# Regression Methods to Test for Linkage With Covariates

### Description

A method to test genetic linkage with covariates by regression models that use the IBD status for relative pairs as the dependent variable and pair-specific covariates as the independent variables. Correlations of IBD statistics and covariates for relative pairs within the same pedigree are accounted for.

### Usage

1 2 3 4 5 |

### Arguments

`formula` |
either "~1" for no covariates to get only linkage tests, or a function of the paired covariates (e.g., "~pairs.sum(cov1, cov1)") for tests that include covariates. |

`status.method ` |
Character string indicating which relative pairs to apply the ibdreg method: "AA", "UU", "AU", or "ALL". These correspond to: Affected-Affected, Unaffected-Unaffected, Affected-Unaffected, and all pairs, respectively. |

`ibd.dat ` |
an ibd.dat object, created by create.ibd.dat() with elements: ped.id, person1.id, person2.id, which collectively identify relative pairs, post0, post1, post2, which are the posterior probabilities of sharing 0, 1, and 2 alleles IBD at each chromosome position, and prior0, prior1, prior2, which are the null prior probabilities of sharing 0, 1, and 2 alleles ibd. |

`ibd.var ` |
a list containing an element for each pedigree. The elements include ped.id, person1.id, person2.id, and the variance-covariance matrix of ibd statistics between pairs of subject pairs. |

`status` |
column name of data that has affection status (1=unaffected; 2=affected; NA=missing) |

`ped.id ` |
column name of data that has pedigree id |

`person.id ` |
column name of data that has a person's id, which only have to be unique within pedigrees |

`data` |
a data frame containing all variables in the model formula, in addition to status, ped.id, and person.id |

`c.scale ` |
choice for scaling factor on covariates, "minimax" (same as LODPAL) and "nodom" (no dominance-variance) |

`subset` |
an optional vector specifying a subset of observations in data |

`weights` |
an optional vector of weights to be used in the regression method |

`na.action ` |
a function that defines how missing values (NA) are handled. The default is set by the 'na.action' setting of 'options', and is 'na.fail' by default. |

`min.pairs ` |
minimum number of relative pairs needed for linkage tests to be calculated on a specific status group (e.g. AA pairs) |

`epsilon` |
minimum value for singular values in generalized inverse calculations |

`... ` |
further arguments passed to or from other methods |

### Details

The tests for genetic linkage use quasi-likelihood score statistics, formulated in terms of weighted least squares regression. The covariates in the regression framework are scaled according to the degree of relationship between relative pairs within the pedigree (c.scale). The method yields the following tests for linkage and/or covariate effect for relative pairs: (i) Linkage only; (ii) Linkage with covariate effects; (iii) Covariate effect on IBD sharing (e.g, heterogeneity), assuming either a model-based variance-covariance matrix or a robust variance-covariance matrix. Tests (i) - (iii) are evaluated as unconstrained (two-sided test) and constrained for excess allele sharing in one direction. If formula is \~1, there are no covariates, so the tests will be for linkage only.

Another test (iv) is for linkage using all relative pairs. This test imposes constraints on allele sharing for one-sides tests favoring linkage, achieved by constraining IBD allele sharing for pairs as AA > UU > null, and AU < null, where null is the expected IBD sharing without linkage.

Tests (i) - (iv) are performed using quasi-likelihood scores, and their distributions are asymptotically chi-square or mixture chi-square.

Another set of tests (v) are z-scores measuring the departure from expected allele sharing for each pedigree, at each position. These are provided for diagnostic purposes in the linkage.tests results for AA, UU, and AU pairs.

Correlations of relative pairs from the same pedigree are accounted for by a covariance matrix for ibd statistics within pedigrees. This variance-covariance matrix is calculated using results from merlin (with options "–ibd –matrices").

### Value

A list with the following components:

`Call` |
function call to ibdreg |

`relpair.tbl` |
table with number of relative pairs in each pedigree |

`status.tbl` |
table of counts for AA, UU, and AU relative pairs |

`AA.linkage` |
an object of class linkage.tests; includes score statistics for linkage for AA relative pairs that includes tests (i) - (iii), (v) (see details) |

`UU.linkage` |
an object of class linkage.tests; includes score statistics for linkage for UU relative pairs that includes tests (i) - (iii), (v) (see details) |

`AU.linkage` |
an object of class linkage.tests; includes score statistics for linkage for AU relative pairs that includes tests (i) - (iii), (v) (see details) |

`ALL.linkage` |
object of class linkage.all; includes score statistics for linkage with ALL pairs (test iv). |

### References

Schaid DJ, Sinnwell JP, Thibodeau SN. Testing Genetic Linkage with Affected Relative Pairs and Covariates by Quasi-Likelihood Score Statistics. Submitted.

### See Also

`create.ibd.dat`

,
`sim.ibd.var`

,
`exact.ibd.var`

,
`linkage.tests`

,
`linkage.all`

,
`print.ibdreg`

,
`plot.ibdreg`

### Examples

1 2 3 4 5 6 7 | ```
## see manual for examples, the data requirements are here:
# make a data.frame with ped.id, person.id, status, and covariates
# make ibd.dat object using create.ibd.dat
# make ibd.var object using create.ibd.var
# call ibdreg
``` |