prob_rank_givenEffect: Probability of rank of test given effect size
In mshasan/OPWeight: Optimal p-value weighting with independent information

Description Usage Arguments Details Value Author(s) See Also Examples

Comnpute the probability of rank of a test being higher than any other tests given the effect size from external information.

1	prob_rank_givenEffect(k, et, ey, nrep = 10000, m0, m1)

`k`	Integer, rank of a test
`et`	Numeric, effect of the targeted test for importance sampling
`ey`	Numeric, mean covariate efffect from the external information
`nrep`	Integer, number of replications for importance sampling
`m0`	Integer, number of true null hypothesis
`m1`	Integer, number of true alternative hypothesis

If one wants to test

H_0: epsilon_i=0 vs. H_a: epsilon_i > 0,

then ey should be mean of the covariate effect sizes, This is called hypothesis testing for the continuous effect sizes.

If one wants to test

H_0: epsilon_i=0 vs. H_a: epsilon_i = epsilon,

then ey should be median or any discrete value of the covariate effect sizes. This is called hypothesis testing for the Binary effect sizes.

If monitor = TRUE then a window will open to see the progress of the computation. It is useful for a large number of tests

m1 and m0 can be estimated using qvalue from a bioconductor package qvalue.

prob Numeric, probability of the rank of a test

Mohamad S. Hasan, shakilmohamad7@gmail.com

dnorm pnorm rnorm qvalue

# compute the probability of the rank of a test being third if all tests are
# from the true null
prob <- prob_rank_givenEffect(k = 3, et = 0, ey = 0, nrep = 10000,
                                      m0 = 50, m1 = 50)

# compute the probabilities of the ranks of a test being rank 1 to 100 if the
# targeted test effect is 2 and the overall mean covariate effect is 1.
ranks <- 1:100
prob <- sapply(ranks, prob_rank_givenEffect, et = 2, ey = 1, nrep = 10000,
                              m0 = 50, m1 = 50)

# plot
plot(ranks,prob)