From 918a2b2e68242079792b4c9293dcdacea40e322e Mon Sep 17 00:00:00 2001 From: EeethB Date: Wed, 8 Nov 2023 16:40:40 -0600 Subject: [PATCH] Update power docs --- R/graph_calculate_power.R | 19 ++++--- man/adjust_p.Rd | 12 ++--- man/adjusted-weights.Rd | 12 ++--- man/calc-test_values.Rd | 12 ++--- man/example-graphs.Rd | 12 ++--- man/graph_calculate_power.Rd | 31 +++++++----- man/graph_create.Rd | 12 ++--- man/graph_generate_weights.Rd | 12 ++--- man/graph_update.Rd | 12 ++--- man/testing-fast.Rd | 12 ++--- man/testing.Rd | 12 ++--- vignettes/glossary.Rmd | 94 +++++++++++++++++------------------ 12 files changed, 132 insertions(+), 120 deletions(-) diff --git a/R/graph_calculate_power.R b/R/graph_calculate_power.R index 99739350..ea85b3ef 100644 --- a/R/graph_calculate_power.R +++ b/R/graph_calculate_power.R @@ -46,14 +46,19 @@ #' matrix of test results for the simulation, resulting in a `sim_n` length #' vector. The mean of this vector is returned as "Probability of success" #' -#' @return A list with five elements -#' * power_local - rejection proportion for each hypothesis individually -#' * power_expected - average number of hypotheses rejected in a single -#' simulation -#' * power_at_least_1 - proportion of simulations which reject any hypothesis -#' * power_all - proportion of simulations which reject all hypotheses -#' * power_success - proportion of simulations which reject any of the +#' @return A list with three elements +#' * inputs - A list of input parameters +#' * power - A list of measures of how often hypotheses are rejected +#' * power_local - Rejection proportion for each hypothesis individually +#' * power_expected - Average number of hypotheses rejected in a single +#' simulation +#' * power_at_least_1 - Proportion of simulations which reject any +#' hypothesis +#' * power_all - Proportion of simulations which reject all hypotheses +#' * power_success - Proportion of simulations which reject any of the #' hypotheses specified in `sim_success` +#' * details - An optional list of datasets showing simulated p-values and +#' results for each simulation #' #' @export #' diff --git a/man/adjust_p.Rd b/man/adjust_p.Rd index 93c59507..2abc98ef 100644 --- a/man/adjust_p.Rd +++ b/man/adjust_p.Rd @@ -48,29 +48,29 @@ graphicalMCP:::adjust_p_parametric(p, w, corr2) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/adjusted-weights.Rd b/man/adjusted-weights.Rd index ceafb39d..48ff90fb 100644 --- a/man/adjusted-weights.Rd +++ b/man/adjusted-weights.Rd @@ -84,29 +84,29 @@ graphicalMCP:::adjust_weights_simes(gw_0, p, list(4:6)) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/calc-test_values.Rd b/man/calc-test_values.Rd index fca24502..eae05563 100644 --- a/man/calc-test_values.Rd +++ b/man/calc-test_values.Rd @@ -45,29 +45,29 @@ graphicalMCP:::test_values_simes(p, w, .05) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/example-graphs.Rd b/man/example-graphs.Rd index 08b6b6b7..1c4da935 100644 --- a/man/example-graphs.Rd +++ b/man/example-graphs.Rd @@ -50,29 +50,29 @@ bonferroni_holm(3, hyp_names = paste("dose", letters[1:3])) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/graph_calculate_power.Rd b/man/graph_calculate_power.Rd index cd9857cb..42f85881 100644 --- a/man/graph_calculate_power.Rd +++ b/man/graph_calculate_power.Rd @@ -51,16 +51,23 @@ body will be used as the name. Lambda functions also work starting with R simulations and test results should be included in the output or not} } \value{ -A list with five elements +A list with three elements \itemize{ -\item power_local - rejection proportion for each hypothesis individually -\item power_expected - average number of hypotheses rejected in a single +\item inputs - A list of input parameters +\item power - A list of measures of how often hypotheses are rejected +\itemize{ +\item power_local - Rejection proportion for each hypothesis individually +\item power_expected - Average number of hypotheses rejected in a single simulation -\item power_at_least_1 - proportion of simulations which reject any hypothesis -\item power_all - proportion of simulations which reject all hypotheses -\item power_success - proportion of simulations which reject any of the +\item power_at_least_1 - Proportion of simulations which reject any +hypothesis +\item power_all - Proportion of simulations which reject all hypotheses +\item power_success - Proportion of simulations which reject any of the hypotheses specified in \code{sim_success} } +\item details - An optional list of datasets showing simulated p-values and +results for each simulation +} } \description{ It's often difficult to tell how likely a given hypothesis is to be rejected. @@ -116,29 +123,29 @@ graph_calculate_power( \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/graph_create.Rd b/man/graph_create.Rd index 31ce395b..4377a862 100644 --- a/man/graph_create.Rd +++ b/man/graph_create.Rd @@ -104,29 +104,29 @@ g \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/graph_generate_weights.Rd b/man/graph_generate_weights.Rd index 88061674..0bc639ee 100644 --- a/man/graph_generate_weights.Rd +++ b/man/graph_generate_weights.Rd @@ -48,29 +48,29 @@ graph_generate_weights(par_gate) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/graph_update.Rd b/man/graph_update.Rd index 