abf.normal: Calculate approximate Bayes factor (ABF) for normal prior.
In tobyjohnson/gtx: Genetics ToolboX

Description Usage Arguments Details Value Author(s) Examples

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

1	abf.normal(beta, se, priorscale, gridrange = 3, griddensity = 20)

`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.
`gridrange`	Parameter controlling range of grid for numerical integration.
`griddensity`	Parameter controlling density of points in grid for numerical integration.

This uses the same normal approximation for the likelihood function as “Bayes factors for genome-wide association studies: comparison with P-values” by John Wakefield, 2009, Genetic Epidemiology 33(1):79-86 at http://dx.doi.org/10.1002/gepi.20359. In that work, an analytical expression for the approximate Bayes factor was derived, which is implemented in abf.Wakefield. This function uses a numerical algorithm to calculate the (approximate) Bayes factor, which may be a useful starting point if one wishes to change the assumptions so that the analytical expression of Wakefield (2009) no longer applies (as in abf.t).

A vector of approximate Bayes factors.

Toby Johnson Toby.x.Johnson@gsk.com

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.numeric <- with(agtstats, max1(abf.normal(beta, se.GC, 0.05)))
with(agtstats, plot(BF.normal, BF.numeric)) # excellent agreement