BFDP: Bayesian false-discovery probability

Description

This function calculates BFDP, the approximate $P(H_0|\hat\theta)$, given an estiamte of the log relative risk, $\hat\theta$, the variance of this estimate, $V$, the prior variance, $W$, and the prior probability of a non-null association. When logscale=TRUE, the function accepts an estimate of the relative risk, $\hat{RR}$, and the upper point of a 95% confidence interval $RR_{hi}$.

Usage

BFDP(a,b,pi1,W,logscale=FALSE)

Arguments

parameter value at which the power is to be evaluated

the variance for a, or the uppoer point ($RR_{hi}$) of a 95%CI if logscale=FALSE

pi1

the prior probabiility of a non-null association

the prior variance

logscale

FALSE=the orginal scale, TRUE=the log scale

Value

The returned value is a list with the following components:
PH0probability given a,b)
PH1probability given a,b,W)
BFBayes factor, $P_{H_0}/P_{H_1}$
BFDPBayesian false-discovery probability
ABFapproxmiate Bayes factor
ABFDPapproximate Bayesian false-discovery probability

References

Wakefield J (2007) Bayesian measure of the probability of false discovery in genetic epidemiology studies. Am J Hum Genet 81:208-227

Examples

Run this code

# Example from BDFP.xls by Jon Wakefield and Stephanie Monnier
# Step 1 - Pre-set an BFDP-level threshold for noteworthiness: BFDP values below this threshold
#          are noteworthy
# The threshold is given by R/(1+R) where R is the ratio of the cost of a false non-discovery
# to the cost of a false discovery

T <- 0.8

# Step 2 - Enter up values for the prior that there is an association

pi0 <- c(0.7,0.5,0.01,0.001,0.00001,0.6)

# Step 3 - Enter the value of the OR that is the 97.5% point of the prior, for example if we
#          pick the value 1.5 we believe that the prior probability that the odds ratio is
#          bigger than 1.5 is 0.025.

ORhi <- 3

W <- (log(ORhi)/1.96)^2
W

# Step 4 - Enter OR estimate and 95% confidence interval (CI) to obtain BFDP

OR <- 1.316
OR_L <- 1.10
OR_U <- 2.50
logOR <- log(OR)
selogOR <- (log(OR_U)-log(OR))/1.96
r <- W/(W+selogOR^2)
r
z <- logOR/selogOR
z
ABF <- exp(-z^2*r/2)/sqrt(1-r)
ABF
FF <- (1-pi0)/pi0
FF
BFDPex <- FF*ABF/(FF*ABF+1)
BFDPex
pi0[BFDPex>T]

## now turn to BFDP

pi0 <- c(0.7,0.5,0.01,0.001,0.00001,0.6)
ORhi <- 3
OR <- 1.316
OR_U <- 2.50
W <- (log(ORhi)/1.96)^2
z <- BFDP(OR,OR_U,pi0,W)
z