bacon 1.13.2

**modified**: Sat Jan 20 08:18:27 2018
**compiled**: Thu Oct 17 21:56:39 2019

*bacon* can be used to remove inflation and bias often
observed in epigenome- and transcriptome-wide association
studies (Iterson, Zwet, and Heijmans 2017).

To this end *bacon* constructs an empirical null
distribution using a Gibbs Sampling algorithm by fitting a
three-component normal mixture on z-scores. One component is forced,
using prior knowledge, to represent the null distribution with mean
and standard deviation representing the bias and inflation. The other
two components are necessary to capture the amount of true
associations present in the data, which we assume unknown but small.

*bacon* provides functionality to inspect the output of
the Gibbs Sampling algorithm, i.e., plots of traces, posterior
distributions and the mixture fit, are provided. Furthermore,
inflation- and bias-corrected test-statistics or P-values are
extracted easily. In addition, functionality for performing
fixed-effect meta-analysis are provided as well.

The function `bacon`

requires a vector or a matrix of z-scores, e.g.,
those extracted from association analyses using a linear regression
approach. For fixed-effect meta-analysis a matrix of effect-sizes and
standard-errors is required.

This vignette illustrates the use of *bacon* using
simulated z-scores, effect-sizes and standard errors to avoid long
run-times. If multiple sets of test-statisics or effect-sizes and
standard-errors are provided, the Gibbs Sampler algorithm can be
executed in parallel to reduce computation time using functionality
provide by *BiocParallel*-package.

A vector containing \(5000\) z-scores is generated from a normal mixture
distribution, \(90\%\) of the z-scores were drawn from a biased and
inflated null distribution, \(\mathcal{N}(0.2, 1.3)\), and the remaining
z-scores from \(\mathcal{N}(\mu, 1)\), where \(\mu \sim \mathcal{N}(4, 1)\). The `rnormmix`

-function provided by `Bacon`

generates a vector of
random test-statistics described above optionally with different
parameters.

`y <- rnormmix(5000, c(0.9, 0.2, 1.3, 1, 4, 1))`

The function `bacon`

executes the Gibbs Sampler algorithm and stores
all in- and out-put in an object of class `Bacon`

. Several
accessor-functions are available to access data contained in the
`Bacon`

-object, e.g.Â for obtaining the estimated parameters of the
mixture fit or explicitly the bias and inflation. Actually, the latter
two are the mean and standard deviation of the null component (mu.0
and sigma.0).

```
bc <- bacon(y)
bc
```

```
## Bacon-object containing 1 set(s) of 5000 test-statistics.
## ...estimated bias: 0.17.
## ...estimated inflation: 1.3.
##
## Empirical null estimates are based on 5000 iterations with a burnin-period of 2000.
```

`estimates(bc)`

```
## p.0 p.1 p.2 mu.0 mu.1 mu.2 sigma.0 sigma.1 sigma.2
## [1,] 0.924 0.0526 0.0238 0.172 3.01 -2.99 1.31 3.13 2.54
```

`inflation(bc)`

```
## sigma.0
## 1.31
```

`bias(bc)`

```
## mu.0
## 0.172
```

Several methods are provided to inspect the output of the Gibbs Sampler algorithm, such as traces-plots of all estimates, plots of posterior distributions, provide as a scatter plot between two parameters, and the actual fit of the three component mixture to the histogram of z-scores.

`traces(bc, burnin=FALSE)`