Assessment of SNP-SNP interactions by using square contingency table analysis

KARADAĞ, ÖZGE; ALTUN, GÖKÇEN; AKTAŞ, SERPIL

doi:10.1590/0001-3765202020190465

ÖZGE KARADAĞ

Hacettepe University, Department of Statistics, 06800, Beytepe, Ankara, Turkey

https://orcid.org/0000-0002-2650-1458

GÖKÇEN ALTUN

Bartın University, Department of Computer Technology and Information Systems, 74100, Bartın, Turkey

https://orcid.org/0000-0003-4311-6508

SERPIL AKTAŞ

Hacettepe University, Department of Statistics, 06800, Beytepe, Ankara, Turkey

https://orcid.org/0000-0003-3364-6388

Correspondence to: Özge Karadağ E-mail: ozgekaradag@hacettepe.edu.tr

AUTHOR CONTRIBUTIONS

ÖK, GA and SA idealized and supervised the research. ÖK and GA analyzed the data, prepared tables, authored or reviewed drafts of the paper. SA contributed to discussion and approved the final draft; all authors actively contributed to manuscript preparation.

Tables (9)

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(a)

SNP-V aa aA AA Total Case n .1 n .2 n .3 n Control m .1 m .2 m .3 m Total n 𝐵 .1 n 𝐵 .2 n 𝐵 .3 N

(b)

Controls U \ V aa aA AA Total aa m 11 m 12 m 13 m 1. aA m 21 m 22 m 23 m 2. AA m 31 m 32 m 33 m 3. Total m .1 m .2 m .3 m

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Table II
Results for top associated 25 variants (listed according to chromosomal position).

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Table III
Results under symmetry models.

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(a)

(b)

(c)

(d)

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Table V
Model comparison results.

SNP-U	aa	aA	AA	Total
Case	$n_{1 .}$	$n_{2 .}$	$n_{3 .}$	$n$
Control	$m_{1 .}$	$m_{2 .}$	$m_{3 .}$	$m$
Total	$n_{𝐴 .1}$	$n_{𝐴 .2}$	$n_{𝐴 .3}$	N

SNP-V	aa	aA	AA	Total
Case	$n_{.1}$	$n_{.2}$	$n_{.3}$	$n$
Control	$m_{.1}$	$m_{.2}$	$m_{.3}$	$m$
Total	$n_{𝐵 .1}$	$n_{𝐵 .2}$	$n_{𝐵 .3}$	N

Cases	U \ V	aa	aA	AA	*Total*
	aa	$n_{11}$	$n_{12}$	$n_{13}$	$n_{1.}$
	aA	$n_{21}$	$n_{22}$	$n_{23}$	$n_{2.}$
	AA	$n_{31}$	$n_{32}$	$n_{33}$	$n_{3.}$
	Total	$n_{.1}$	$n_{.2}$	$n_{.3}$	n

Controls	U \ V	aa	aA	AA	*Total*
	aa	$m_{11}$	$m_{12}$	$m_{13}$	$m_{1.}$
	aA	$m_{21}$	$m_{22}$	$m_{23}$	$m_{2.}$
	AA	$m_{31}$	$m_{32}$	$m_{33}$	$m_{3.}$
	Total	$m_{.1}$	$m_{.2}$	$m_{.3}$	m

SNP-U	aa	aA	AA	Total
Case	$n_{1 .}$	$n_{2 .}$	$n_{3 .}$	$n$
Control	$m_{1 .}$	$m_{2 .}$	$m_{3 .}$	$m$
Total	$n_{𝐴 .1}$	$n_{𝐴 .2}$	$n_{𝐴 .3}$	N

Cases	U \ V	aa	aA	AA	*Total*
	aa	$n_{11}$	$n_{12}$	$n_{13}$	$n_{1.}$
	aA	$n_{21}$	$n_{22}$	$n_{23}$	$n_{2.}$
	AA	$n_{31}$	$n_{32}$	$n_{33}$	$n_{3.}$
	Total	$n_{.1}$	$n_{.2}$	$n_{.3}$	n

No	Chr	Position	n₁	n₂	n₃	b	$𝐬 𝐞 (𝐛)$	$𝛘^{2}$	p-value
1	1	87705031	447	340	62	0.293	0.063	21.995	2.73x10-06
2	1	94479725	566	252	31	-0.332	0.073	20.717	5.32x10-06
3	3	60483876	618	218	13	0.361	0.081	19.988	7.79x10-06
4	5	110501261	630	194	25	-0.366	0.082	19.918	8.08x10-06
5	5	110506386	630	194	25	-0.366	0.082	19.918	8.08x10-06
6	5	110515510	628	196	25	-0.374	0.082	20.839	4.99x10-06
7	5	110529043	610	213	26	-0.361	0.079	20.728	5.29x10-06
8	5	110543925	624	200	25	-0.374	0.081	21.244	4.04x10-06
9	7	11766844	208	449	192	-0.263	0.057	21.390	3.74x10-06
10	7	11766964	208	448	193	-0.264	0.057	21.614	3.33x10-06
11	7	52257371	226	436	187	-0.267	0.058	21.232	4.06x10-06
12	7	144982124	733	115	1	0.524	0.114	21.142	4.26x10-06
13	9	10749312	368	376	105	-0.268	0.059	20.909	4.81x10-06
14	11	129152516	313	421	115	-0.272	0.058	21.929	2.82x10-06
15	11	129155346	311	420	118	-0.264	0.058	20.838	4.99x10-06
16	13	105385655	745	102	2	0.522	0.116	20.337	6.49x10-06
17	17	15291162	258	437	154	-0.259	0.057	20.917	4.79x10-06
18	19	47351966	621	213	15	-0.382	0.079	22.895	1.71x10-06
19	19	48295716	686	159	4	-0.455	0.099	21.214	4.10x10-06
20	19	48296296	686	159	4	-0.455	0.099	21.214	4.10x10-06
21	19	48296505	687	158	4	-0.465	0.099	21.990	2.73x10-06
22	19	48297228	684	161	4	-0.447	0.099	20.557	5.78x10-06
23	21	40292951	450	346	53	-0.303	0.066	21.323	3.88x10-06
24	21	40295176	453	339	57	-0.318	0.065	24.132	8.99x10-07

