# abf.t: Calculate approximate Bayes factor (ABF) for t distribution... In gtx: Genetics ToolboX

## Description

Calculates an approximation to the Bayes Factor for an alternative model where the parameter beta is a priori t distributed, by approximating the likelihood function with a normal distribution.

## Usage

 `1` ```abf.t(beta, se, priorscale, df = 1, gridrange = 3, griddensity = 20) ```

## Arguments

 `beta` Vector of effect size estimates. `se` Vector of associated standard errors. `priorscale` Scalar specifying the scale (standard deviation) of the prior on true effect sizes. `df` Degrees of freedom for t distribution prior. `gridrange` Parameter controlling range of grid for numerical integration. `griddensity` Parameter controlling density of points in grid for numerical integration.

## Details

This uses the same normal approximation for the likelihood function as “Bayes factors for genome-wide association studies: comparison with P-values” by John Wakeley, 2009, Genetic Epidemiology 33(1):79-86 at http://dx.doi.org/10.1002/gepi.20359. However, in contrast to that work, a t distribution is used for the prior, which means it is necessary to use a numerical algorithm to calculate the (approximate) Bayes factor.

## Value

A vector of approximate Bayes factors.

## Author(s)

Toby Johnson Toby.x.Johnson@gsk.com

## Examples

 ```1 2 3 4 5 6 7``` ```data(agtstats) agtstats\$pval <- with(agtstats, pchisq((beta/se.GC)^2, df = 1, lower.tail = FALSE)) max1 <- function(bf) return(bf/max(bf, na.rm = TRUE)) agtstats\$BF.normal <- with(agtstats, max1(abf.Wakefield(beta, se.GC, 0.05))) agtstats\$BF.t <- with(agtstats, max1(abf.t(beta, se.GC, 0.0208))) with(agtstats, plot(-log10(pval), log(BF.normal))) with(agtstats, plot(-log10(pval), log(BF.t))) ```

### Example output

```Loading required package: survival
```

gtx documentation built on May 2, 2019, 5:08 a.m.