weight_continuous: Weight for the continuous effect sizes In mshasan/OPWeight: Optimal p-value weighting with independent information

Description

Compute weight from the probability of the rank given the effect size for the continuous effect size

Usage

 `1` ```weight_continuous(alpha, et, m, tail = 1L, delInterval = 0.001, ranksProb) ```

Arguments

 `alpha` Numeric, significance level of the hypothesis test `et` Numeric, mean effect size of the test statistics `m` Integer, totoal number of hypothesis test `tail` Integer (1 or 2), right-tailed or two-tailed hypothesis test. default is right-tailed test. `delInterval` Numeric, interval between the `delta` values of a sequence. Note that, `delta` is a LaGrange multiplier, necessary to normalize the weight `ranksProb` Numeric vector of ranks probability of the tests given the effect size

Details

If one wants to test

H_0: epsilon_i = 0 vs. H_a: ε_i > 0,

then `et` and `ey` should be mean value of the test and covariate effect sizes, respectively. This is called hypothesis testing for the continuous effect sizes.

Value

`weight` Numeric vector of normalized weight of the tests for the continuous case

Author(s)

`prob_rank_givenEffect` `weight_binary`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```# 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 prob2 <- sapply(ranks, prob_rank_givenEffect, et = 2, ey = 1, nrep = 10000, m0 = 50, m1 = 50) # plot the prooabbility plot(ranks, prob2) # compute weight for the continuous case weight_cont <- weight_continuous(alpha = .05, et = 1, m = 100, tail = 1, delInterval = .0001, ranksProb = prob2) # plot the weight plot(ranks, weight_cont) ```