Multi-clustering study on the association between human leukocyte antigen-DP-DQ and hepatitis B virus-related hepatocellular carcinoma and cirrhosis in Viet Nam

Table 4 Pairwise linkage disequilibrum results

Hepatitis		rs3077	rs9277535	Cirrhosis		rs3077	rs9277535	HCC		rs3077	rs9277535	Healthy Control		rs3077	rs9277535
rs2856718	D	-0.038	-0.006	rs2856718	D	-0.032	-0.012	rs2856718	D	-0.028	-0.015	rs2856718	D	-0.041	-0.025
	D'	0.340	0.069		D'	0.288	0.117		D'	0.298	0.166		D'	0.272	0.198
	Corr.(R)	-0.173	-0.030		Corr.(R)	-0.146	-0.055		Corr.(R)	-0.136	-0.073		Corr.(R)	-0.175	-0.112
	R2	0.030	0.001		R2	0.021	0.003		R2	0.019	0.005		R2	0.031	0.013
	χ2	28.168	0.874		χ2	10.691	1.498		χ2	9.352	2.651		χ2	19.260	7.903
	P value	< 0.0001	0.350		P value	0.001	0.221		P value	0.002	0.103		P value	< 0.0001	0.005
	n	471	471		n	250	250		n	251	251		n	315	315
rs3077	D		0.072	rs3077	D		0.074	rs3077	D		0.066	rs3077	D		0.109
	D'		0.450		D'		0.419		D'		0.405		D'		0.565
	Corr.(R)		0.391		Corr.(R)		0.385		Corr.(R)		0.387		Corr.(R)		0.496
	R2		0.153		R2		0.148		R2		0.150		R2		0.246
	χ2		143.729		χ2		74.223		χ2		75.122		χ2		155.016
	P value		< 2.2 × 10-16		P value		< 2.2 × 10-16		P value		< 2.2 × 10-16		P value		< 2.2 × 10-16
	n		471		n		250		n		251		n		315

D: The coefficient of linkage disequilibrium. The coefficient of linkage disequilibrium D is not always a convenient measure of linkage disequilibrium because its range of possible values depends on the frequencies of the alleles it refers to. This makes it difficult to compare the level of linkage disequilibrium between different pairs of alleles. Lewontin suggested normalising D by dividing it by the theoretical maximum difference between the observed and expected haplotype frequencies as follows: D'= D/D_max where D_max = max{-P_AP_B, -(1-P_A)} when D < 0; where D_max = min{P_A(1-P_B), (1-P_A)P_B when D > 0. An alternative to D' is the correlation coefficient between pairs of loci, usually expressed as its square, R²: the correlation coefficient between pairs of loci. R² = D²/[P_A(1-P_A) P_B(1-P_B)]. The measures R² and D’ have limits to their ranges and do not range over all values of zero to one for all pairs of loci. The maximum of R² depends on the allele frequencies at the two loci being compared and can only range fully from zero to one where either the allele frequencies at both loci are equal, P_A = P_B when D > 0 or when the allele frequencies have the relationship P_A = 1-P_B when D < 0. While D’ can always take a maximum value of 1, its minimum value for two loci is equal to |R| for those loci. HCC: Hepatocellular carcinoma.