Genetic association studies of common variants in case control samples usually compare directly the differences in frequencies of an allele or genotype between case and control populations, with the assumption that a significant difference in frequencies is indication to association between the locus and increase risk of disease. Many statistical tests for binomial or multinomial proportions can be used for such analysis, including Fisher's exact test, \(\chi^2\) test and Cochran-Armitage Trend Test. For rare variants association tests, single variant analysis will be underpowered (see Sahai H. 1996(H. Sahai and A. Khurshid (1996) Formulas and tables for the determination of sample sizes and power in clinical trials for testing differences in proportions for the matched pair design: a review. Fundamental & Clinical Pharmacology doi:10.1111/j.1472-8206.1996.tb00614.x. http://doi.wiley.com/10.1111/j.1472-8206.1996.tb00614.x) for power and sample size estimation for tests for proportions). Still single variant tests can be useful when only summary statistics is avaiable for controls (e.g., only MAF is available from public database), or one wants to compare the differences in frequency between populations for other purposes. For single variants analysis we offer the Fisher's exact test routine which is abit conservative but guarantees type I error control for small sample sizes. Fisher's test method in VAT is implemented as a special function for vtools update command, which is very efficient.
For Single variant tests adjusting for covariates, or tests for quantitative phenotypes, please refer to the multivariate methods in VAT.
The function Fisher_exact(num_var_alleles_case, num_var_alleles_ctrl, 2*num_gt_case, 2*num_gt_ctrl) tests for association of an alternate allele with a phenotype (i.e., case or control) status. Given a variant site to be tested, the function takes in the following 4 parameters, that are obtainable through vtools functions:
num_var_alleles_case: number of alternative alleles for the case samplesnum_var_alleles_ctrl: number of alternative alleles for the control samplesnum_gt_case: total number of genotypes for the case samplesnum_gt_ctrl: total number of genotypes for the control samplesvtools update variant --from_stat 'num_gt_case=#(GT)' 'num_var_alleles_case=#(alt)' --samples "filename in ('V1.vcf', 'V2.vcf')"
Counting variants: 100% [================================] 2 69.2/s in 00:00:00
INFO: Adding field num_var_alleles_case
INFO: Adding field num_gt_case
Updating variant: 100% [==============================] 1,341 41.9K/s in 00:00:00
INFO: 1340 records are updated
vtools update variant --from_stat "num_gt_ctrl=#(GT)" "num_var_alleles_ctrl=#(alt)" --samples "filename = 'V3.vcf'"
Counting variants: 100% [===============================] 1 220.3/s in 00:00:00
INFO: Adding field num_var_alleles_ctrl
INFO: Adding field num_gt_ctrl
Updating variant: 100% [=============================] 988 42.7K/s in 00:00:00
INFO: 987 records are updated
And calcualte p-value for the Fisher's exact test:
vtools update variant --set "prop_pval=Fisher_exact(num_var_alleles_case, num_var_alleles_ctrl, 2*num_gt_case, 2*num_gt_ctrl)"
INFO: Adding field prop_pva