# GWAS for Studies having Repeated Measurements on Related Individuals

### Description

It is used to perform genome-wide association studies on individuals that are both related and have repeated measurements. The function computes score statistic based p-values for a linear mixed model including random polygenic effects and a random effect for repeated measurements. A p-value is computed for each marker and the null hypothesis tested is a zero additive marker effect.

### Usage

1 2 |

### Arguments

`formula.FixedEffects` |
Formula including the response variable and cofactors as fixed effects. |

`genabel.data` |
An GenABEL object including marker information. This object has one observtion per individuals. |

`phenotype.data` |
A data frame including the repeated observations and IDs. |

`id.name` |
The column name of the IDs in phen.data |

`GRM` |
An optional genetic relationship matrix (GRM) can be included as input. Otherwise the GRM is computed within the function. |

`V` |
An optional (co)variance matrix can be included as input. Otherwise it is computed using the hglm function. |

`memory` |
Used to optimize computations. The maximum number of elements in a matrix that can be stored efficiently. |

### Details

A generalized squares (GLS) is fitted for each marker given a (co)variance matrix V.
The computations are made fast by transforming the GLS to
an ordinary least-squares (OLS) problem using an eigen-decomposition of V.
The OLS are computed using QR-factorization. If V is not specified then a model
including random polygenic effects and permanent environmental effects is
fitted (using the hglm package) to compute V. A GenABEL object (scan.gwaa class)
is returned (including also the `hglm`

results).
Let e.g. GWAS1 be an object returned by the `rGLS`

function.
Then a Manhattan plot can be produced by calling `plot(GWAS1)`

and
the top SNPs using `summary(GWAS1)`

. Both of these functions are
generic GenABEL functions.

The results from the fitted linear mixed model without any SNP effect included
are produced by calling `summary(GWAS1@call$hglm)`

.

### Author(s)

Lars Ronnegard

### Examples

1 2 3 4 5 6 7 | ```
data(Phen.Data) #Phenotype data with repeated observations
data(gen.data) #GenABEL object including IDs and marker genotypes
GWAS1 <- rGLS(y ~ age + sex, genabel.data = gen.data, phenotype.data = Phen.Data)
plot(GWAS1, main="")
summary(GWAS1)
#Summary for variance component estimation without SNP effects
summary(GWAS1@call$hglm)
``` |