr10	SCD	0	0.092	3e-06	0.22
ENSG00000107771	chr10	CCSER2	0.031	0.587	2.4e-05	0.13
ENSG00000108055	chr10	SMC3	0.004	0.31	3.3e-05	0.18
ENSG00000108094	chr10	CUL2	0.039	0.959	4e-06	0.13
ENSG00000119969	chr10	HELLS	0.033	0.566	−5.8e-05	0.13
ENSG00000136758	chr10	YME1L1	0.025	0.71	−1.1e-05	0.14
ENSG00000138107	chr10	ACTR1A	0.02	0.803	−2e-06	0.14
ENSG00000138160	chr10	KIF11	0.005	0.297	−4.1e-05	0.17
ENSG00000138182	chr10	KIF20B	0.004	0.164	0.000208	0.18
ENSG00000148498	chr10	PARD3	0.007	0.726	−1.3e-05	0.16
ENSG00000148660	chr10	CAMK2G	0.011	0.917	−7e-06	0.15
ENSG00000151461	chr10	UPF2	0.006	0.167	6e−05	0.17
ENSG00000151465	chr10	CDC123	0.044	0.839	−3e-06	0.12
ENSG00000155252	chr10	PI4K2A	0.033	0.345	4.1e-05	0.13
ENSG00000165632	chr10	TAF3	0.011	0.843	1.9e-05	0.15
ENSG00000165637	chr10	VDAC2	0.031	0.914	−1e-06	0.13
ENSG00000165732	chr10	DDX21	0.035	0.039	−3.5e-05	0.13
ENSG00000166135	chr10	HIF1AN	0.041	0.816	−2.1e-05	0.12
ENSG00000170759	chr10	KIF5B	0.015	0.586	−6e-06	0.15
ENSG00000171314	chr10	PGAM1	0.002	0.228	1.9e-05	0.19
ENSG00000172731	chr10	LRRC20	0.001	0.168	3.6e-05	0.2
ENSG00000173848	chr10	NET1	0.011	0.492	4e-06	0.16
ENSG00000176171	chr10	BNIP3	0.001	0.416	8e-06	0.21
ENSG00000180066	chr10	C10orf91	0.007	0.036	0.000144	0.16
ENSG00000181192	chr10	DHTKD1	0.004	0.029	4.8e-05	0.17
ENSG00000181915	chr10	ADO	0.005	0.078	7.6e-05	0.17
ENSG00000187522	chr10	HSPA14	0.002	0.214	7.8e-05	0.19
ENSG00000196072	chr10	BLOC1S2	0.05	0.142	−4.7e-05	0.12
ENSG00000196968	chr10	FUT11	0.001	0.04	8.7e-05	0.21
ENSG00000197771	chr10	MCMBP	0.014	0.232	−5.9e-05	0.15
ENSG00000198825	chr10	INPP5F	0.003	0.164	0.000155	0.18
ENSG00000213390	chr10	ARHGAP19	0.003	0.603	−6.2e-05	0.18
ENSG00000260917	chr10	AL158212.3	0.01	0.119	0.000361	0.16
ENSG00000108239	chr10	TBC1D12	0.079	0.384	−0.000121	0.11
ENSG00000136738	chr10	STAM	0.083	0.628	−3.2e-05	0.11
ENSG00000165660	chr10	ABRAXAS2	0.076	0.684	−3.6e-05	0.11
ENSG00000173145	chr10	NOC3L	0.089	0.457	7.3e-05	0.1

^aSimple linear regression using percent tumor invasion as response variable.
^bMultiple linear regression using percent tumor invasion as response variable and all 39 genes as independent variables.
^cMultiple linear regression coefficient estimate using percent tumor invasion as response variable and all 39 genes as independent variables.
^dCorrelation with percent tumor invasion.

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Keywords for this article

instability; pathway analysis; sparse; supervised network

Identification of supervised and sparse functional genomic pathways

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Abstract

Acknowledgement

Appendix 1: List of algorithms

Algorithm 1 DNSMI at δ level for observation matrices YN×1, XN×q and GN×p for a search grid containing h elements on c1 direction and l elements on c2 direction.

Algorithm 2 Average Mean Squared Error tuned PMD decomposition of NSM (AMSE-PMD).

Algorithm 3 Supervised Sparse Canonical Correlation Analysis with SCCA from Parkhomenko et al. (2009) (sSCCA-P).

Algorithm 4 Supervised Sparse Canonical Correlation Analysis with SCCA from Witten and Tibshirani (2009) (sSCCA-W).

Appendix 2: Notation dictionary

Appendix 3: Annotations of DNA methylation sites and transcriptome from DNSMI on UCEC project.

References

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Algorithm 1 DNSMI at δ level for observation matrices YN×1, XN×q and GN×p for a search grid containing h elements on c₁ direction and l elements on c₂ direction.