Example Overview
-In a 2-arm controlled clinical trial with one primary endpoint, there -are 3 null hypotheses based on populations defined defined by biomarker -status. In each case the null hypothesis assumes no difference in the -distribution of the time until a primary endpoint is reached between the -treatment and control groups:
--
-
- H1: Biomarker A positive population
-
- - H2: Biomarker B positive population -
- H3: Overall population -
-
-
-Multiplicity Strategy
-We will use a graphical approach to visualize the multiplicity -strategy.
-# Transition matrix and initial weights
-m <- matrix(c(
- 0, 3/7, 4/7,
- 3/7, 0, 4/7,
- 0.5, 0.5, 0
-), nrow = 3, byrow = TRUE)
-
-w <- c(0.3, 0.3, 0.4) # Initial weights
-
-# Visualize strategy
-name_hypotheses <- c("H1: Biomarker A positive", "H2: Biomarker B positive", "H3: Overall Population")
-
-hplot <- gMCPLite::hGraph(
- 3,
- alphaHypotheses = w, m = m,
- nameHypotheses = name_hypotheses, trhw = .2, trhh = .1,
- digits = 5, trdigits = 3, size = 5, halfWid = 1, halfHgt = 0.5,
- offset = 0.2, trprop = 0.4,
- fill = as.factor(c(2, 3, 1)),
- palette = c("#BDBDBD", "#E0E0E0", "#EEEEEE"),
- wchar = "w"
-)
-hplot
-
-
-
-
-Study Setup
-We assume 2 analyses: an interim analysis (IA) and a final analysis -(FA). For the multiplicity adjustments, we need the number of events in -the treatment and control groups combined that are available for testing -each hypothesis at both analyses for each population and the -intersection of populations. In the following AB positive means positive -for both biomarker A and biomarker B.
-# Create event data systematically
-create_event_data <- function() {
- populations <- rep(c("A positive", "B positive", "AB positive", "overall"), 2)
- analyses <- rep(c(1, 2), each = 4)
- events <- c(100, 110, 80, 225, 200, 220, 160, 450) # IA, then FA
-
- tibble(
- population = populations,
- analysis = analyses,
- event = events
- )
-}
-
-event_tbl <- create_event_data()
-event_tbl %>%
- gt() %>%
- tab_header(title = "Event Count by Population and Analysis")
-
-
-
-
-
-| Event Count by Population and Analysis | -||
| population | -analysis | -event | -
|---|---|---|
| A positive | -1 | -100 |
| B positive | -1 | -110 |
| AB positive | -1 | -80 |
| overall | -1 | -225 |
| A positive | -2 | -200 |
| B positive | -2 | -220 |
| AB positive | -2 | -160 |
| overall | -2 | -450 |
We assume the following unadjusted p-values at each analysis for each -hypothesis.
-# Observed p-values
-obs_tbl <- tribble(
- ~hypothesis, ~analysis, ~obs_p,
- "H1", 1, 0.02,
- "H2", 1, 0.01,
- "H3", 1, 0.012,
- "H1", 2, 0.015,
- "H2", 2, 0.012,
- "H3", 2, 0.010
-) %>%
- mutate(obs_Z = -qnorm(obs_p))
-
-obs_tbl %>%
- gt() %>%
- tab_header(title = "Nominal p-values")
-
-
-
-
-
-| Nominal p-values | -|||
| hypothesis | -analysis | -obs_p | -obs_Z | -
|---|---|---|---|
| H1 | -1 | -0.020 | -2.053749 |
| H2 | -1 | -0.010 | -2.326348 |
| H3 | -1 | -0.012 | -2.257129 |
| H1 | -2 | -0.015 | -2.170090 |
| H2 | -2 | -0.012 | -2.257129 |
| H3 | -2 | -0.010 | -2.326348 |
-p_obs_IA <- (obs_tbl %>% filter(analysis == 1))$obs_p
-p_obs_FA <- (obs_tbl %>% filter(analysis == 2))$obs_pWe now have all the information we need to perform testing and -adjusting p-values.
-
-
-
-Information Fractions
-Next we calculate information fractions at interim and final -analyses. The final event count at each analysis is assumed to be the -planned count for each population.