SNP Pair	Complete Symmetry		Quasi Symmetry		Marginal Homogeneity
SNP Pair	G²	p-value	G²	p-value	G²	p-value
1 \ 23	0.765	0.580	0.027	0.869	0.740	0.691
1 \ 24	0.245	0.970	0.016	0.900	0.230	0.892
2 \ 7	6.415	0.093	0.320	0.571	6.120	0.050
3 \ 4	6.785	0.079	1.477	0.224	5,270	0.072
3 \ 5	6.785	0.079	1.477	0.224	5.270	0.072
3 \ 6	6.480	0.090	1.437	0.231	5.000	0.082
3 \ 7	5.702	0.127	1.268	0.260	4.370	0.112
3 \ 8	7.298	0.063	2.728	0.099	4.530	0.104
3 \ 18	0.704	0.872	0.469	0.481	0.210	0.901
4 \ 18	3.525	0.317	0.176	0.675	3.330	0.189
5 \ 18	3.525	0.317	0.176	0.675	3.330	0.189
6 \ 18	3.306	0.347	0.158	0.691	3.130	0.209
7 \ 18	3.356	0.340	0.147	0.702	3.180	0.204
8 \ 18	2.953	0.399	0.126	0.723	2.810	0.246
9 \ 11	1.328	0.723	0.301	0.583	1.030	0.598
10 \ 11	1.369	0.713	0.337	0.562	1.030	0.597
12 \ 16	4.813	0.816	3.653	0.056	1.150	0.362
14 \ 15	6.931	0.074	0.000	0.988	5.030	0.081
23 \ 24	7.473	0.058	0.000	0.998	5.840	0.054

1 \ 24	AA	AG	GG
AA	207	201	39
AG	204	119	17
GG	42	19	1

207	202.2	40.8
202.8	119	17.7
40.2	18.3	1

207	201.3	38.7
203.7	119	17.3
42.3	18.7	11

207	202.5	40.5
202.5	119	18
40.5	18	1

1 \ 24	AA	AG	GG
AA	207	201	39
AG	204	119	17
GG	42	19	1

207	202.2	40.8
202.8	119	17.7
40.2	18.3	1

207	201.3	38.7
203.7	119	17.3
42.3	18.7	11

207	202.5	40.5
202.5	119	18
40.5	18	1

SNP Pair	Complete Symmetry			Quasi Symmetry			Marginal Homogeneity
SNP Pair	df	G²	AIC	df	G²	AIC	df	G²	AIC
1 \ 23	3	0.765	-5.235	1	0.027	-1.973	2	0.740	-3.260
1 \ 24	3	0.245	-5.755	1	0.016	-1.984	2	0.230	-3.770
2 \ 7	3	6.415	0.415	1	0.320	-1.68	2	6.120	2.120
3 \ 4	3	6.785	0.785	1	1.477	-0.523	2	5.270	1.270
3 \ 5	3	6.785	0.785	1	1.477	-0.523	2	5.270	1.270
3 \ 6	3	6.480	0.48	1	1.437	-0.563	2	5.000	1.000
3 \ 7	3	5.702	-0.298	1	1.268	-0.732	2	4.370	0.370
3 \ 8	3	7.298	1.298	1	2.728	0.728	2	4.530	0.530
3 \ 18	3	0.704	-5.296	1	0.469	-1.531	2	0.210	-3.790
4 \ 18	3	3.525	-2.475	1	0.176	-1.824	2	3.330	-0.670
5 \ 18	3	3.525	-2.475	1	0.176	-1.824	2	3.330	-0.670
6 \ 18	3	3.306	-2.694	1	0.158	-1.842	2	3.130	-0.870
7 \ 18	3	3.356	-2.644	1	0.147	-1.853	2	3.180	-0.820
8 \ 18	3	2.953	-3.047	1	0.126	-1.874	2	2.810	-1.190
9 \ 11	3	1.328	-4.672	1	0.301	-1.699	2	1.030	-2.970
10 \ 11	3	1.369	-4.631	1	0.337	-1.663	2	1.030	-2.970
12 \ 16	3	4.813	-1.187	1	3.653	1.653	2	1.150	-2.850
14 \ 15	3	6.931	0.931	1	0.000	-2.000	2	5.030	1.030
23 \ 24	3	7.473	1.473	1	0.000	-2.000	2	5.840	1.840

[1] Correspondence to: Özge Karadağ E-mail: ozgekaradag@hacettepe.edu.tr

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Assessment of SNP-SNP interactions by using square contingency table analysis

Abstract