Cubic exact solutions for the estimation of pairwise haplotype frequencies: implications for linkage disequilibrium analyses and a web tool 'CubeX'

Table 1 Illustrative examples of comparison of CubeX with PHASE [16] and MIDAS [7] (Hill EM).

			Haplotype frequencies (rounded to 5 decimal places)						Haplotype numbers (rounded to nearest haplotype)
Example	SNP pair	Haplotype	REAL frequency	PHASE frequency	MIDAS frequency	CUBEX alpha	CUBEX beta	CUBEX gamma	REAL number	PHASE number	MIDAS number	CUBEX alpha	CUBEX beta	CUBEX gamma
1	Pair1_2	AC	0.0875	0.08689	0.0875	na	0.0875	na	14	14	14	na	14	na
	Pair1_2	AT	0.725	0.72561	0.725	na	0.725	na	116	116	116	na	116	na
	Pair1_2	TC	0	0.00061	0	na	0	na	0	0	0	na	0	na
	Pair1_2	TT	0.1875	0.18689	0.1875	na	0.1875	na	30	30	30	na	30	na
2	Pair1_5	AG	0.75	0.75318	0.75478	0.75478	na	0.75	120	121 *	121 *	121 *	na	120
	Pair1_5	AA	0.0625	0.05932	0.05772	0.05772	na	0.0625	10	9 *	9 *	9 *	na	10
	Pair1_5	TG	0.1875	0.18432	0.18272	0.18272	na	0.1875	30	29 *	29 *	29 *	na	30
	Pair1_5	TA	0	0.00318	0.00478	0.00478	na	0	0	1 *	1 *	1 *	na	0
3	Pair1_9	AT	0.05625	0.06477	0.05633	na	0.0563	0.075	9	10 *	9	na	9	12 *
	Pair1_9	AC	0.75625	0.74773	0.75617	na	0.7562	0.7375	121	120 *	121	na	121	118 *
	Pair1_9	TT	0.01875	0.01023	0.01867	na	0.0187	0	3	2 *	3	na	3	0 *
	Pair1_9	TC	0.16875	0.17727	0.16883	na	0.1688	0.1875	27	28 *	27	na	27	30 *
4	Pair2_3	CG	0.05625	0.04724	0.0465	0.0465	na	na	9	8 *	7 *	7 *	na	na
	Pair2_3	CT	0.03125	0.04026	0.041	0.041	na	na	5	6 *	7 *	7 *	na	na
	Pair2_3	TG	0.48125	0.49026	0.491	0.491	na	na	77	78 *	79 *	79 *	na	na
	Pair2_3	TT	0.43125	0.42224	0.4215	0.4215	na	na	69	68 *	67 *	67 *	na	na
5	pair5_9	GT	0.075	0.07313	0.06664	na	0.0666	0.075	12	12	11 *	na	11 *	12
	pair5_9	GC	0.8625	0.86437	0.87086	na	0.8709	0.8625	138	138	139 *	na	139 *	138
	pair5_9	AT	0	0.00187	0.00836	na	0.0084	0	0	0	1 *	na	1 *	0
	pair5_9	AC	0.0625	0.06063	0.05414	na	0.0541	0.0625	10	10	9 *	na	9 *	10

A selection of comparisons using direct haplotyped APOE data [25]. Full data are present as a additional table. For haplotype numbers (rounded to the nearest number) incorrect answers are marked '*', correct answers are unmarked. Examples: (1) Phase, MIDAS and CubeX (1 solution) give correct answer. (2) Only CubeX gives the correct answer as one of its two solutions. (3) MIDAS and CubeX give the correct answer, PHASE and the other CubeX solution are wrong. (4) All three approaches are wrong. (5) PHASE and CubeX give the correct answer, MIDAS and the other CubeX solution are wrong.

ISSN: 1471-2105