-# Helper function to extract events
-get_events <- function(analysis_num, population_name) {
- event_tbl %>%
- filter(analysis == analysis_num, population == population_name) %>%
- pull(event)
-}
-
-# Extract event counts
-events_IA <- event_tbl %>% filter(analysis == 1)
-events_FA <- event_tbl %>% filter(analysis == 2)
-
-a_pos_IA <- get_events(1, "A positive")
-b_pos_IA <- get_events(1, "B positive")
-ab_pos_IA <- get_events(1, "AB positive")
-overall_IA <- get_events(1, "overall")
-
-a_pos_FA <- get_events(2, "A positive")
-b_pos_FA <- get_events(2, "B positive")
-ab_pos_FA <- get_events(2, "AB positive")
-overall_FA <- get_events(2, "overall")
-
-# Calculate information fractions
-IF_IA <- c(
- (a_pos_IA + overall_IA) / (a_pos_FA + overall_FA), # H1
- (b_pos_IA + overall_IA) / (b_pos_FA + overall_FA), # H2
- (ab_pos_IA + overall_IA) / (ab_pos_FA + overall_FA) # H3
-)
-
-tibble(
- Hypothesis = c("H1", "H2", "H3"),
- Information_Fraction = IF_IA
-) %>%
- gt() %>%
- tab_header(title = "Information Fractions at Interim Analysis") %>%
- fmt_number(columns = 2, decimals = 3)
-
-
-
-
-
-| Information Fractions at Interim Analysis | -|
| Hypothesis | -Information_Fraction | -
|---|---|
| H1 | -0.500 |
| H2 | -0.500 |
| H3 | -0.500 |
-
-
-
-
-Correlation Matrix
-Now we can create a correlation matrix for all tests performed based -on the methods of Anderson et al. (2022) -(or Chen et al. (2021)).
-# Create correlation matrix using event intersections
-event_intersections <- tribble(
- ~H1, ~H2, ~Analysis, ~Event,
- # Analysis 1 - Interim
- 1, 1, 1, a_pos_IA,
- 2, 2, 1, b_pos_IA,
- 3, 3, 1, overall_IA,
- 1, 2, 1, ab_pos_IA,
- 1, 3, 1, a_pos_IA,
- 2, 3, 1, b_pos_IA,
- # Analysis 2 - Final
- 1, 1, 2, a_pos_FA,
- 2, 2, 2, b_pos_FA,
- 3, 3, 2, overall_FA,
- 1, 2, 2, ab_pos_FA,
- 1, 3, 2, a_pos_FA,
- 2, 3, 2, b_pos_FA
-)
-
-# Generate correlation from events
-correlation_matrix <- generate_corr(event_intersections)
-
-correlation_matrix %>%
- round(3) %>%
- knitr::kable(caption = "Correlation Matrix (6x6)")| H1_A1 | -H2_A1 | -H3_A1 | -H1_A2 | -H2_A2 | -H3_A2 | -
|---|---|---|---|---|---|
| 1.000 | -0.763 | -0.667 | -0.707 | -0.539 | -0.471 | -
| 0.763 | -1.000 | -0.699 | -0.539 | -0.707 | -0.494 | -
| 0.667 | -0.699 | -1.000 | -0.471 | -0.494 | -0.707 | -
| 0.707 | -0.539 | -0.471 | -1.000 | -0.763 | -0.667 | -
| 0.539 | -0.707 | -0.494 | -0.763 | -1.000 | -0.699 | -
| 0.471 | -0.494 | -0.707 | -0.667 | -0.699 | -1.000 | -
-
-
-Sequential P-value Calculations
-# Helper function for systematic calculations
-calculate_seq_p_systematic <- function(test_analysis, p_obs_IA, p_obs_FA, w, m, correlation_matrix, IF_IA) {
-
- combinations <- c("H1, H2, H3", "H1, H2", "H1, H3", "H2, H3", "H1", "H2", "H3")
-
- results <- map_dfr(combinations, ~ {
- seq_p <- calc_seq_p(
- test_analysis = test_analysis,
- test_hypothesis = .x,
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = correlation_matrix,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
- )
-
- tibble(
- combination = .x,
- sequential_p = seq_p
- )
- })
-
- return(results)
-}
-
-# Calculate for both interim and final analyses
-ia_results <- calculate_seq_p_systematic(1, p_obs_IA, p_obs_FA, w, m, correlation_matrix, IF_IA) %>%
- mutate(analysis = "Interim")
-
-fa_results <- calculate_seq_p_systematic(2, p_obs_IA, p_obs_FA, w, m, correlation_matrix, IF_IA) %>%
- mutate(analysis = "Final")
-
-
-Results Summary
-# Combined results table
