diseq {GeneticsBase} | R Documentation

## Estimate or Compute Confidence Interval for the Single-Marker Disequilibrium

### Description

Estimate or compute confidence interval for single-marker disequilibrium.

### Usage

    diseq.ci(object, marker, R = 1000, conf = 0.95, correct = TRUE, na.rm =
    TRUE, ...)
    diseq.inner(object, marker, ...)

### Arguments

`object` | geneSet object
`marker` | marker names
`R` | Number of bootstrap iterations to use when computing the confidence interval. Defaults to 1000.
`conf` | Confidence level to use when computing the confidence level for D-hat. Defaults to 0.95, should be in (0,1).
`correct` | See details.
`na.rm` | logical. Should missing values be removed?
`...` | optional additional parameters passed

### Details

For a single-gene marker, `diseq` computes the Hardy-Weinberg (dis)equilibrium statistic D, D', r (the correlation coefficient), and r^2 for each pair of allele values, as well as an overall summary value for each measure across all alleles. `print.diseq` displays the contents of a `diseq` object. `diseq.ci` computes a bootstrap confidence interval for this estimate.

For consistency, I have applied the standard definitions for D, D', and r from the Linkage Disequilibrium case, replacing all marker probabilities with the appropriate allele probabilities.

Thus, for each allele pair,

D
  is defined as the half of the raw difference in frequency between the observed number of heterozygotes and the expected number:

  D = 1/2 * ( p(ij) + p(ji) ) - p(i)*p(j)

D'
  rescales D to span the range [-1,1]

  D' = D / Dmax

  where, if D > 0:

  Dmax = min(p(i)p(j), p(j)p(i)) = p(i)p(j)

  or if D < 0:

  Dmax = min( p(i) * (1 - p(j)), p(j)( 1 - (1-p(i) ) ) )

r
  is the correlation coefficient between two alleles, and can be computed by

  r = -D / sqrt( p(i)*(1-p(i)) * p(j)*(1-p(j)) )

where

-
  p(i) defined as the observed probability of allele 'i',
-
  p(j) defined as the observed probability of allele 'j', and
-
  p(ij) defined as the observed probability of the allele pair 'ij'.

When there are more than two alleles, the summary values for these statistics are obtained by computing a weighted average of the absolute value of each allele pair, where the weight is determined by the expected frequency. For example:

D.overall = sum |D(ij)| * p(ij)

Bootstrapping is used to generate confidence interval in order to avoid reliance on parametric assumptions, which will not hold for alleles with low frequencies (e.g. D' following a a Chi-square distribution).

See the function {HWE} from "genetics" package for testing Hardy-Weinberg Equilibrium, D=0.

### Author(s)

Gregory R. Warnes warnes@bst.rochester.edu and Nitin Jain nitin.jain@pfizer.com

[Package GeneticsBase version 1.6.0 Index]