Linkage Disequilibrium - Example: Human Leukocyte Antigen (HLA) Alleles

Example: Human Leukocyte Antigen (HLA) Alleles

HLA constitutes a group of cell surface antigens as MHC of humans. Because HLA genes are located at adjacent loci on the particular region of a chromosome and presumed to exhibit epistasis with each other or with other genes, a sizable fraction of alleles are in linkage disequilibrium.

An example of such linkage disequilibrium is between HLA-A1 and B8 alleles in unrelated Danes referred to by Vogel and Motulsky (1997).

Because HLA is codominant and HLA expression is only tested locus by locus in surveys, LD measure is to be estimated from such a 2x2 table to the right.

expression frequency of antigen :

;

expression frequency of antigen :

;

frequency of gene :

,

and

.

Denoting the '―' alleles at antigen i to be 'x,' and at antigen j to be 'y,' the observed frequency of haplotype xy is

and the estimated frequency of haplotype xy is

.

Then LD measure is expressed as

.

Standard errors are obtained as follows:

,

.

Then, if

exceeds 2 in its absolute value, the magnitude of is large statistically significantly. For data in Table 1 it is 20.9, thus existence of statistically significant LD between A1 and B8 in the population is admitted.

Table 2 shows some of the combinations of HLA-A and B alleles where significant LD was observed among Caucasians.

Vogel and Motulsky (1997) argued how long would it take that linkage disequilibrium between loci of HLA-A and B disappeared. Recombination between loci of HLA-A and B was considered to be of the order of magnitude 0.008. We will argue similarly to Vogel and Motulsky below. In case LD measure was observed to be 0.003 in Caucasians in the list of Mittal it is mostly non-significant. If had reduced from 0.07 to 0.003 under recombination effect as shown by, then . Suppose a generation took 25 years, this means 10,000 years. The time span seems rather short in the history of humans. Thus observed linkage disequilibrium between HLA-A and B loci might indicate some sort of interactive selection.

The presence of linkage disequilibrium between an HLA locus and a presumed major gene of disease susceptibility corresponds to any of the following phenomena:

• Relative risk for the person having a specific HLA allele to become suffered from a particular disease is greater than 1.
• The HLA antigen frequency among patients exceeds more than that among a healthy population. This is evaluated by value to exceed 0.

• 2x2 association table of patients and healthy controls with HLA alleles shows a significant deviation from the equilibrium state deduced from the marginal frequencies.

(1) Relative risk

Relative risk of an HLA allele for a disease is approximated by the odds ratio in the 2x2 association table of the allele with the disease. Table 3 shows association of HLA-B27 with ankylosing spondylitis among a Dutch population. Relative risk of this allele is approximated by

.

Woolf's method is applied to see if there is statistical significance. Let

and

.

Then

follows the chi-square distribution with . In the data of Table 3, the significant association exists at the 0.1% level. Haldane's modification applies to the case when either of is zero, where replace and with

and

,

respectively.

In Table 4, some examples of association between HLA alleles and diseases are presented.

(1a) Allele frequency excess among patients over controls

Even high relative risks between HLA alleles and the diseases were observed, only the magnitude of relative risk would not be able to determine the strength of association. value is expressed by

,

where and are HLA allele frequencies among patients and healthy populations, respectively. In Table 4, column was added in this quotation. Putting aside 2 diseases with high relative risks both of which are also with high values, among other diseases, juvenile diabetes mellitus (type 1) has a strong association with DR4 even with a low relative risk.

(2) Discrepancies from expected values from marginal frequencies in 2x2 association table of HLA alleles and disease

This can be confirmed by test calculating

.

where . For data with small sample size, such as no marginal total is greater than 15 (and consequently ), one should utilize Yates's correction for continuity or Fisher's exact test.