# Partition a sample into an ancestry representative 'unrelated subset' and a 'related subset'

### Description

`pcairPartition`

is used to partition a sample from a genetic study into an ancestry representative 'unrelated subset' and a 'related subset'. The 'unrelated subset' contains individuals who are all mutually unrelated to each other and representative of the ancestries of all individuals in the sample, and the 'related subset' contains individuals who are related to someone in the 'unrealted subset'.

### Usage

1 2 | ```
pcairPartition(kinMat, kin.thresh = 2^(-11/2), divMat = NULL,
div.thresh = -2^(-11/2), unrel.set = NULL)
``` |

### Arguments

`kinMat` |
A symmetric matrix of pairwise kinship coefficients for every pair of individuals in the sample (the values on the diagonal do not matter, but the upper and lower triangles must both be filled) used for partitioning the sample into the 'unrelated' and 'related' subsets. See 'Details' for how this interacts with |

`kin.thresh` |
Threshold value on |

`divMat` |
A symmetric matrix of pairwise ancestry divergence measures for every pair of individuals in the sample (the values on the diagonal do not matter, but the upper and lower triangles must both be filled) used for partitioning the sample into the 'unrelated' and 'related' subsets. See 'Details' for how this interacts with |

`div.thresh` |
Threshold value on |

`unrel.set` |
An optional vector of IDs for identifying individuals that are forced into the unrelated subset. See 'Details' for how this interacts with |

### Details

We recommend using software that accounts for population structure to estimate pairwise kinship coefficients to be used in `kinMat`

. Any pair of individuals with a pairwise kinship greater than `kin.thresh`

will be declared 'related.' Kinship coefficient estimates from the KING-robust software are typically used as measures of ancestry divergence in `divMat`

. Any pair of individuals with a pairwise divergence measure less than `div.thresh`

will be declared ancestrally 'divergent'. Typically, `kin.thresh`

and `div.thresh`

are set to be the amount of error around 0 expected in the estimate for a pair of truly unrelated individuals. If `unrel.set = NULL`

, the PC-AiR algorithm is used to find an 'optimal' partition (see 'References' for a paper describing the algorithm). If `unrel.set`

and `kinMat`

are both specified, then all individuals with IDs in `unrel.set`

are forced in the 'unrelated subset' and the PC-AiR algorithm is used to partition the rest of the sample; this is especially useful for including reference samples of known ancestry in the 'unrelated subset'.

### Value

A list including:

`rels` |
A vector of IDs for individuals in the 'related subset'. |

`unrels` |
A vector of IDs for individuals in the 'unrelated subset'. |

### Note

`pcairPartition`

is called internally in the function `pcair`

but may also be used on its own to partition the sample into an ancestry representative 'unrelated' subset and a 'related' subset without performing PCA.

### Author(s)

Matthew P. Conomos

### References

Conomos M.P., Miller M., & Thornton T. (2015). Robust Inference of Population Structure for Ancestry Prediction and Correction of Stratification in the Presence of Relatedness. Genetic Epidemiology, 39(4), 276-293.

Manichaikul, A., Mychaleckyj, J.C., Rich, S.S., Daly, K., Sale, M., & Chen, W.M. (2010). Robust relationship inference in genome-wide association studies. Bioinformatics, 26(22), 2867-2873.

### See Also

`pcair`

which uses this function for finding principal components in the presence of related individuals.
`king2mat`

for creating a matrix of kinship coefficent estimates or pairwise ancestry divergence measures from KING output text files that can be used as `kinMat`

or `divMat`

.

### Examples

1 2 3 4 5 | ```
# load saved matrix of KING-robust estimates
data("HapMap_ASW_MXL_KINGmat")
# partition the sample
part <- pcairPartition(kinMat = HapMap_ASW_MXL_KINGmat,
divMat = HapMap_ASW_MXL_KINGmat)
``` |