Question

You are interested in identifying SNPs associated with diabetes. You conduct a case-control study using 500,000 SNPs. The allele frequencies of one of the SNPs between cases and controls are listed below:

	Cases	Controls
G	2,300	4,000
A	3,500	3,360

Using a chi-square test, determine if there is a significant association of this SNP with diabetes. Show your work. Include the chi-square statistic, the degrees of freedom, and the p-value.

Given your p-value, does this SNP have a significant association diabetes?

Answer 1

To conduct Chi square test we first compute the expected frequencies:

In general, the expected frequency for a cell in the i^th row and the j^th column is equal to

where E_i,j is the expected frequency for cell i,j, Ti is the total for the i^th row, T_j is the total for the j^th column, and T is the total number of observations.

The expected frequencies are given in the table below ( the bracket value shows the expected frequencies)

The chi- square statistics is given by :

= 81.81 + 64.47 +75.13 + 59.20

= 280.606

The P-value for the chi-square test is P(>X²), the probability of observing a value at least as extreme as the test statistic for a chi-square distribution with (r-1)(c-1) degrees of freedom.

The p -value for χ² = 280.606 , for df = (2-1) (2-1) = 1

P(χ² > 280.606) = < 0.00001

Since p-value < 0.05, hence null hypothesis is rejected ate 5% significant level.

Thus we can conclude that SNP have a significant association diabetes.