Hardy-Weinberg Equilibrium

WISARD provides several helpful measures for variants in each chromosome. This section describes about

• Summary
  • Founder-only
  • All-individual
• Filtering variants by HWE test

Summary [top]

Deviations from Hardy-Weinberg equilibrium (HWE) can indicate inbreeding, population stratification, and genotyping errors. Hardy-Weinberg Equilibrium test is often used for quality control (QC) of genetic variant. For case-control sample, HWE test with controls is recommended for QC and for cohort-based sample, HWE test with all samples is recommended. In particular, HWE test only with cases is sometimes useful for association analysis. WISARD provides HWE test and variant filtering based on the result. Small p-value indicates some evidence of Hardy-Weinberg disequilibrium.

WISARD provides two statistics for HWE: exact method (Wigginton et al AJHG 2005) and chi-sqaure method. While p-value from the exact method is always stable, the p-value from chi-square method can be unstable if sample size is relatively small.

For family-based samples, WISARD calculates HWE for two different sets of samples: founder-only and all-individuals. It should be noted that estimates from both strategies are same for population-based samples (such as case-control design), but for family-based samples, their estimates can be substantially different.

Founder-only

Founder-only indicates that HWE for each variant is calculated by using only founders and it can be calculated with WISARD by using "--hwe" or "--hwe founder" option. This approach is computationally fast and easy to compute. However, if there are many founders with missing genotype, this approach is not efficient anymore. WISARD calculates HWE in this way by default and the output file extension is ".hwe".

Perform HWE test with founders

C:\Users\WISARD> wisard --bed test_miss0.bed --hwe founder

Above code produces the following [prefix].founders.hwe.

founders.hwe is...			A computed HWE using only founder samples (TSV)
Column	Format	Modifier	Description
CHR	integer	NONE	Incorporated number of individuals for the test
VARIANT	integer	NONE	Incorporated number of individuals for the test
POS	integer	NONE	Incorporated number of individuals for the test
ALT	integer	NONE	Incorporated number of individuals for the test
ANNOT	integer	NONE	Incorporated number of individuals for the test
GENO	integer/integer/integer	NONE	Number of alleles for each of aa/Aa/AA, respectively
O(HET)	integer	NONE	Observed number of heterozygotes
E(HET)	real	NONE	Expected number of heterozygotes
STAT_HWE	real	NONE	Statistic of Hardy-Weinberg Equilibrium test
P_HWE	real	NONE	Computed exact p-value of HWE test
NIND	integer	NONE	Incorporated number of individuals for the test

All-individual

This approach is computationally fast and easy to compute. However nonfounders' genotype is not informative for HWE if founders' genotype is known. If family sizes are heterogeneous, the estimaed HWE using all individuals can be inefficient. In order to calculate HWE using all individuals, use option "--hwe all".

Perform HWE test with all individuals

C:\Users\WISARD> wisard --bed test_miss0.bed --hwe all

Above code produces the following [prefix].all.hwe.

all.hwe is...			A computed HWE using all samples (TSV)
Column	Format	Modifier	Description
CHR	Positive integer	NONE	The rank of least conditional variance
VARIANT	Positive integer	NONE	The rank of least conditional variance
POS	Positive integer	NONE	The rank of least conditional variance
ALT	Positive integer	NONE	The rank of least conditional variance
ANNOT	Positive integer	NONE	The rank of least conditional variance
GENO	integer/integer/integer	NONE	Number of alleles for each of aa/Aa/AA, respectively
O(HET)	integer	NONE	Observed number of heterozygotes
E(HET)	real	NONE	Expected number of heterozygotes
STAT_HWE	real	NONE	Statistic of Hardy-Weinberg Equilibrium test
P_HWE	real	NONE	Exact p-value of HWE test
NIND	integer	NONE	Incorporated number of individuals for the test

Filtering variants by HWE test [top]

WISARD provides a simple option to filter variants of which pvalues for HWE are in a certain range by using --filhwe option. In this case, the exact method is applied to calculate p-value for HWE.

NOTE!

The parameter of this option supports range type parameter

Exclude by p-value of HWE test under 1e-7

C:\Users\WISARD> wisard --filhwe "<1e-7" --ped test_miss0.ped

Include by p-value of HWE test greater than 0.05

C:\Users\WISARD> wisard --inchwe "(0.05,1]" --ped test_miss0.ped

In these examples, --hwe option is not specified and thus HWE is calculated by the default method, founder-only. If you want to filter variants with HWE calculated by using all individuals, "--hwe all" option must be added.

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