mtp {elitism}R Documentation

Multiple Test Procedures

Description

Given a set of p-values and the level of significance, returns decisions whether the corresponding hypotheses should be rejected or not, including the hybrid Hochberg-Hommel procedure (Gou et al., 2014) and Quick procedure (Gou and Zhang, 2022).

Usage

mtp(p, alpha = 0.05, method = "gtxr", n = length(p))

Arguments

p

vector of p-values.

alpha

the level of significance.

method

multiplicity correction method, including the Holm procedure ("holm"), the Hochberg procedure ("hochberg", "chochberg"), the Hommel procedure ("hommel", "hommelq", "hommell", "hommellsi", "hommellsb"), the Rom procedure ("rom", "rom1", "roma", "romx"), the Gou-Tamhane-Xi-Rom procedure ("gtxr", "gtxr0i", "gtxr1ci", "gtxr2di", "gtxr0b", "gtxr1cb", "gtxr2db"), and the Quick procedure ("quick", "quick00i", "quick01i", "quick10i", "quick11i", "quickxi", "quick00b", "quick01b", "quick10b", "quick11b", "quickxb").

n

number of p-values.

Details

Given a set of p-values, returns a binary vector of decisions, where 1 stands for rejection, and 0 stands for acceptance. There are six families of procedures.

  1. Holm procedure (1 procedure)

    1. holm, the Holm (1979) step-down method.

  2. Hochberg procedure (2 procedures)

    1. hochberg, the Hochberg (1988) step-up method.

    2. chochberg, the conservative Hochberg method developed by Gou and Tamhane (2018).

  3. Hommel procedure (5 procedures)

    1. hommel, the Hommel (1988) step-up method, linear time algorithm with standard binary search, equivalent to hommellsb.

    2. hommelq, the Hommel (1988) step-up method, quadratic time algorithm.

    3. hommell, the Hommel (1988) step-up method, linear time algorithm by Meijer, Krebs and Goeman (2019).

    4. hommellsb, the Hommel (1988) step-up method, linear time algorithm by Meijer, Krebs and Goeman (2019), with standard binary search enhancement.

    5. hommellsi, the Hommel (1988) step-up method, linear time algorithm by Meijer, Krebs and Goeman (2019), with interpolation search enhancement.

  4. Rom procedure (4 procedure)

    1. rom, the Rom (1990) step-up method, equivalent to romx.

    2. rom1, the Rom-1 method proposed by Gou and Zhang (2020).

    3. roma, the Rom-1A method proposed by Gou and Zhang (2020).

    4. romx, the Rom (1990) step-up method.

  5. Gou-Tamhane-Xi-Rom procedure (7 procedure)

    1. gtxr, the zeroth order hybrid Hommel-Hochberg procedure, proposed by Gou et al. (2014), equivalent to gtxr0b.

    2. gtxr0b, the zeroth order GTXR procedure, with standard binary search enhancement.

    3. gtxr1cb, the GTXR procedure with refined c critical constants, with standard binary search enhancement.

    4. gtxr2db, the GTXR procedure with refined d critical constants, with standard binary search enhancement.

    5. gtxr0i, the zeroth order GTXR procedure, with interpolation search enhancement.

    6. gtxr1ci, the GTXR procedure with refined c critical constants, with interpolation search enhancement.

    7. gtxr2di, the GTXR procedure with refined d critical constants, with interpolation search enhancement.

  6. Quick procedure (11 procedure)

    1. quick, the Quick method, proposed by Gou and Zhang (2020), equivalent to quick00b.

    2. quick00b, the zeroth order Quick procedure, proposed by Gou and Zhang (2020), with standard binary search enhancement.

    3. quick01b, the Quick procedure with refined d critical constants, with standard binary search enhancement.

    4. quick10b, the Quick procedure with refined c critical constants, with standard binary search enhancement.

    5. quick11b, the Quick procedure with refined c and d critical constants, with standard binary search enhancement.

    6. quickxb, the exact Quick procedure with refined c critical constants, with standard binary search enhancement.

    7. quick00i, the zeroth order Quick procedure, proposed by Gou and Zhang (2020), with interpolation search enhancement.

    8. quick01i, the Quick procedure with refined d critical constants, with interpolation search enhancement.

    9. quick10i, the Quick procedure with refined c critical constants, with interpolation search enhancement.

    10. quick11i, the Quick procedure with refined c and d critical constants, with interpolation search enhancement.

    11. quickxi, the exact Quick procedure with refined c critical constants, with interpolation search enhancement.

Value

a list, including a binary vector of rejections, the total number of comparisons, and an indicator of consonance.

Author(s)

Jiangtao Gou

References

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65-70.

Hochberg, Y. and Tamhane, A. C. (1987). Multiple Comparison Procedures. John Wiley and Sons, New York.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika 75, 800-802.

Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika 75, 383-386.

Rom, D. M. (1990). A sequentially rejective test procedure based on a modified Bonferroni inequality. Biometrika 77, 663-665.

Wright, S. P. (1992). Adjusted p-values for simultaneous inference. Biometrics 48, 1005-1013.

Gou, J., Tamhane, A. C., Xi, D., and Rom, D. (2014). A class of improved hybrid Hochberg-Hommel type step-up multiple test procedures. Biometrika 101, 899-911.

Gou, J., and Tamhane, A. C. (2014). On generalized Simes critical constants. Biometrical Journal 56, 1035-1054.

Gou, J., and Tamhane, A. C. (2018). Hochberg procedure under negative dependence. Statistica Sinica 28, 339-362.

Tamhane, A. C., and Gou, J. (2018). Advances in p-value based multiple test procedures. Journal of Biopharmaceutical Statistics 28, 10-27.

Meijer, R. J., Krebs, T. J. P., and Goeman, J. J. (2019). Hommel's procedure in linear time. Biometrical Journal 61, 73-82.

Tamhane, A. C., and Gou, J. (2022). Chapter 2 Multiple test procedures based on p-values. In X. Cui, T. Dickhaus, Y. Ding, and J. C. Hsu (Eds.), Handbook of multiple comparisons (Vol. 45, pp. 11-34).

Gou, J.(2022). Quick multiple test procedures and p-value adjustments, Statistics in Biopharmaceutical Research 14, 636-650.

See Also

elitism::p.adjust

Examples

library(elitism)
 pvalues.raw <- c(0.002,0.007,0.005,0.024,0.022,0.009,0.007,0.036,0.060,0.035)
 pkev <- new.env(); pkev$global.count.IS <- 0; pkev$global.count.FS <- 0;
 decision.hoch <- mtp(pvalues.raw, alpha = 0.025, method = "hochberg")
 pkev <- new.env(); pkev$global.count.IS <- 0; pkev$global.count.FS <- 0;
 decision.quick <- mtp(pvalues.raw, alpha = 0.025, method = "quick")
 pkev <- new.env(); pkev$global.count.IS <- 0; pkev$global.count.FS <- 0;
 decision.gtxr <- mtp(pvalues.raw, alpha = 0.025, method = "gtxr")
[Package elitism version 1.1.1 Index]