# Fits a mixture of Gaussian to CNV data

### Description

This function fits a mixture of Gaussians to Copy Number Variant data to explore potential correlations between the copy number and a quantitative trait.

### Usage

1 2 3 4 5 6 7 8 |

### Arguments

`signal` |
The vector of intensity values, meant to be a proxy for the number of copies. |

`batch` |
Factor, that describes how the data points should be separated in batches, corresponding to different tehnologies to measure the number of DNA copies, or maybe different cohorts in a case control framework. |

`sample` |
Optional (but recommended). A character vector containing a name for each data point, typically the name of the individuals. |

`qt` |
Quantitative trait values. |

`ncomp` |
Number of components one wants to fit to the data. |

`n.H0` |
Number of times the EM should be used to maximize the likelihood under the null hypothesis of no association, each time with a different random starting point. The run that maximizes the likelihood is stored. |

`n.H1` |
Number of times the EM should be used to maximize the likelihood under the alternate hypothesis of association present, each time with a different random starting point. The run that maximizes the likelihood is stored. |

`model.mean` |
Formula that relates the location of the means for the clusters with the number of copies and the different batches if there are multiple batches. The default is “~ strata(cn)” that assumes a free model for the cluster locations for each copy number.” ~ strata(cn, batch)” assumes free variances for each combination of copy number and batch. More traditional model specifications such as ' ~ cn' are also possible, but will converge more slowly and might have numerical stability issues. |

`model.var` |
A formula as above, but to model the variances. The default is the free variance model for each copy number “~ strata(cn)” and the same model specifications as model.means can be used. |

`model.qt` |
A formula that relates the number of copies with the case/control status. The default is a linear trend model “~ cn”. Note that this formula will only matter under the alternate hypothesis and has no effect under the null. |

`beta.estimated` |
Optional. It is used if one wants to fit the model for a particular value of the log odds parameter beta (essentially if one is interested in the profile likelihood). In this case the disease model should be set to ' ~ 1' and the model to 'H1'. It will then provide the best model assuming the value of beta (the log odds ratio parameter) provided by the user. |

`start.mean` |
Optional. A set of starting values for the means. Must be numeric and the size must match ncomp. |

`start.var` |
Optional. A set of starting values for the variances. Must be numeric and the size must match ncomp. |

`control` |
A list of parameters that control the behavior of the fitting. |

### Value

`model.H0` |
The parameters for the best fit under H0. |

`posterior.H0` |
The output dataframe with the estimate posterior distribution under H0 as well as the most likely call. |

`status.H0` |
A character that describes the status of the fit under H0. The possible values are 'C' (converged), 'M' (maximum iterations reached), 'P' (posterior distribution problem). Fits that don't return 'C' should be excluded. |

`model.H1` |
The parameters for the best fit under H1. |

`posterior.H1` |
The output dataframe with the estimate posterior distribution under H1 |

`status.H1` |
A character that describes the status of the fit under H1. The possible values are 'C' (converged), 'M' (maximum iterations reached), 'P' (posterior distribution problem). Fits that don't return 'C' should be excluded. |

### Author(s)

Vincent Plagnol <vincent.plagnol@cimr.cam.ac.uk> and Chris Barnes <christopher.barnes@imperial.ac.uk>

### See Also

apply.pca apply.ldf

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
#Load data for CNV for two control cohorts
data(A112)
raw.signal <- as.matrix(A112[, -c(1,2)])
dimnames(raw.signal)[[1]] <- A112$subject
#Extract CNV signal using principal components
pca.signal <- apply.pca(raw.signal)
#Extract batch, sample
sample <- factor(A112$subject)
batches <- rep("ALL",length(sample))
#Create a fake quantitative trait
trait <- rnorm(length(sample),mean=9.0,sd=1.0)
#Fit the CNV with a three component model
fit.pca <- CNVtest.qt(signal = pca.signal, sample = sample, batch = batches,
qt = trait, ncomp = 3, n.H0=3, n.H1=3,
model.qt = "~ cn")
if(fit.pca[['status.H0']] == 'C' && fit.pca[['status.H1']] == 'C'){
#Calculate the likelihood ratio
LR <- -2*(fit.pca$model.H0$lnL - fit.pca$model.H1$lnL)
#Calculate the pvalue. Has 1 dof since we fit a trend model
pvalue <- 1 - pchisq(LR,1)
}
``` |