-combined_results <- bind_rows(ia_results, fa_results)
-
-combined_results %>%
- gt() %>%
- tab_header(title = "Sequential p-values - Comprehensive Results") %>%
- fmt_number(columns = "sequential_p", decimals = 4) %>%
- tab_style(
- style = cell_fill(color = "lightblue"),
- locations = cells_body(rows = analysis == "Interim")
- ) %>%
- tab_style(
- style = cell_fill(color = "lightgreen"),
- locations = cells_body(rows = analysis == "Final")
- )
-
-
-
-
-
-| Sequential p-values - Comprehensive Results | -||
| combination | -sequential_p | -analysis | -
|---|---|---|
| H1, H2, H3 | -0.1943 | -Interim |
| H1, H2 | -0.1400 | -Interim |
| H1, H3 | -0.1553 | -Interim |
| H2, H3 | -0.1529 | -Interim |
| H1 | -0.1678 | -Interim |
| H2 | -0.0839 | -Interim |
| H3 | -0.1007 | -Interim |
| H1, H2, H3 | -0.0206 | -Final |
| H1, H2 | -0.0210 | -Final |
| H1, H3 | -0.0165 | -Final |
| H2, H3 | -0.0162 | -Final |
| H1 | -0.0159 | -Final |
| H2 | -0.0127 | -Final |
| H3 | -0.0106 | -Final |
-
-
-Adjusted Sequential P-values
-# Calculate adjusted sequential p-values (max over relevant combinations)
-calculate_adjusted <- function(results_df) {
- h1_adj <- max(
- results_df$sequential_p[results_df$combination == "H1, H2, H3"],
- results_df$sequential_p[results_df$combination == "H1, H2"],
- results_df$sequential_p[results_df$combination == "H1, H3"],
- results_df$sequential_p[results_df$combination == "H1"]
- )
-
- h2_adj <- max(
- results_df$sequential_p[results_df$combination == "H1, H2, H3"],
- results_df$sequential_p[results_df$combination == "H1, H2"],
- results_df$sequential_p[results_df$combination == "H2, H3"],
- results_df$sequential_p[results_df$combination == "H2"]
- )
-
- h3_adj <- max(
- results_df$sequential_p[results_df$combination == "H1, H2, H3"],
- results_df$sequential_p[results_df$combination == "H1, H3"],
- results_df$sequential_p[results_df$combination == "H2, H3"],
- results_df$sequential_p[results_df$combination == "H3"]
- )
-
- tibble(
- hypothesis = c("H1", "H2", "H3"),
- adjusted_sequential_p = c(h1_adj, h2_adj, h3_adj)
- )
-}
-
-# Calculate for both analyses
-ia_adjusted <- calculate_adjusted(ia_results) %>% mutate(analysis = "Interim")
-fa_adjusted <- calculate_adjusted(fa_results) %>% mutate(analysis = "Final")
-
-adjusted_results <- bind_rows(ia_adjusted, fa_adjusted)
-
-adjusted_results %>%
- gt() %>%
- tab_header(title = "Adjusted Sequential p-values") %>%
- fmt_number(columns = "adjusted_sequential_p", decimals = 4) %>%
- tab_style(
- style = cell_fill(color = "pink"),
- locations = cells_body(rows = adjusted_sequential_p <= 0.025)
- )
-
-
-
-
-
-| Adjusted Sequential p-values | -||
| hypothesis | -adjusted_sequential_p | -analysis | -
|---|---|---|
| H1 | -0.1943 | -Interim |
| H2 | -0.1943 | -Interim |
| H3 | -0.1943 | -Interim |
| H1 | -0.0210 | -Final |
| H2 | -0.0210 | -Final |
| H3 | -0.0206 | -Final |
-
-
-[](https://github.com/Merck/wpgsd/actions/workflows/R-CMD-check.yaml)
-[](https://app.codecov.io/gh/Merck/wpgsd?branch=main)
-
-
-Weighted parametric group sequential design (WPGSD) allows one to take advantage
-of the known correlation structure in constructing efficacy bounds to control
-family-wise error rate (FWER) for a group sequential design. Here correlation
-may be due to common observations in nested populations, due to common
-observations in overlapping populations, or due to common observations
-in the control arm.
