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