adjust_p_bonferroni {graphicalMCP}

Calculate adjusted p-values

Description

For an intersection hypothesis, an adjusted p-value is the smallest significance level at which the intersection hypothesis can be rejected. The intersection hypothesis can be rejected if its adjusted p-value is less than or equal to \alpha. Currently, there are three test types supported:

• Bonferroni tests for adjust_p_bonferroni(),

• Parametric tests for adjust_p_parametric(),

  • Note that one-sided tests are required for parametric tests.

• Simes tests for adjust_p_simes().

Usage

adjust_p_bonferroni(p, hypotheses)

adjust_p_parametric(
  p,
  hypotheses,
  test_corr = NULL,
  maxpts = 25000,
  abseps = 1e-06,
  releps = 0
)

adjust_p_simes(p, hypotheses)

Arguments

p

A numeric vector of p-values (unadjusted, raw), whose values should be between 0 & 1. The length should match the length of hypotheses.

hypotheses

A numeric vector of hypothesis weights. Must be a vector of values between 0 & 1 (inclusive). The length should match the length of p. The sum of hypothesis weights should not exceed 1.

test_corr

(Optional) A numeric matrix of correlations between test statistics, which is needed to perform parametric tests using adjust_p_parametric(). The number of rows and columns of this correlation matrix should match the length of p.

maxpts

(Optional) An integer scalar for the maximum number of function values, which is needed to perform parametric tests using the mvtnorm::GenzBretz algorithm. The default is 25000.

abseps

(Optional) A numeric scalar for the absolute error tolerance, which is needed to perform parametric tests using the mvtnorm::GenzBretz algorithm. The default is 1e-6.

releps

(Optional) A numeric scalar for the relative error tolerance as double, which is needed to perform parametric tests using the mvtnorm::GenzBretz algorithm. The default is 0.

Value

A single adjusted p-value for the intersection hypothesis.

References

Bretz, F., Maurer, W., Brannath, W., and Posch, M. (2009). A graphical approach to sequentially rejective multiple test procedures. Statistics in Medicine, 28(4), 586-604.

Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted Simes tests. Statistics in Medicine, 35(22), 4041-4055.

Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), 918-931.

See Also

adjust_weights_parametric() for adjusted hypothesis weights using parametric tests, adjust_weights_simes() for adjusted hypothesis weights using Simes tests.

Examples

hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25)
p <- c(0.019, 0.025, 0.05)
adjust_p_bonferroni(p, hypotheses)
set.seed(1234)
hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25)
p <- c(0.019, 0.025, 0.05)
# Using the `mvtnorm::GenzBretz` algorithm
corr <- matrix(0.5, nrow = 3, ncol = 3)
diag(corr) <- 1
adjust_p_parametric(p, hypotheses, corr)
hypotheses <- c(H1 = 0.5, H2 = 0.25, H3 = 0.25)
p <- c(0.019, 0.025, 0.05)
adjust_p_simes(p, hypotheses)