-
-## Installation
-
-The easiest way to get wpgsd is to install from CRAN:
-
-```r
-install.packages("wpgsd")
-```
-
-Alternatively, to use a new feature or get a bug fix,
-you can install the development version of wpgsd from GitHub:
-
-```r
-# install.packages("remotes")
-remotes::install_github("Merck/wpgsd")
-```
-
-## Current limitations
-
-There are some limitations that are currently being addressed.
-Please use the package with caution in production environments.
-
-- The current implementation may have limitations when handling more
- complex scenarios beyond what has been demonstrated.
-- The API is subject to potential breaking changes as it is currently
- being reviewed and refactored.
-- Further validation is needed to ensure the reliability of the package.
-- More documentation is expected in the future releases.
-
-## References
-
-Anderson, K. M., Guo, Z., Zhao, J., & Sun, L. Z. (2022).
-A unified framework for weighted parametric group sequential design.
-_Biometrical Journal_, 64(7), 1219--1239.
-
-BibTeX entry:
-
-```
-@article{anderson2022unified,
- title = {A unified framework for weighted parametric group sequential design},
- author = {Anderson, Keaven M and Guo, Zifang and Zhao, Jing and Sun, Linda Z},
- journal = {Biometrical Journal},
- volume = {64},
- number = {7},
- pages = {1219--1239},
- year = {2022},
- publisher = {Wiley Online Library}
-}
-```
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diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/event_table_integration.R b/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/event_table_integration.R
deleted file mode 100644
index 06fb2b6..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/event_table_integration.R
+++ /dev/null
@@ -1,71 +0,0 @@
-# Example integration of EventTable S7 class with existing wpgsd functions
-# This shows how EventTable can work with generate_corr()
-
-library(wpgsd)
-library(tibble)
-
-# Example 1: Using EventTable with generate_corr()
-# Create event data using the EventTable class
-event_data_raw <- tibble::tribble(
- ~H1, ~H2, ~Analysis, ~Event,
- 1, 1, 1, 155,
- 2, 2, 1, 160,
- 3, 3, 1, 165,
- 1, 2, 1, 85,
- 1, 3, 1, 85,
- 2, 3, 1, 85,
- 1, 1, 2, 305,
- 2, 2, 2, 320,
- 3, 3, 2, 335,
- 1, 2, 2, 170,
- 1, 3, 2, 170,
- 2, 3, 2, 170
-)
-
-# Create EventTable object
-event_table <- EventTable(data = event_data_raw)
-print("Created EventTable:")
-print(event_table)
-
-# Use with generate_corr (currently expects tibble/data.frame)
-# The @data slot extracts the underlying tibble
-correlation_matrix <- generate_corr(event_table@data)
-print("Generated correlation matrix:")
-print(correlation_matrix)
-
-# Example 2: Data validation before processing
-cat("\nExample 2: Data validation\n")
-cat("==========================\n")
-
-# Try to create EventTable with invalid data
-tryCatch({
- invalid_data <- tibble::tibble(
- H1 = c(1, 2, -1), # Invalid: negative hypothesis index
- H2 = c(1, 2, 3),
- Analysis = c(1, 1, 1),
- Event = c(100, 200, 150)
- )
-
- invalid_table <- EventTable(data = invalid_data)
-}, error = function(e) {
- cat("Validation caught error:", e$message, "\n")
-})
-
-# Example 3: Subsetting capabilities
-cat("\nExample 3: Subsetting\n")
-cat("=====================\n")
-
-# Get only first analysis
-analysis_1 <- subset_event_table(event_table, analysis = 1)
-cat("Analysis 1 events:\n")
-print(analysis_1@data)
-
-# Get only H1-H2 hypothesis pairs
-h1_h2_events <- subset_event_table(event_table, hypotheses = c(1, 2))
-cat("\nH1-H2 hypothesis events:\n")
-print(h1_h2_events@data)
-
-# Example 4: Summary information
-cat("\nExample 4: Summary\n")
-cat("==================\n")
-summary(event_table)
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/test_event_table.R b/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/test_event_table.R
deleted file mode 100644
index d55ecbf..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/examples/test_event_table.R
+++ /dev/null
@@ -1,50 +0,0 @@
-# Test script for EventTable S7 class
-# This demonstrates how to use the new EventTable class
-
-library(wpgsd)
-library(tibble)
-
-# Create sample event data as used in the package
-event_data <- tibble::tribble(
- ~H1, ~H2, ~Analysis, ~Event,
- 1, 1, 1, 155,
- 2, 2, 1, 160,
- 3, 3, 1, 165,
- 1, 2, 1, 85,
- 1, 3, 1, 85,
- 2, 3, 1, 85,
- 1, 1, 2, 305,
- 2, 2, 2, 320,
- 3, 3, 2, 335,
- 1, 2, 2, 170,
- 1, 3, 2, 170,
- 2, 3, 2, 170
-)
-
-# Create EventTable object
-event_table <- EventTable(data = event_data)
-
-# Print the object
-print(event_table)
-
-# Get summary
-summary(event_table)
-
-# Subset by analysis
-subset_analysis_1 <- subset_event_table(event_table, analysis = 1)
-print("Analysis 1 subset:")
-print(subset_analysis_1)
-
-# Subset by hypotheses
-subset_h1_h2 <- subset_event_table(event_table, hypotheses = c(1, 2))
-print("H1-H2 subset:")
-print(subset_h1_h2)
-
-# Convert existing tibble to EventTable
-converted_table <- as_event_table(event_data)
-print("Converted table:")
-print(converted_table)
-
-# Validate data
-validate_event_table_data(event_data)
-print("Data validation passed!")
