Calculates a threshold to identify a significant QTL (M.P. Boer & J.T.N.M. Thissen).

### Options

`PRINT` = string token |
What to print (`summary` ); default `summ` |
---|---|

`POPULATIONTYPE` = string token |
Type of population (`BC1` , `DH1` , `F2` , `RIL` , `BCxSy` , `CP` ); must be set |

`THRMETHOD` = string token |
Which method to use (`bonferroni` , `liji` ); default `liji` |

`STATISTICTYPE` = string token |
Which type of test statistic to use (`wald` , `minlog10p` ); default `minl` |

`ALPHALEVEL` = scalar |
Defines the genome-wide significance level; default 0.05 |

`DISTANCE` = scalar |
Distance between evaluation points for `THRMETHOD=bonferroni` ; default 4 |

`DF` = scalar |
Degrees of freedom for the Wald test; default 1 |

### Parameters

`CHROMOSOMES` = factors |
Chromosome for each locus; must be set |
---|---|

`POSITIONS` = variates |
Position on the chromosome for each locus; must be set |

`ADDITIVEPREDICTORS` = pointers |
The additive genetic predictors |

`ADD2PREDICTORS` = pointers |
The second (paternal) additive genetic predictors if `POPULATIONTYPE` is `CP` |

`DOMINANCEPREDICTORS` = pointers |
The dominance genetic predictors if `POPULATIONTYPE` is `F2` or `CP` |

`THRESHOLD` = scalars |
Saves the calculated threshold |

### Description

`QTHRESHOLD`

calculates a genome wide significance threshold to use as a critical value to reject the null hypothesis of no QTL effect. The genome-wide type I error rate is defined by the option `ALPHALEVEL`

. The threshold is based on a modified Bonferroni correction. The `THRMETHOD`

option specifies the method for calculating the number of tests to used as the denominator. The default setting, `liji`

, uses the effective number of independent tests, as described by Li & Ji (2005). Alternatively, the setting `bonferroni`

assumes one independent test at every fixed distance on the genome, defined by the `DISTANCE`

option (default 4 centiMorgans). By default, the threshold is expressed as the P value on a -log10 scale, but you can set option `STATISTICTYPE=Wald`

to use the absolute Wald test statistic instead. Marker and map information must be supplied by the `ADDITIVEPREDICTORS`

, `CHROMOSOMES`

and `POSITIONS`

parameters. The `DOMINANCEPREDICTORS`

parameter can supply dominance genetic predictors for population types `F2`

, `RIL`

, `BCxSy`

and `CP`

, and the `ADD2PREDICTORS`

parameter can supply the second (paternal) additive genetic predictors for population type `CP`

. The corresponding degrees of freedom for the Wald test must be set by the `DF`

parameter; this is equal to 1 in a single-environment QTL analysis, or to the number of environments in a multi-environment QTL analysis.

The calculated threshold can be saved using the `THRESHOLD`

parameter. By default the threshold is printed, but you can suppress this by setting option `PRINT=*`

.

Options: `PRINT`

, `POPULATIONTYPE`

, `THRMETHOD`

, `STATISTICTYPE`

, `ALPHALEVEL`

, `DISTANCE`

, `DF`

.

Parameters: `CHROMOSOMES`

, `POSITIONS`

, `ADDITIVEPREDICTORS`

, `ADD2PREDICTORS`

, `DOMINANCEPREDICTORS`

, `THRESHOLD`

.

### Method

`QTHRESHOLD`

calculates a genome-wide significance threshold based on a modified Bonferonni correction, where the effective number of tests is used as the denominator instead of the total number of tests. By default the procedure estimates the effective number of independent tests by a singular value decomposition of the correlation matrix between all markers (see Li & Ji 2005 or Cheverud 2001). Alternatively, `QTHRESHOLD`

assumes that the effective number of tests along the genome can be approximated by n independent tests:

*n* = ceiling(*L*/*D*)

where *L* is the total genome length (in cM), *D* is the distance between evaluation points (in cM) supplied by the `DISTANCE`

option, and ceiling(*x*) gives the smallest integer not less than *x*. If the `DISTANCE`

option is unset, *n* is set to the length of the `CHROMOSOMES`

variate.

Using the Bonferonni correction, the genome wide significance threshold *T* is approximated by Χ^{2}_{df}(1-α/*n*), where *df* is the number of degrees of freedom.

### Action with `RESTRICT`

Restrictions are not allowed.

### References

Cheverud, J.M. (2001). A simple correction for multiple comparisons in interval mapping genome scans. *Heredity*, 87, 52-58.

Li, J, & Ji, L. (2005). Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix. *Heredity*, 95, 221-227.

### See also

Procedures: `FDRBONFERRONI`

, `FDRMIXTURE`

.

Commands for: Statistical genetics and QTL estimation.

### Example

CAPTION 'QTHRESHOLD example'; STYLE=meta SPLOAD [PRINT=*] '%GENDIR%/Examples/F2maizemarkers.gwb'; SHEETNAME='LOCI' & '%GENDIR%/Examples/F2maizemarkers.gwb'; SHEETNAME='ADDPREDICTORS' QTHRESHOLD [THRMETHOD=liji; STATISTICTYPE=minlog; ALPHA=0.05]\ CHROMOSOMES=mkchr; POSITIONS=mkpos; ADDITIVEPREDICTORS=addpred QTHRESHOLD [THRMETHOD=liji; STATISTICTYPE=wald; ALPHA=0.05; DF=1]\ CHROMOSOMES=mkchr; POSITIONS=mkpos; ADDITIVEPREDICTORS=addpred QTHRESHOLD [THRMETHOD=liji; STATISTICTYPE=wald; ALPHA=0.05; DF=10]\ CHROMOSOMES=mkchr; POSITIONS=mkpos; ADDITIVEPREDICTORS=addpred QTHRESHOLD [THRMETHOD=bonferroni; STATISTICTYPE=wald; DF=1; DISTANCE=*]\ CHROMOSOMES=mkchr; POSITIONS=mkpos QTHRESHOLD [THRMETHOD=bonferroni; STATISTICTYPE=wald; DF=1; DISTANCE=50]\ CHROMOSOMES=mkchr; POSITIONS=mkpos QTHRESHOLD [THRMETHOD=bonferroni; STATISTICTYPE=minlog; DISTANCE=*]\ CHROMOSOMES=mkchr; POSITIONS=mkpos