gtx (version 0.0.8)

abf.normal: Calculate approximate Bayes factor (ABF) for normal prior.

Description

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

Usage

abf.normal(beta, se, priorscale, 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.

gridrange

Parameter controlling range of grid for numerical integration.

griddensity

Parameter controlling density of points in grid for numerical integration.

Value

A vector of approximate Bayes factors.

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 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 has to be used 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).

Examples

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