5e3e2683..bb0c1b59 100644 --- a/man/graph_update.Rd +++ b/man/graph_update.Rd @@ -53,29 +53,29 @@ graph_update(g, 2:3) \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/testing-fast.Rd b/man/testing-fast.Rd index 128b0f00..fb0fb198 100644 --- a/man/testing-fast.Rd +++ b/man/testing-fast.Rd @@ -66,29 +66,29 @@ graphicalMCP:::graph_test_shortcut_fast( \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/man/testing.Rd b/man/testing.Rd index 50bd53d0..d3e1b197 100644 --- a/man/testing.Rd +++ b/man/testing.Rd @@ -111,29 +111,29 @@ graph_test_closure( \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), 586b +Medicine, 28(4), 586–604. \url{https://doi.org/10.1002/sim.3495} Bretz, F., Maurer, W., and Hommel, G. (2011). Test and power considerations for multiple endpoint analyses using sequentially rejective graphical -procedures. Statistics in Medicine, 30(13), 1489b +procedures. Statistics in Medicine, 30(13), 1489–1501. \url{https://doi.org/10.1002/sim.3988} Bretz, F., Posch, M., Glimm, E., Klinglmueller, F., Maurer, W., and Rohmeyer, K. (2011). Graphical approaches for multiple comparison procedures using weighted Bonferroni, Simes, or parametric tests. Biometrical Journal, 53(6), -894b +894–913. \url{https://doi.org/10.1002/bimj.201000239} Lu, K. (2016). Graphical approaches using a Bonferroni mixture of weighted -Simes tests. Statistics in Medicine, 35(22), 4041b +Simes tests. Statistics in Medicine, 35(22), 4041–4055. \url{https://doi.org/10.1002/sim.6985} Xi, D., Glimm, E., Maurer, W., and Bretz, F. (2017). A unified framework for weighted parametric multiple test procedures. Biometrical Journal, 59(5), -918b +918–931. \url{https://doi.org/10.1002/bimj.201600233} Xi, D., and Bretz, F. (2019). Symmetric graphs for equally weighted tests, with application to the Hochberg procedure. Statistics in Medicine, 38(27), -5268b +5268–5282. \url{https://doi.org/10.1002/sim.8375} Rohmeyer K, Klinglmueller F (2020). \emph{gMCP: Graph Based Multiple Test Procedures}. R package version 0.8-15, diff --git a/vignettes/glossary.Rmd b/vignettes/glossary.Rmd index 7e0472c4..2cf09c10 100644 --- a/vignettes/glossary.Rmd +++ b/vignettes/glossary.Rmd @@ -17,50 +17,50 @@ knitr::opts_chunk$set( To improve the readability of the code, we provide the glossary to serve as an educational document to grow people's understanding of the graphical approach to multiple comparison procedures. Most terms are inputs or outputs of exported functions and some are used only in the internal code. If any definition could be clarified or improved, please submit an issue to the GitHub repository. -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| Entity | Definition | A liases | Varia ble(s) | R elated | -+=====================================+================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================+===========================================+===================================+====================================+ -| **G raph** | A set of nodes and directed edges representing a graphical multiple comparison procedure. | | `graph` | Hypot heses, Trans itions | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Hypoth eses** | The nodes with weights in a **graph**. Each node represents a null hypothesis, associated with a **hypothesis** weights. The corresponding **significance level** is the weight times `alpha`. | we ights, hypo thesis w eights | `hypot heses` | Wei ghting str ategy, Trans itions | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| | Terms associated with **hypotheses** get their variable names: hypothesis names, and number of hypotheses. | | `hyp_n ames`, `num _hyps` | | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **T ransit ions** | The directed edges with weights in a **graph**. Each edge defines the proportion of the **hypothesis** weight to be propagated from the origin hypothesis to the end hypothesis, when the origin is rejected. | | `transi tions` | Hypo theses | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **In tersec tion** **hypoth esis** | An intersection hypothesis is an intersection of multiple null hypotheses, which means that all associated hypotheses are true. Plural often implies all intersections of all subsets of hypotheses. | i nterse ction, s ub-gra ph(s), c losure | `in tersec tions` | Wei ghting st rategy | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Wei ghting stra tegy** | The set of all **intersections** and their hypothesis **weights** according to Algorithm 1 in @bretz-2011-graphical. | inters ection we ights, c losure w eights | `w eighti ng_str ategy` | | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Ad justed wei ghts** | The set of hypothesis **weights**, adjusted according to a multiple comparison procedure: | | `adjus ted_we ights` | | -| | | | | | -| | - Bonferroni: No change from the hypothesis weights from a graph | | | | -| | - Simes: Sum of hypothesis weights for hypotheses with smaller p-values in an intersection hypothesis | | | | -| | - Parametric: Multiply Bonferroni weights by c-value, which is calculated based on the joint distribution of test statistics of the associated intersection hypothesis A hypothesis may be rejected if its **p-value** is less than or equal to its **adjusted weight** times `alpha`. | | | | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **P-va lues** | The set of p-values before multiplicity adjustment. | | `p` | Ad justed & o rdered p- values | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **O rdered p-va lues** | **P-values** sorted from the smallest to the largest. They are mainly used for Simes tests. | | `orde red_p` | (Adj usted) P- values | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Ad justed p-va lues** | **P-values** that have been adjusted according to the multiple comparison procedure. A hypothesis may be rejected if its **adjusted p-value** is less than or equal to `alpha`. | | `adjus ted_p` | (Or dered) P- values | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Signif icance l evel** | The threshold chosen to test a null hypothesis, which may be rejected if its **p-value** is less than or equal to its **significance level**. | | `alpha` | P- values | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Test t ypes** | A specification of which testing type to use for intersection hypotheses - Bonferroni, Simes, and parametric are currently supported. | tests | `test_ types` | T esting st rategy | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Test gr oups** | A partition of all null hypotheses in a **graph** specifying which **hypotheses** should be tested together. | groups | `gr oups`, `test_g roups` | T esting st rategy | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **T esting stra tegy** | **Test types** and **test groups** combined with a **graph**. | | | | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Ma rginal p ower** | The power to reject a null **hypothesis** at the **significance level** `alpha` (without multiplicity adjustment). This is closely related to the non-centrality parameter, which is the expected mean of the standardized test statistics under the alternative hypothesis. In this package, the asymptotic normal distribution with a variance of 1 is assumed and then the non-centrality is the mean of this distribution. The relationship between the **marginal power** and the non-centrality parameter is `noncentral ity_parameter = qnorm(1 - alpha ) - qnorm(1 - marginal_power)`. | | `mar ginal_ power` | | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| - \*Corre lation ma trix\*\* | Specification of correlations between test statistics for **hypotheses**. There are two types of the correlation matrix. The correlation for testing `test_corr` is used to perform parametric tests. It may contain `NA`s. The correlation for simulation `test_sim` is used to simulate **p-values** from the alternative hypotheses for to assess **power**, under assumptions. It does not contain `NA`s. | | `corr`, `test_ corr`, `sim _corr` | T esting st rategy & power | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **Suc cess** | A specification of which null **hypotheses** must be rejected to consider a clinical trial a success. | | `sim_su ccess` | Power | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| **P ower** | With a given **graph**, **testing strategy**, `alpha`, and the underlying distributionunder the alternative hypotheses, the estimated likelihood that a particular combination of null hypotheses will be rejected. | | `po wer_*` | S uccess | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| - Delete a **h ypothe sis**\* | Remove a **hypothesis** from a graph, and update the graph according to algorithm 1 of @bretz-2011-graphical. This is an operation on a graph. | | | Reject a hypo thesis | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ -| - Reject a **h ypothe sis**\* | Under a given **graph**, **testing strategy**, and `alpha`, a hypothesis is rejected if its **p-value** is sufficiently small, which is determined by the graphical multiple comparison procedure. | | | Delete a hypo thesis | -+-------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| Entity | Definition | A liases | Varia ble(s) | R elated | ++====================================+================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================================+===========================================+===================================+====================================+ +| **G raph** | A set of nodes and directed edges representing a graphical multiple comparison procedure. | | `graph` | Hypot heses, Trans itions | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Hypoth eses** | The nodes with weights in a **graph**. Each node represents a null hypothesis, associated with a **hypothesis** weights. The corresponding **significance level** is the weight times `alpha`. | we ights, hypo thesis w eights | `hypot heses` | Wei ghting str ategy, Trans itions | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| | Terms associated with **hypotheses** get their variable names: hypothesis names, and number of hypotheses. | | `hyp_n ames`, `num _hyps` | | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **T ransit ions** | The directed edges with weights in a **graph**. Each edge defines the proportion of the **hypothesis** weight to be propagated from the origin hypothesis to the end hypothesis, when the origin is rejected. | | `transi tions` | Hypo theses | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **In