prob_rank_givenEffect_simu: Probability of rank of test given effect size by simulations

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

Description

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

Usage

prob_rank_givenEffect_simu(
  s,
  ey,
  e.one,
  m0,
  m1,
  effectType = c("binary", "continuous")
)

Arguments

s	number of samples of test statistics composed of null and alternative tests
ey	Numeric, covariate test efffect from the external information
e.one	Numeric, one test effect that will vary across all tests
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.

This is a simulation approach to compute the probability of the rank, P(rank | effect = ey) to verify the actual P(rank | effect = ey). Suppose, we have a vector of m = m1+m0 observations, where the first m1 observations are from the true alternative and second m0 are from the true null models. If we pick two tests one from the first position and the other from the (m0+1)-th position, then we would expect that the first observation's rank is greater than m0, and (m1+1)-th observation's rank is less than or equal to m1. However, this is not always true, especially when the effect size of the test statistics is low, but the above scenerio become obvious as the the effect size increases. m1 and m0 can be estimated using qvalue from a bioconductor package qvalue.

Value

r0 Integer, rank of the null test statistic
r1 Integer, rank of the alternative test statistic

Author(s)

Mohamad S. Hasan, [e-mail]

See Also

runif rnorm qvalue

Examples

# total number of sample generated (use sample size at least 1,000,000)
sampleSize = 10000
m0 = 50
m1 = 50
m = m0 +m1

# compute rank of the tests
rank <- sapply(1:sampleSize, prob_rank_givenEffect_simu, ey = 1, e.one = 1,
                          m0 = m0, m1 = m1, effectType = "continuous")

# rank may generate missing valuse because of the large effcet size,
# therefore, to make a matplot one needs vector of equal size. This procedure
# will replace the missing value to make the equal sized vectors
# probability of the rank of a null test
prob0 <- rep(NA, m)
prob0_x <- tapply(rank[1,], rank[1,], length)/sampleSize
prob0[as.numeric(names(prob0_x))] <- as.vector(prob0_x)

# probability of the rank of an alternative test
prob1 <- rep(NA, m)
prob1_x <- tapply(rank[2,], rank[2,], length)/sampleSize
prob1[as.numeric(names(prob1_x))] <- as.vector(prob1_x)

# plot
matplot(1:m, cbind(prob0, prob1), type = "l")

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