# CNV association testing using T distributions

### Description

Test for CNV association with binary trait (typically case control) using a mixture of T distributions.

### Usage

1 2 3 4 5 6 7 8 9 | ```
CNVtest.binary.T(signal,batch, sample = NULL, disease.status = NULL,
ncomp, n.H0 = 5, n.H1 = 0, output = "compact",
model.mean = "~ strata(batch, cn)",
model.var = "~ strata(batch, cn)",
model.disease = "~ cn",
beta.estimated = NULL,
start.mean = NULL,
start.var = NULL,
control = list(tol = 1e-05, max.iter = 3000, min.freq = 4))
``` |

### 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. |

`disease.status` |
In the case control situation a vector of 0 and 1 indicating which individuals are controls or cases. |

`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. |

`output` |
The default value, “compact”, returns a data frame with one line per sample. Any other setting witll return a much bigger data frame with one line per individual and copy number. This long format is the one used by the underlying fitting algorithm and is only useful if one attempts to use CNVtools in a non standard manner. |

`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. Should be on the following: “~strata(cn)” or “strata(batch, cn)”. |

`model.var` |
A formula describing the variance model, as above. The default is the free variance model “~ strata(cn, batch)” but could also be “~ 1”, “~ strata(cn)” or “~ strata(batch)”. |

`model.disease` |
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. This argument can also be a matrix if one wants to specify multiple starting points. When passing a matrix as argument, the number of columns should equal the number of components, and the number of rows must be greater than max(n.H0, n.H1). When in a row some numbers are missing, CNVtools will pick the starting points randomly (the default). |

`start.var` |
Optional. A set of starting values for the variances. Must be numeric and the size must match ncomp. Can also be a matrix (see start.mean for details). |

`control` |
A list of parameters that control the behavior of the fitting. min.freq is the minimum number of data points in a copy number class before the algorithm sets the frequency of this class to zero. In the presence of a very rare genotype group it might be useful to lower this threshold. Note, however, that estimating the variance if there are very few individuals in a class may not be possible, so setting options such as constant variances (i.e. model.var = ' ~1') might be sensible. |

### 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 and Chris Barnes

### References

Finite Mixture Models (Wiley Series in Probability and Statistics), G. Mc Lachlan and David Peel

### See Also

CNVtest.binary