PEDSTATS Tutorial -- Selection Strategies for Hardy-Weinberg Tests

PEDSTATS is able to test markers for Hardy-Weinberg equilibrium using one of three selection strategies (founders only, all individuals, or a set of unrelated individuals selected by the program). In this section, we consider each of these strategies and describe situations where each may be indicated.

Hardy-Weinberg testing using unrelated individuals

In the ideal case, tests of Hardy-Weinberg should be performed using a sample of unrelated individuals. When this convention is followed, tested genotypes will be independent and genotype and allele frequency estimates will free from bias that might be introduced if they were estimated using correlated genotypes.

One possible strategy for choosing an unrelated set of individuals from family data is to select all founders. Although this approach has the advantage of simplicity, when founder genotypes are unavailable, the resulting test may have too few genotypes to ensure adequate power. In this situation, a good alternative is to first identify a set of individuals with a high proportion of markers genotyped. This restricted set can then be used to select a group of unrelated individuals. In addition to providing an independent set of genotypes, this approach will almost always yield a larger genotype sample than a founders only strategy. It also has the advantage of providing a single sample of individuals that can be used for testing across the entire marker set.

Although PEDSTATS also implements a founders only strategy, by default, it will perform Hardy-Weinberg testing on your data using a strategy that focuses on selecting a set of unrelated individuals that have as few missing genotypes as possible. The algorithm for this "selected unrelated" strategy is as follows:

Selected unrelated strategy

For each family f in the pedigree.

1. Let I_f = {I_f1, I_f2 ... I_fn } represent all individuals in family f, and let M be the number of markers in the data set.
   
   
   
2. Select a set G_f of "most genotyped" individuals from I_f.
   
   
   1. For each individual in I_f, calculate the proportion of markers that have been genotyped for that person
      
      p_fi = N_fi / M where N_fi is the number of markers genotyped for I_fi
      
      
   2. Calculate the family-wise maximum proportion of markers genotyped:
      
      P_max(f) = max { p_f1 , p_f2 ... , p_fn }
      
   3. Let G_f represent the set individuals in family f with individual genotype proportion greater than 90% of the family-wise maximum:
      
      G_f = { I_fi : p_fi >= 0.9 * P_max(f) }
      
      
3. Select a set U_f of unrelated, genotyped individuals for family f by iteratively removing candidates from G_f
   
   
   1. Select the individual I_fk in G_f with the fewest relatives and add them to the unrelated set (U_f) .
   
   
   2. Remove I_fk and all individuals related to I_fk from G_f
   
   
   3. If G_f is empty, stop. Otherwise, go to step 3a.
   
   

Founders only strategy

The Hardy-Weinberg test just described selects a single sample of unrelated individuals for testing of all markers. Although this test will outperform a founders only test under most circumstances, if only a small proportion of selected individuals are genotyped for a marker with available founder genotypes, you might find a founders only test to be useful. You can try this out by typing the command:

       pedstats -p asp.ped -d asp.dat --checkFounders

For the asp.ped data set, Hardy-Weinberg tests using just founder individuals cannot be done due to a low number of founder genotypes. When this is the case, PEDSTATS will indicate which markers were not screened.

HARDY-WEINBERG CHECK AMONG FOUNDERS
===================================

The following markers were not tested for Hardy-Weinberg due to a low
number of genotyped individuals:

   MRK1 MRK2 MRK3 MRK4 MRK5 MRK6 MRK7 MRK8 MRK9 MRK10 MRK11 MRK12 MRK13 MRK14
   MRK15 MRK16 MRK17 MRK18 MRK19 MRK20

Hardy-Weinberg testing using all individuals