Chi-square test• Pearson's chi-square (χ2) test is the best-known of

several chi-square tests. It is mostly used to assess the tests of goodness of fit.

• The usual rule of thumb is that the chi-square test is not suitable when the expected values in any of the cells of the table, given the margins, is below 5, the sampling distribution of the test statistic that is calculated is only approximately equal to the theoretical chi-squared distribution.

n

i i

ii

E

EO

1

22 )(

case controlAllele 1 a b a+bAllele 2 c d c+d

a+c b+d n=a+b+c+d

Genetic Models

• Genotypic P value

A BCases 2a+b b+2c

Controls 2d+e e+2f

AA AB BBCases a b c

Controls d e f

• Allelic P value

a= the number of AA in cases; b=the number of AB in cases; c=the number of BB in casesd= the number of AA in controls; e=the number of AB in controls; c=the number of BB in controls

Genetic Models

A(0) B(r2)Cases 2a+b b+2c

Controls 2d+e e+2f

AA(0) AB(r) BB(2r)Cases a b c

Controls d e f

Multiplicative model:r-fold increased risk for AB, r2 increased risk for BB. Analyzed by allele, not by genotype

Additive model:r-fold increased risk for AB, 2r increased risk for BB. Genotypes analysed by Armitages’s test for trend

Genetic Models

AA AB+BBCases a b+c

Controls d e+f

AA+AB BBCases a+b c

Controls d+e f

Dominant model:Allele B increases risk

Recissive model:Two copies of allele B required for increased risk

Fisher’s exact test

• Fisher's exact test is a statistical significance test used in the analysis of contingency tables where sample sizes are small.

• P= !!!!!)!()!()!()!(

dcbandbcadcba

can

cdc

aba

case controlAllele 1 a b a+bAllele 2 c d c+d

a+c b+d n=a+b+c+d

ODDs Ratio

• The odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group, or to a sample-based estimate of that ratio.

• Odds of allele A in Cases = a x (a + b)/ b x (a + b) = a / b• Odds of allele B in Controls = d x (c + d) / d x (c + d) = c / d• OR=(a d)/(b c)

A B

Cases a b

Controls c d

ODDs Ratio

AA AB BBCases a b c

Controls d e f

Suppose B is the risk allele

ORhomo = ORBB= (c d)/(a f)ORhetero = ORAB= (b d)/(a e)

Population Attributable Risk (PAR)

100)1(1

)1(%

ORPe

ORPePAR

Pe is proportion of exposure in general population.People usually take proportion of exposure in the controls as Pe.(PAR is the reduction in incidence that would be observed if the population were extirely unexposed compared with its current (actual) exposure pattern)

The term permutation is used with different but closely related meanings. They all relate to the notion of mapping the elements of a set to other elements of the same set, i.e., exchanging (or "permuting") elements of a set

Permutation Test

Permutation Test

Permutation Test• Permutation procedures provide a

computationally intensive approach to generating significance levels empirically.

• In samples of unrelated individuals, one simply swaps labels to provide a new dataset sampled under the null hypothesis.

• Because the permutation schemes preserve the correlational structure between SNPs, this provides a less stringent correction for multiple testing in comparison to the Bonferroni, which assumes all tests are independent.

Power of association study

Frequency of haplotype

RR = 1.5 RR = 2.0 RR = 3.0

80% 90% 80% 90% 80% 90%

0.05 2951 3465 888 1043 296 348

0.10 1594 2204 490 576 170 199

0.15 1152 1352 356 424 129 152

0.20 939 1102 300 352 111 130

0.25 819 962 266 313 101 118

0.30 747 877 247 290 96 113

Number of patients and controls required to have 80% or 90% power to detect an association with a two-sided P-value of 10-5 for various risk ratios and population frequency of an allele/haplotype