prob_rank_givenEffect_approx: Probability of rank of test given effect size by normal...

In mshasan/OPWeight: Optimal p-value weighting with independent information

Description

A normal approximation to comnpute the probability of rank of a test being higher than any other test given the effect size from external information.

Usage

prob_rank_givenEffect_approx(
  k,
  et,
  ey,
  nrep = 10000,
  m0,
  m1,
  effectType = c("binary", "continuous")
)

Arguments

k	Integer, rank of a test
et	Numeric, effect of the targeted test for importance sampling
ey	Numeric, mean/median covariate efffect from external information
nrep	Integer, number of replications for importance sampling
m0	Integer, number of true null hypothesis
m1	Integer, number of true alternative hypothesis
effectType	Character ("continuous" or "binary"), type of effect sizes

Details

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.

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

Value

prob Numeric, probability of the rank of a test

Author(s)

Mohamad S. Hasan, [e-mail]

See Also

dnorm pnorm rnorm qvalue

Examples

# 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)

mshasan/OPWeight documentation built on March 3, 2021, 12:41 a.m.