FSFDR.indept.cv: Critical Values for Fixed Sequence FDR Controlling Procedure... In FixSeqMTP: Fixed Sequence Multiple Testing Procedures

Description

Given a set of pre-ordered p-values and accuracy for the result, return the corresponding critical values using the generalized fixed sequence FDR controlling procedure under independence for true nulls (See Theorem 3.2 and 4.2 in Lynch et al. (2016)). The function also provides an option to make decisions given a pre-specified significant level α.

Usage

 `1` ```FSFDR.indept.cv(p, k=1, alpha = 0.05, tol = 1e-6, make.decision = TRUE) ```

Arguments

 `p` numeric vector of p-values (possibly with `NA`s). Any other R is coerced by `as.numeric`. Same as in `p.adjust`. `k` pre-specified number of acceptances allowed in the testing procedure (cannot exceed the length of `p`) `alpha` significant level used to calculate the critical values to make decisions, the default value is 0.05. `tol` desired accuracy. The default value is `1e-6 `. `make.decision` logical; if `TRUE` (default), then the output include the decision rules compared adjusted p-values with significant level alpha

Value

A numeric vector of the critical values (of the same length as `p`) if `make.decision = FALSE`, or a data frame including original p-values, critical values and decision rules if `make.decision = TRUE`.

Yalin Zhu

References

Lynch, G., Guo, W., Sarkar, S. K., & Finner, H. (2016). The Control of the False Discovery Rate in Fixed Sequence Multiple Testing. arXiv preprint arXiv:1611.03146.

`FSFWER.arbidept.cv` for fixed sequence FWER controlling procedures.

Examples

 ```1 2 3 4 5 6 7 8 9``` ```## generate a pre-ordered pvalue vector for 50 hypotheses, where 80% are true nulls set.seed(1234); m <- 50; pi0 <- 0.8; m0 <- m*pi0; m1 <- m-m0 mu <- c(4*0.9^(1:m1), rep(0,m0)) Zstat <- rnorm(n = m, mean = mu) Pval <- 1-pnorm(Zstat) ## conventional fixed sequence procedure FSFDR.indept.cv(p = Pval, alpha = 0.05) ## generalized fixed sequence procedure allowing stop at 5th acceptance FSFDR.indept.cv(p = Pval, alpha = 0.05, k=5) ```

Example output

```          raw.p critical.value decision
1  8.357118e-03     0.05000000   reject
2  2.178743e-04     0.09523810   reject
3  3.161225e-05     0.13636364   reject
4  3.902366e-01     0.17391304   accept
5  2.626586e-03     0.16666667   accept
6  4.246444e-03     0.16000000   accept
7  9.037528e-02     0.15384615   accept
8  1.199500e-01     0.14814815   accept
9  1.622556e-01     0.14285714   accept
10 3.068932e-01     0.13793103   accept
11 6.833875e-01     0.13333333   accept
12 8.409540e-01     0.12903226   accept
13 7.812005e-01     0.12500000   accept
14 4.743024e-01     0.12121212   accept
15 1.686550e-01     0.11764706   accept
16 5.439085e-01     0.11428571   accept
17 6.953278e-01     0.11111111   accept
18 8.189038e-01     0.10810811   accept
19 7.987520e-01     0.10526316   accept
20 7.849583e-03     0.10256410   accept
21 4.466664e-01     0.10000000   accept
22 6.881757e-01     0.09756098   accept
23 6.702298e-01     0.09523810   accept
24 3.229055e-01     0.09302326   accept
25 7.560712e-01     0.09090909   accept
26 9.262201e-01     0.08888889   accept
27 2.827283e-01     0.08695652   accept
28 8.470010e-01     0.08510638   accept
29 5.060391e-01     0.08333333   accept
30 8.253502e-01     0.08163265   accept
31 1.351662e-01     0.08000000   accept
32 6.828178e-01     0.07843137   accept
33 7.609743e-01     0.07692308   accept
34 6.919052e-01     0.07547170   accept
35 9.483534e-01     0.07407407   accept
36 8.785198e-01     0.07272727   accept
37 9.853727e-01     0.07142857   accept
38 9.100387e-01     0.07017544   accept
39 6.157333e-01     0.06896552   accept
40 6.793556e-01     0.06779661   accept
41 7.359952e-02     0.06666667   accept
42 8.573847e-01     0.06557377   accept
43 8.038253e-01     0.06451613   accept
44 6.105002e-01     0.06349206   accept
45 8.399713e-01     0.06250000   accept
46 8.336062e-01     0.06153846   accept
47 8.659218e-01     0.06060606   accept
48 8.947125e-01     0.05970149   accept
49 6.998010e-01     0.05882353   accept
50 6.903526e-01     0.05797101   accept
raw.p critical.value decision
1  8.357118e-03     0.01041667   reject
2  2.178743e-04     0.02061856   reject
3  3.161225e-05     0.03061224   reject
4  3.902366e-01     0.04040404   accept
5  2.626586e-03     0.04000000   reject
6  4.246444e-03     0.04950495   reject
7  9.037528e-02     0.05882353   accept
8  1.199500e-01     0.05825243   accept
9  1.622556e-01     0.05769231   accept
10 3.068932e-01     0.05714286   accept
11 6.833875e-01     0.05660377   accept
12 8.409540e-01     0.05607477   accept
13 7.812005e-01     0.05555556   accept
14 4.743024e-01     0.05504587   accept
15 1.686550e-01     0.05454545   accept
16 5.439085e-01     0.05405405   accept
17 6.953278e-01     0.05357143   accept
18 8.189038e-01     0.05309735   accept
19 7.987520e-01     0.05263158   accept
20 7.849583e-03     0.05217391   accept
21 4.466664e-01     0.05172414   accept
22 6.881757e-01     0.05128205   accept
23 6.702298e-01     0.05084746   accept
24 3.229055e-01     0.05042017   accept
25 7.560712e-01     0.05000000   accept
26 9.262201e-01     0.04958678   accept
27 2.827283e-01     0.04918033   accept
28 8.470010e-01     0.04878049   accept
29 5.060391e-01     0.04838710   accept
30 8.253502e-01     0.04800000   accept
31 1.351662e-01     0.04761905   accept
32 6.828178e-01     0.04724409   accept
33 7.609743e-01     0.04687500   accept
34 6.919052e-01     0.04651163   accept
35 9.483534e-01     0.04615385   accept
36 8.785198e-01     0.04580153   accept
37 9.853727e-01     0.04545455   accept
38 9.100387e-01     0.04511278   accept
39 6.157333e-01     0.04477612   accept
40 6.793556e-01     0.04444444   accept
41 7.359952e-02     0.04411765   accept
42 8.573847e-01     0.04379562   accept
43 8.038253e-01     0.04347826   accept
44 6.105002e-01     0.04316547   accept
45 8.399713e-01     0.04285714   accept
46 8.336062e-01     0.04255319   accept
47 8.659218e-01     0.04225352   accept
48 8.947125e-01     0.04195804   accept
49 6.998010e-01     0.04166667   accept
50 6.903526e-01     0.04137931   accept
```

FixSeqMTP documentation built on May 1, 2019, 10:53 p.m.