|
8 | 8 | ``` |
9 | 9 |
|
10 | 10 |
|
11 | | -## Package Features |
| 11 | +The `MultipleTesting` package offers common algorithms for p-value adjustment |
| 12 | +and combination as well as the estimation of the proportion π₀ of true null |
| 13 | +hypotheses. |
| 14 | + |
| 15 | + |
| 16 | + |
| 17 | + |
| 18 | +## Features |
| 19 | + |
| 20 | +### Adjustment of p-values |
| 21 | + |
| 22 | +* Bonferroni |
| 23 | +* Benjamini-Hochberg |
| 24 | +* Adaptive Benjamini-Hochberg with known π₀ or π₀ estimation method (see section below) |
| 25 | +* Benjamini-Yekutieli |
| 26 | +* Benjamini-Liu |
| 27 | +* Hochberg |
| 28 | +* Holm |
| 29 | +* Hommel |
| 30 | +* Sidak |
| 31 | +* Forward Stop |
| 32 | +* Barber-Candès |
| 33 | + |
| 34 | +```julia |
| 35 | +adjust(pvals, Bonferroni()) |
| 36 | +adjust(pvals, BenjaminiHochberg()) |
| 37 | +adjust(pvals, BenjaminiHochbergAdaptive(0.9)) |
| 38 | +adjust(pvals, BenjaminiHochbergAdaptive(Storey())) |
| 39 | +adjust(pvals, BenjaminiYekutieli()) |
| 40 | +adjust(pvals, BenjaminiLiu()) |
| 41 | +adjust(pvals, Hochberg()) |
| 42 | +adjust(pvals, Holm()) |
| 43 | +adjust(pvals, Hommel()) |
| 44 | +adjust(pvals, Sidak()) |
| 45 | +adjust(pvals, ForwardStop()) |
| 46 | +adjust(pvals, BarberCandes()) |
| 47 | +``` |
| 48 | + |
| 49 | +The adjustment can also be performed on the `k` smallest out of `n` p-values: |
| 50 | + |
| 51 | +```julia |
| 52 | +adjust(pvals, n, PValueAdjustmentMethod) |
| 53 | +``` |
| 54 | + |
| 55 | + |
| 56 | +### Estimation of π₀ |
| 57 | + |
| 58 | +* Storey |
| 59 | +* Storey's closed-form bootstrap |
| 60 | +* Least Slope |
| 61 | +* Two Step |
| 62 | +* RightBoundary (Storey's estimate with dynamically chosen λ) |
| 63 | +* Beta-Uniform Mixture (BUM) |
| 64 | +* Censored BUM |
| 65 | +* Flat Grenander |
| 66 | +* Oracle for known π₀ |
| 67 | + |
| 68 | +```julia |
| 69 | +estimate_pi0(pvals, Storey()) |
| 70 | +estimate_pi0(pvals, StoreyBootstrap()) |
| 71 | +estimate_pi0(pvals, LeastSlope()) |
| 72 | +estimate_pi0(pvals, TwoStep()) |
| 73 | +estimate_pi0(pvals, TwoStep(0.05)) |
| 74 | +estimate_pi0(pvals, TwoStep(0.05, BenjaminiHochbergAdaptive(0.9)) |
| 75 | +estimate_pi0(pvals, RightBoundary()) |
| 76 | +estimate_pi0(pvals, CensoredBUM()) |
| 77 | +estimate_pi0(pvals, BUM()) |
| 78 | +estimate_pi0(pvals, FlatGrenander()) |
| 79 | +estimate_pi0(pvals, Oracle(0.9)) |
| 80 | +``` |
| 81 | +
|
| 82 | +
|
| 83 | +### Combination of p-values |
| 84 | +
|
| 85 | +* Fisher |
| 86 | +* Stouffer, optionally with weights |
| 87 | +* Logit |
| 88 | +* Tippett |
| 89 | +* Simes |
| 90 | +* Wilkinson |
| 91 | +* Minimum of adjusted p-values |
| 92 | +
|
| 93 | +```julia |
| 94 | +combine(pvals, FisherCombination()) |
| 95 | +combine(pvals, StoufferCombination()) |
| 96 | +combine(pvals, weights, StoufferCombination()) |
| 97 | +combine(pvals, LogitCombination()) |
| 98 | +combine(pvals, TippettCombination()) |
| 99 | +combine(pvals, SimesCombination()) |
| 100 | +combine(pvals, WilkinsonCombination(rank)) |
| 101 | +combine(pvals, MinimumCombination(PValueAdjustment())) |
| 102 | +``` |
| 103 | +
|
| 104 | +
|
| 105 | +### Higher criticism |
| 106 | +
|
| 107 | +* Higher criticism scores |
| 108 | +* Higher criticism threshold |
| 109 | +
|
| 110 | +```julia |
| 111 | +estimate(pvals, HigherCriticismScores()) |
| 112 | +estimate(pvals, HigherCriticismThreshold()) |
| 113 | +``` |
| 114 | +
|
12 | 115 |
|
13 | 116 | ## Manual |
14 | 117 |
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