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Organize outputs for testing an intersection hypothesis

Source: R/test_values.R
test_values.Rd

An intersection hypothesis can be tested by a mixture of test types including Bonferroni, parametric and Simes tests. This function organize outputs of testing and prepare them for graph_report.

Usage

test_values_bonferroni(p, hypotheses, alpha, intersection = NA)

test_values_parametric(p, hypotheses, alpha, intersection = NA, test_corr)

test_values_simes(p, hypotheses, alpha, intersection = NA)

Arguments

p

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

hypotheses

A numeric vector of hypothesis weights in a graphical multiple comparison procedure. Must be a vector of values between 0 & 1 (inclusive). The length should match the row and column lengths of transitions. The sum of hypothesis weights should not exceed 1.

alpha

A numeric value of the overall significance level, which should be between 0 & 1. The default is 0.025 for one-sided hypothesis testing problems; another common choice is 0.05 for two-sided hypothesis testing problems. Note when parametric tests are used, only one-sided tests are supported.

intersection

(optional) A numeric scalar used to name the intersection hypothesis in a weighting strategy.

test_corr

(Optional) A list of numeric correlation matrices. Each entry in the list should correspond to each test group. For a test group using Bonferroni or Simes tests, its corresponding entry in test_corr should be NA. For a test group using parametric tests, its corresponding entry in test_corr should be a numeric correlation matrix specifying the correlation between test statistics for hypotheses in this test group. The length should match the number of elements in test_groups.

Value

A data frame with rows corresponding to individual hypotheses involved in the intersection hypothesis with hypothesis weights hypotheses. There are following columns:

  • Intersection - Name of this intersection hypothesis,

  • Hypothesis - Name of an individual hypothesis,

  • Test - Test type for an individual hypothesis,

  • p - (Unadjusted or raw) p-values for a individual hypothesis,

  • c_value- C value for parametric tests,

  • Weight - Hypothesis weight for an individual hypothesis,

  • Alpha - Overall significance level \(\alpha\),

  • Inequality_holds - Indicator to show if the p-value is less than or equal to its significance level.

    • For Bonferroni and Simes tests, the significance level is the hypothesis weight times \(\alpha\).

    • For parametric tests, the significance level is the c value times the hypothesis weight times \(\alpha\).

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.