An EM algorithm based on an internal list for estimating haplotype distributions of rare variants from pooled genotype data

Kuk, Anthony YC; Li, Xiang; Xu, Jinfeng

doi:10.1186/1471-2156-14-82

Table 3 Average estimates of haplotype frequencies for a 25 loci case

From: An EM algorithm based on an internal list for estimating haplotype distributions of rare variants from pooled genotype data

		k=2					k=4
Position of ‘1’	TRUE	CDMLE	EML	EM- CDL	EM-ATCDL	EM-TCDL	CDMLE	EM-CDL	EM-ATCDL	EM-TCDL
					(a) n=100
None	0.7995	0.7973	0.8279	0.8283	0.8003	0.8067	0.7961	0.8535	0.7957	0.8119
		(0.0232)	(0.0169)	(0.0170)	(0.0215)	(0.0192)	(0.0204)	(0.0118)	(0.0179)	(0.0144)
1	0.0509	0.0508	0.0412	0.0412	0.0477	0.0477	0.0502	0.0344	0.0457	0.0494
		(0.0155)	(0.0115)	(0.0115)	(0.0119)	(0.0112)	(0.0152)	(0.0083)	(0.0093)	(0.0086)
2	0.0034	0.0036	0.0019	0.0019	0.0031	0.0024	0.0032	0.0008	0.0028	0.0020
		(0.0040)	(0.0022)	(0.0022)	(0.0025)	(0.0027)	(0.0044)	(0.0012)	(0.0023)	(0.0029)
3	0.0436	0.0441	0.0353	0.0353	0.0425	0.0408	0.0435	0.0277	0.0396	0.0411
		(0.0139)	(0.0104)	(0.0104)	(0.0112)	(0.0107)	(0.0144)	(0.0077)	(0.0097)	(0.0080)
5	0.0034	0.0035	0.0019	0.0019	0.0031	0.0027	0.0031	0.0008	0.0028	0.0015
		(0.0039)	(0.0021)	(0.0021)	(0.0028)	(0.0029)	(0.0043)	(0.0011)	(0.0017)	(0.0024)
6	0.0034	0.0027	0.0017	0.0016	0.0029	0.0022	0.0038	0.0013	0.0030	0.0019
		(0.0035)	(0.0021)	(0.0021)	(0.0028)	(0.0030)	(0.0050)	(0.0017)	(0.0022)	(0.0026)
9	0.0073	0.0092	0.0056	0.0056	0.0085	0.0087	0.0073	0.0029	0.0074	0.0079
		(0.0065)	(0.0039)	(0.0039)	(0.0046)	(0.0052)	(0.0066)	(0.0026)	(0.0045)	(0.0062)
11	0.0034	0.0041	0.0022	0.0022	0.0036	0.0029	0.0032	0.0008	0.0027	0.0016
		(0.0048)	(0.0025)	(0.0025)	(0.0029)	(0.0031)	(0.0046)	(0.0013)	(0.0021)	(0.0025)
15	0.0034	0.0039	0.0021	0.0021	0.0032	0.0026	0.0034	0.0009	0.0029	0.0017
		(0.0052)	(0.0028)	(0.0028)	(0.0032)	(0.0033)	(0.0050)	(0.0013)	(0.0021)	(0.0025)
19	0.0068	0.0069	0.0039	0.0039	0.0061	0.0055	0.0075	0.0022	0.0058	0.0051
		(0.0056)	(0.0031)	(0.0031)	(0.0040)	(0.0044)	(0.0066)	(0.0020)	(0.0031)	(0.0042)
20	0.0068	0.0073	0.0041	0.0041	0.0061	0.0058	0.0080	0.0023	0.0057	0.0051
		(0.0060)	(0.0035)	(0.0035)	(0.0042)	(0.0045)	(0.0065)	(0.0020)	(0.0028)	(0.0040)
21	0.0034	0.0038	0.0020	0.0020	0.0032	0.0029	0.0041	0.0011	0.0033	0.0022
		(0.0041)	(0.0022)	(0.0022)	(0.0027)	(0.0031)	(0.0051)	(0.0014)	(0.0023)	(0.0028)
22	0.0102	0.0117	0.0070	0.0070	0.0095	0.0099	0.0110	0.0043	0.0096	0.0091
		(0.0075)	(0.0047)	(0.0047)	(0.0053)	(0.0054)	(0.0085)	(0.0033)	(0.0046)	(0.0056)
23	0.0034	0.0032	0.0018	0.0018	0.0028	0.0024	0.0038	0.0010	0.0029	0.0019
		(0.0039)	(0.0023)	(0.0023)	(0.0028)	(0.0030)	(0.0045)	(0.0012)	(0.0021)	(0.0026)
24	0.0102	0.0096	0.0060	0.0060	0.0095	0.0098	0.0114	0.0043	0.0098	0.0118
		(0.0065)	(0.0041)	(0.0041)	(0.0051)	(0.0057)	(0.0076)	(0.0028)	(0.0047)	(0.0057)
1, 3	0.0040	0.0048	0.0039	0.0039	0.0045	0.0043	0.0071	0.0049	0.0061	0.0052
