Systemic lupus erythematosus and rheumatoid arthritis

4. Statistics in genetic association studies 
To check whether the observed distributions of genotypes are as expected the 
Hardy-Weinberg equilibrium (HWE) is calculated.
10
A chi-square (
χ
2
) 
calculation is performed in order to detect significant differences between the 
observed and the expected frequencies. 
χ
2
= 
Σ
(Obs – Exp)
2
/ Exp 
If the significance level is set at 95%, 
χ
2
-values above 3.84 are considered as 
significant deviations from the Hardy-Weinberg equilibrium. 
There are a number of reasons why genotype frequencies of the control 
population could deviate from HWE, 
i.e.
, genotyping errors, too small sample 
size, inbreeding, or population stratification.
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If the patient population deviates 
from HWE it could be due to disease causing mutations. 
If an allele is associated with the disease, the allele frequency is significantly 
more frequent among patients compared with controls. One way of calculating 
the difference is by a conventional 
χ
2
-test. At the statistical significance level of 
95%, p-values equal to or lower than 0.05 are considered significant and thus 
the null hypothesis (
H
0
), 
i.e.
, there is no difference in allele frequencies between 
patients and controls, can be rejected. 
It is also important to know if the association of an allele confers a protective 
effect or a risk. One method of investigating this association is calculation of an 
odds ratio (OR).