# Modelling the reduction of faecal egg count data

### Description

Models the reduction in faecal egg counts data with a (un)paired (zero-inflated) Poisson-gamma model formulation using the Stan modelling language. It is computationally several-fold faster compare to conventional MCMC techniques. For the installation instruction of Stan, please read: Stan Installation.

### Usage

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### Arguments

`preFEC` |
vector of pre-treatment faecal egg counts |

`postFEC` |
vector of post-treatment faecal egg counts |

`rawCounts` |
logical. If true, |

`preCF` |
correction factor(s) before treatment |

`postCF` |
correction factor(s) after treatment |

`paired` |
logical. If true, uses the model for the paired design. Otherwise uses the model for the unpaired design |

`zeroInflation` |
logical. If true, uses the model with zero-inflation. Otherwise uses the model without zero-inflation |

`muPrior` |
a list with hyper-prior information for the baseline mean parameter |

`kappaPrior` |
a list with hyper-prior information for the dispersion parameter |

`deltaPrior` |
a list with hyper-prior information for the reduction |

`phiPrior` |
a list with hyper-prior information for the zero-inflation parameter |

`nsamples` |
a positive integer specifying how many iterations for each chain (including burn-in samples) |

`nburnin` |
number of burn-in samples |

`thinning` |
thinning parameter, a positive integer specifying the period for saving samples |

`nchain` |
a positive integer specifying the number of chains |

`ncore` |
number of cores to use when executing the chains in parallel |

`adaptdelta` |
the target acceptance rate, a value between 0 and 1 |

`verbose` |
logical. If true, prints progress and debugging information |

### Details

The first time each model with non-default priors is applied, it can take up to 20 seconds for stan to compile the model. Currently the function only support prior distributions with two parameters. For a complete list of supported priors and their parameterization, please consult the list of distributions in Stan.

Sometimes the function outputs informational message from Stan regarding the Metropolis proposal rejections, this is due to the sampler hit the boundary of the parameter space. For some variables, the boundary point is not supported in the distribution. This is not a concern if there are only a few such warnings.

### Value

An object of S4 class `stanfit`

representing the fitted results. For more information, please see the `stanfit-class`

in `rstan`

reference manual.

Prints out the posterior summary of `fecr`

as the reduction, `meanEPG.untreated`

as the mean faecal egg counts before treatment, and `meanEPG.treated`

as the mean faecal egg counts after treatment. The posterior summary contains the mean, standard deviation (sd), 2.5%, 25%, 50%, 75% and 97.5% percentiles, the 95% highest posterior density interval (HPDLow95 and HPDHigh95) and the posterior mode. NOTE: we recommend to use the 95% HPD interval and the mode for further statistical analysis.

### Author(s)

Craig Wang craig.wang@uzh.ch

### See Also

`simData2s`

for simulating faecal egg counts data with two samples

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 | ```
## Not run:
## load the sample data as a vector
data(epgs)
## apply zero-infation model to the data vector
model<-fecr_stan(epgs[,1],epgs[,2],rawCounts=FALSE,preCF=10,paired=TRUE,zeroInflation=TRUE)
samples<-stan2mcmc(model$stan.samples)
## a demonstration
demo("fecm_stan", package = "eggCounts")
## End(Not run)
``` |