R: Bayesian false-discovery probability

BFDP {gap} | R Documentation

## Bayesian false-discovery probability

### Description

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

### Note

Adapted from BFDP functions by Jon Wakefield on 17th April, 2007.

### Author(s)

Jon Wakefield, Jing Hua Zhao

### References

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

### 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

    ## End(Not run)

[Package gap version 1.2.3-6 Index]