Systemic lupus erythematosus and rheumatoid arthritis

Patients Controls 
Allele 
Observed Observed 
A1 
Obs (PA1) 
Obs (CA1) 
A2 
Obs (PA2) 
Obs (CA2) 
If calculating the odds ratio for allele A1 then: 
OR = 
( 
Obs (PA1) / Obs (PA2) 
) / ( 
Obs (CA1)
 / 
Obs (CA2)
 )
= 
= 
( 
Obs (PA1) x Obs (CA2) 
) / ( 
Obs (CA1)
 
x
 
Obs (PA2)
 )
If the odds ratio is greater than 1.00, the allele A1 confers an increased risk for 
disease compared with allele A2. However, if the odds ratio is less than 1.00, 
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the allele confers a protective effect. A significant association is fulfilled when 
the confidence interval (CI) does not include 1.00.
An important tool when studying multiple SNPs in a region is linkage 
disequilibrium (LD). Alleles of two neighbouring SNPs have a tendency of 
segregating together and when linked alleles are associated it is called linkage 
disequilibrium. LD is the non-random, or non-independent, association between 
alleles at two or more loci. For example, allele A and allele B at different loci 
are at allele frequencies p(A) and p(B) in the population. If the loci are 
independent, one would expect the AB haplotype at a frequency of p(A)p(B). If 
the AB haplotype frequency is either higher or lower than p(A)p(B), meaning 
that the alleles are observed together, then the two loci are said to be in LD.
12
LD between two SNPs or markers is measured by D’ or by the correlation 
coefficient, r
2
. Both the D’ and r
2
measures are based on the pairwise-
disequilibrium coefficient, D, which is the difference between the probability of 
observing alleles from two markers on the same haplotype and observing them 
independently in the population.
13
D’ values ranges from 0 to 1 and a D’ value 
of 1 means that all copies of the minor allele for one SNP are always observed 
with one of the two alleles of the other SNP. A D’ value of 0 means that the two 
loci are randomly inherited. The r
2
measure ranges between 0 and 1 and an r
2
value of 0 also implies independence. However, an r
2
value of 1 has a more 
strict interpretation than D’; r
2
=1.0 when the allele frequency are identical for 
the two SNPs. With an r
2
of 1.0 for two SNPs means that given the allele 
frequencies for one SNP, one can predict the allele frequencies for the other 
SNP. D’ is very unstable for small sample sizes so r
2
is used more frequently in 
the assessment of LD. Knowledge about LD is invaluable when constructing 
haplotypes and interpreting results from genetic associations. Associations 
between an allele and a phenotype can occur due to a number of reasons. It 
could be a true association, by chance or it could be an artefact owing to the 
allele being in LD with the real phenotype causing allele. LD is also very useful 
when fine-mapping regions of interest. For example, the 
PTPN22
gene harbours 
47 SNPs (Figure 5) according to the build 36 assembly from the HapMap data. 
Using pair-wise tagging with a r
2
threshold of 0.8, only 10 of those 47 SNPs 
(called tagSNPs) are necessary to genotype since their allele frequencies can be 
used to predict the allele frequencies of the other 37 SNPs. 
There are some pitfalls in genetic statistics. Type I errors (the test result is false 
positive) and type II errors (the test result is false negative) are normally 
corrected for using the conservative Bonferroni correction. Another way of 
correcting for multiple testing is to perform a permutation test, which is a 
computerized test where 
χ
2
-tests are calculated based on the observed 
frequencies from randomised samplings of the test population. 
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Figure 5.
LD pattern with r
2
values for the SNPs in the PTPN22 gene. r
2
values are presented in a 
grey scale, where black corresponds to a r
2
value of 1.0 and white corresponds to a r
2
value of 0.