tersec tion** **hypoth esis** | An intersection hypothesis is an intersection of multiple null hypotheses, which means that all associated hypotheses are true. Plural often implies all intersections of all subsets of hypotheses. | i nterse ction, s ub-gra ph(s), c losure | `in tersec tions` | Wei ghting st rategy | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Wei ghting stra tegy** | The set of all **intersections** and their hypothesis **weights** according to Algorithm 1 in @bretz-2011-graphical. | inters ection we ights, c losure w eights | `w eighti ng_str ategy` | | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Ad justed wei ghts** | The set of hypothesis **weights**, adjusted according to a multiple comparison procedure: | | `adjus ted_we ights` | | +| | | | | | +| | - Bonferroni: No change from the hypothesis weights from a graph | | | | +| | - Simes: Sum of hypothesis weights for hypotheses with smaller p-values in an intersection hypothesis | | | | +| | - Parametric: Multiply Bonferroni weights by c-value, which is calculated based on the joint distribution of test statistics of the associated intersection hypothesis A hypothesis may be rejected if its **p-value** is less than or equal to its **adjusted weight** times `alpha`. | | | | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **P-va lues** | The set of p-values before multiplicity adjustment. | | `p` | Ad justed & o rdered p- values | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **O rdered p-va lues** | **P-values** sorted from the smallest to the largest. They are mainly used for Simes tests. | | `orde red_p` | (Adj usted) P- values | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Ad justed p-va lues** | **P-values** that have been adjusted according to the multiple comparison procedure. A hypothesis may be rejected if its **adjusted p-value** is less than or equal to `alpha`. | | `adjus ted_p` | (Or dered) P- values | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Signif icance l evel** | The threshold chosen to test a null hypothesis, which may be rejected if its **p-value** is less than or equal to its **significance level**. | | `alpha` | P- values | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Test t ypes** | A specification of which testing type to use for intersection hypotheses - Bonferroni, Simes, and parametric are currently supported. | tests | `test_ types` | T esting st rategy | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Test gr oups** | A partition of all null hypotheses in a **graph** specifying which **hypotheses** should be tested together. | groups | `gr oups`, `test_g roups` | T esting st rategy | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **T esting stra tegy** | **Test types** and **test groups** combined with a **graph**. | | | | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Ma rginal p ower** | The power to reject a null **hypothesis** at the **significance level** `alpha` (without multiplicity adjustment). This is closely related to the non-centrality parameter, which is the expected mean of the standardized test statistics under the alternative hypothesis. In this package, the asymptotic normal distribution with a variance of 1 is assumed and then the non-centrality is the mean of this distribution. The relationship between the **marginal power** and the non-centrality parameter is `noncentral ity_parameter = qnorm(1 - alpha ) - qnorm(1 - marginal_power)`. | | `mar ginal_ power` | | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| - \*Corre lation ma trix\*\* | Specification of correlations between test statistics for **hypotheses**. There are two types of the correlation matrix. The correlation for testing `test_corr` is used to perform parametric tests. It may contain `NA`s. The correlation for simulation `test_sim` is used to simulate **p-values** from the alternative hypotheses for to assess **power**, under assumptions. It does not contain `NA`s. | | `corr`, `test_ corr`, `sim _corr` | T esting st rategy & power | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **Suc cess** | A specification of which null **hypotheses** must be rejected to consider a clinical trial a success. | | `sim_su ccess` | Power | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| **P ower** | With a given **graph**, **testing strategy**, `alpha`, and the underlying distributionunder the alternative hypotheses, the estimated likelihood that a particular combination of null hypotheses will be rejected. | | `po wer_*` | S uccess | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| - Delete a **h ypothe sis**\* | Remove a **hypothesis** from a graph, and update the graph according to algorithm 1 of @bretz-2011-graphical. This is an operation on a graph. | | | Reject a hypo thesis | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+ +| - Reject a **h ypothe sis**\* | Under a given **graph**, **testing strategy**, and `alpha`, a hypothesis is rejected if its **p-value** is sufficiently small, which is determined by the graphical multiple comparison procedure. | | | Delete a hypo thesis | ++------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------+-----------------------------------+------------------------------------+