This function calculates BFDP, the approximate Pr( H0 | thetahat ),
given an estiamte of the log relative risk, thetahat, 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, RRhat, and the upper point of a 95% confidence interval RRhi.
Usage
BFDP(a,b,pi1,W,logscale=FALSE)
Arguments
a
parameter value at which the power is to be evaluated
b
the variance for a, or the uppoer point (RRhi) of a 95%CI if logscale=FALSE
pi1
the prior probabiility of a non-null association
W
the prior variance
logscale
FALSE=the orginal scale, TRUE=the log scale
Value
The returned value is a list with the following components:
PH0
probability given a,b)
PH1
probability given a,b,W)
BF
Bayes factor, PH0/PH1
BFDP
Bayesian false-discovery probability
ABF
approxmiate Bayes factor
ABFDP
approximate 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
Note
adapted from BFDP functions by Jon Wakefield on 17th April, 2007
Author(s)
Jon Wakefield, Jing Hua Zhao
See Also
FPRP
Examples
## Not run:
# 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