Estimating linkage disequilibrium from genotypes under Hardy-Weinberg equilibrium

BMC Genomic Data

Table 4 Selected results from the analysis of APOE dataset

Loci pair	Real count		MIDAS		CubeX 1st solution		CubeX 2nd solution		CML		Possible alternative solution?	CML alternative solution		LRT	CML Decision
1–2	14	116	14	116	14	116	NA		14	116	No	NA		NA	NA
1–2	0	30	0	30	0	30	NA		0	30	No	NA		NA	NA
1–3	69	61	64	66	64	66	NA		64	66	No	NA		NA	NA
1–3	17	13	22	8	22	8	NA		22	8	No	NA		NA	NA
1–5	120	10	121	9	121	9	120	10	121	9	Yes	120	10	0.15	Accept alternative
1–5	30	0	29	1	29	1	30	0	29	1	Yes	30	0	0.15	Accept alternative
1–9	9	121	9	121	9	121	12	118	9	121	Yes	12	118	1.84	Accept alternative
1–9	3	27	3	27	3	27	0	30	3	27	Yes	0	30	1.84	Accept alternative
4–8	98	3	99	2	99	2	98	3	99	2	Yes	98	3	0.06	Accept alternative
4–8	59	0	58	1	58	1	59	0	58	1	Yes	59	0	0.06	Accept alternative
5–7	141	9	141	9	141	9	131	19	141	9	Yes	131	19	45.91	Reject alternative
5–7	0	10	0	10	0	10	10	0	0	10	Yes	10	0	45.91	Reject alternative
5–9	12	138	11	139	11	139	12	138	11	139	Yes	12	138	1.37	Accept alternative
5–9	0	10	1	9	1	9	0	10	1	9	Yes	0	10	1.37	Accept alternative

Selected results from the analysis of APOE dataset. The second column shows the real haplotype counts which had been experimentally identified. MIDAS estimates are shown in the next column. CubeX 1st solution refers to the α or β solution set. CubeX 2nd solution refers to the γ solution set should it exist. Constrained ML’s estimates are presented in the sixth column. Log-likelihood was maximised within the entire feasible region. The next step is to decide whether a simpler solution is possible (e.g. there are only 3 haplotypes instead of 4). If we cannot rule of the possibility of having a simpler solution, the log-likelihood is then maximised within the restricted range, with 2 free parameters. LRT statistics are reported, which equal 2 times the differences between the log-likelihoods of the two solutions. If the LRT statistic is greater than \( {\chi}_{1,0.95}^2=3.84 \), we reject the alternative (simpler) solution at 5% confidence level. Complete results are shown in Additional file 1

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