		(0.0049)	(0.0037)	(0.0037)	(0.0041)	(0.0040)	(0.0070)	(0.0040)	(0.0046)	(0.0048)
1, 9	0.0029	0.0030	0.0021	0.0021	0.0023	0.0018	0.0051	0.0023	0.0028	0.0017
		(0.0035)	(0.0024)	(0.0024)	(0.0033)	(0.0033)	(0.0055)	(0.0021)	(0.0031)	(0.0032)
6, 7	0.0204	0.0210	0.0150	0.0148	0.0215	0.0195	0.0203	0.0104	0.0210	0.0219
		(0.0098)	(0.0072)	(0.0072)	(0.0075)	(0.0077)	(0.0105)	(0.0043)	(0.0068)	(0.0060)
3, 14	0.0034	0.0035	0.0021	0.0021	0.0020	0.0028	0.0031	0.0012	0.0015	0.0021
		(0.0037)	(0.0022)	(0.0022)	(0.0032)	(0.0031)	(0.0038)	(0.0015)	(0.0024)	(0.0026)
3, 6, 7	0.0034	0.0037	0.0028	0.0029	0.0025	0.0030	0.0047	0.0028	0.0022	0.0016
		(0.0047)	(0.0036)	(0.0036)	(0.0044)	(0.0047)	(0.0053)	(0.0025)	(0.0033)	(0.0035)
1, 6, 7, 24	0.0034	0.0031	0.0021	0.0021	0.0006	0.0006	0.0036	0.0018	0.0006	0.0000
		(0.0033)	(0.0023)	(0.0023)	(0.0023)	(0.0021)	(0.0037)	(0.0018)	(0.0017)	(0.0004)
1, 12, 13, 22, 25	0.0034	0.0037	0.0024	0.0024	0.0026	0.0029	0.0038	0.0016	0.0005	0.0025
		(0.0038)	(0.0025)	(0.0025)	(0.0031)	(0.0029)	(0.0035)	(0.0015)	(0.0018)	(0.0027)
Sum of remaining		0.0376	0.0248	0.0248	0.0117	0.0124	0.0893	0.0366	0.0255	0.0109
haplotype probabilities
Sum of probabilities		0.0247	0.0241	0.0244	0.0218	0.0286	0.0296	0.0285	0.0179	0.0367
of missed haplotypes
Sum of squared errors		0.00166	0.00186	0.00189	0.00110	0.00106	0.00201	0.00415	0.00091	0.00089
Length of list		26.77	116.28	26.77	19.06	18.25	45.23	45.23	25.38	15.62
SD of length		(3.26)	(81.30)	(3.26)	(3.03)	(2.18)	(3.94)	(3.94)	(4.78)	(2.40)
					(a) *n=200*
None	0.7995	0.7979	0.8248	0.8250	0.7981	0.8009	0.7990	0.8451	0.7970	0.8040
		(0.0150)	(0.0117)	(0.0117)	(0.0148)	(0.0132)	(0.0154)	(0.0086)	(0.0133)	(0.0125)
1	0.0509	0.0514	0.0433	0.0433	0.0492	0.0503	0.0502	0.0387	0.0462	0.0507
		(0.0103)	(0.0082)	(0.0082)	(0.0089)	(0.0088)	(0.0121)	(0.0069)	(0.0077)	(0.0080)
2	0.0034	0.0035	0.0020	0.0020	0.0033	0.0031	0.0037	0.0011	0.0030	0.0024
		(0.0032)	(0.0018)	(0.0018)	(0.0024)	(0.0026)	(0.0035)	(0.0011)	(0.0013)	(0.0021)
3	0.0436	0.0430	0.0362	0.0362	0.0435	0.0426	0.0441	0.0322	0.0406	0.0426
		(0.0092)	(0.0075)	(0.0075)	(0.0082)	(0.0074)	(0.0105)	(0.0054)	(0.0071)	(0.0065)
5	0.0034	0.0033	0.0018	0.0018	0.0032	0.0028	0.0034	0.0011	0.0030	0.0023
		(0.0028)	(0.0016)	(0.0016)	(0.0020)	(0.0023)	(0.0035)	(0.0011)	(0.0013)	(0.0021)
6	0.0034	0.0038	0.0023	0.0023	0.0033	0.0031	0.0033	0.0014	0.0028	0.0022
		(0.0031)	(0.0019)	(0.0020)	(0.0021)	(0.0025)	(0.0035)	(0.0013)	(0.0014)	(0.0019)
9	0.0073	0.0080	0.0054	0.0054	0.0079	0.0088	0.0081	0.0036	0.0070	0.0092
		(0.0038)	(0.0026)	(0.0026)	(0.0032)	(0.0037)	(0.0043)	(0.0019)	(0.0026)	(0.0031)
11	0.0034	0.0032	0.0018	0.0018	0.0030	0.0027	0.0032	0.0010	0.0029	0.0023
		(0.0026)	(0.0016)	(0.0016)	(0.0022)	(0.0024)	(0.0031)	(0.0011)	(0.0015)	(0.0021)
15	0.0034	0.0035	0.0019	0.0019	0.0030	0.0028	0.0038	0.0012	0.0031	0.0028
		(0.0033)	(0.0018)	(0.0018)	(0.0023)	(0.0025)	(0.0031)	(0.0010)	(0.0015)	(0.0021)
19	0.0068	0.0063	0.0039	0.0039	0.0062	0.0061	0.0066	0.0026	0.0056	0.0057
		(0.0039)	(0.0025)	(0.0025)	(0.0029)	(0.0034)	(0.0041)	(0.0015)	(0.0018)	(0.0026)
20	0.0068	0.0068	0.0042	0.0042	0.0062	0.0063	0.0063	0.0026	0.0054	0.0059
		(0.0039)	(0.0025)	(0.0025)	(0.0028)	(0.0030)	(0.0038)	(0.0015)	(0.0022)	(0.0026)
21	0.0034	0.0038	0.0022	0.0022	0.0035	0.0032	0.0037	0.0012	0.0031	0.0025
		(0.0035)	(0.0020)	(0.0020)	(0.0023)	(0.0026)	(0.0034)	(0.0011)	(0.0015)	(0.0021)
22	0.0102	0.0105	0.0071	0.0071	0.0097	0.0103	0.0112	0.0052	0.0086	0.0098
		(0.0058)	(0.0037)	(0.0037)	(0.0041)	(0.0041)	(0.0052)	(0.0022)	(0.0030)	(0.0029)
23	0.0034	0.0039	0.0022	0.0022	0.0031	0.0030	0.0035	0.0011	0.0030	0.0025
		(0.0027)	(0.0015)	(0.0016)	(0.0021)	(0.0022)	(0.0030)	(0.0010)	(0.0015)	(0.0021)
24	0.0102	0.0105	0.0069	0.0069	0.0107	0.0114	0.0106	0.0049	0.0088	0.0115
		(0.0050)	(0.0033)	(0.0033)	(0.0043)	(0.0042)	(0.0059)	(0.0023)	(0.0036)	(0.0043)
1, 3	0.0040	0.0046	0.0037	0.0037	0.0041	0.0040	0.0052	0.0041	0.0049	0.0047
		(0.0041)	(0.0032)	(0.0032)	(0.0033)	(0.0034)	(0.0048)	(0.0029)	(0.0030)	(0.0031)
1, 9	0.0029	0.0036	0.0026	0.0026	0.0030	0.0022	0.0030	0.0018	0.0027	0.0010
		(0.0027)	(0.0019)	(0.0019)	(0.0026)	(0.0028)	(0.0031)	(0.0015)	(0.0022)	(0.0020)
6, 7	0.0204	0.0191	0.0148	0.0146	0.0215	0.0199	0.0206	0.0124	0.0212	0.0223
		(0.0067)	(0.0048)	(0.0047)	(0.0056)	(0.0054)	(0.0073)	(0.0037)	(0.0048)	(0.0046)
3, 14	0.0034	0.0030	0.0019	0.0019	0.0020	0.0027	0.0036	0.0015	0.0025	0.0029
		(0.0029)	(0.0018)	(0.0018)	(0.0026)	(0.0025)	(0.0026)	(0.0011)	(0.0020)	(0.0018)
3, 6, 7	0.0034	0.0039	0.0029	0.0029	0.0021	0.0027	0.0038	0.0025	0.0024	0.0019
		(0.0035)	(0.0025)	(0.0025)	(0.0029)	(0.0031)	(0.0041)	(0.0022)	(0.0028)	(0.0029)
1, 6, 7, 24	0.0034	0.0039	0.0028	0.0028	0.0007	0.0006	0.0039	0.0020	0.0002	0.0000
		(0.0025)	(0.0019)	(0.0019)	(0.0019)	(0.0018)	(0.0026)	(0.0014)	(0.0009)	(0.0002)
1, 12, 13, 22, 25	0.0034	0.0035	0.0025	0.0024	0.0027	0.0032	0.0033	0.0017	0.0004	0.0031
		(0.0022)	(0.0016)	(0.0017)	(0.0023)	(0.0023)	(0.0026)	(0.0013)	(0.0014)	(0.0020)
Sum of remaining		0.0340	0.0227	0.0227	0.0102	0.0074	0.0703	0.0310	0.0255	0.0076
haplotype probabilities
Sum of probabilities		0.0103	0.0097	0.0100	0.0132	0.0173	0.0131	0.0118	0.0111	0.0200
of missed haplotypes
Sum of squared errors		0.00077	0.00125	0.00126	0.00059	0.00054	0.00101	0.00281	0.00055	0.00048
Length of list		39.65	152.30	39.65	22.08	19.63	71.24	71.24	29.29	19.81
SD of length		(3.90)	(71.65)	(3.90)	(4.20)	(3.70)	(5.02)	(5.02)	(5.82)	(5.22)

Average estimates of haplotype frequencies for a 25 loci case based on 100 simulations of n pools of k individuals each using CDMLE (collapsed data MLE), EML (EM with combinatorially determined list), EM-CDL (EM with CD list), EM-ATCDL (augmented and trimmed CD list) and EM-TCDL (CD list with trimming and no augmentation), with standard errors in parentheses.

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