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/CITATION b/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/CITATION
deleted file mode 100644
index 4cf24a4..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/CITATION
+++ /dev/null
@@ -1,12 +0,0 @@
-bibentry(
- "Article",
- title = "A unified framework for weighted parametric group sequential design",
- author = "Keaven M Anderson and Zifang Guo and Jing Zhao and Linda Z Sun",
- journal = "Biometrical Journal",
- volume = "64",
- number = "7",
- pages = "1219--1239",
- year = "2022",
- publisher = "Wiley Online Library",
- doi = "10.1002/bimj.202100085",
-)
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/compute_correlations_prompts.txt b/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/compute_correlations_prompts.txt
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--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/compute_correlations_prompts.txt
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@@ -1,76 +0,0 @@
-Three functions are defined here, one for checking input data (`check_event_data()`) and
-another for computing correlations (`compute_correlations()`) and one (`gen_corr()`) for transforming a data frame where correlations are computed
-to a correlation matrix.
-All three should be exported.
-When users enter the `event` input to `compute_correlations()`, it is advised to call `check_event_data()` first by
-specifying check = TRUE (the default).
-Output will be output either as a data frame or as a correlation matrix, as specified below.
-An exported function `gen_corr()` will do a transformation from the data frame output to a symmetric matrix.
-
-Let M > 1 be the integer number of hypotheses to be tested.
-Assume there are integer K > 1 analyses.
-Let real-valued Z[i, k] be the standardized normal test statistic for
-hypothesis i, 1 <= i <= M, analysis k, 1 <= k <= K.
-We wish to compute and return correlations for all hypothesis tests
-performed across analyses.
-For tests Z[i1, k1], Z[i2, k2], 1 <= i1 <= i2 <= M, 1 <= k1 <= k2 <= K that are
-performed we will provide the count of events (for time-to-event outcomes) or
-sample size (for other outcomes) that are common between the two tests.
-This is input in a data frame called `event`
-with the following columns:
-
-`H1` - hypothesis i1 = H1
-`H2` - hypothesis i2 = H2
-`Analysis` - value in 1,2,...,K
-`Event` - event count for time-to-event endpoints, otherwise sample size which
-is included in the both test Z[H1, Analysis] and Z[H2, Analysis].
-
-Other arguments for `compute_correlations()` are
-
-`check` - logical indicating whether to perform input checks using `check_event_data()` (default is TRUE)
-`return_matrix` - logical indicating whether to return a correlation matrix (default is TRUE)
-
-The function `check_event_data()` will have the argument `event` as specified above.
-Data checks in `check_event_data()` :
-- Check that `event` is a data frame and return an informative error message if not.
-- Check that columns specified above exist and return informative error message, if not.
-- Check that H1 <= H2 for each row and provide informative error message, if not.
-- Check that the combination of H1, H2, Analysis is a unique in the input;
-this should be evaluated and appropriate error message returned if not unique.
-Check that Event is an integer >= 0 for all rows and provide an
-appropriate error message, if not.
-- Check that unique values of Analysis are sequential positive integers with
-minimum value 1 and maximum value > 1; K from above will be the maximum value.
-Return an informative error message if any of these checks fail.
-- Check that unique values of H1 are sequential integers with minimum value 1
-and maximum value > 1; M from above will be the maximum value.
-Same for H2.
-Return an informative error message if any of these checks fail.
-- Check that for k=1,...,K that if there is a row with H1 < H2, then there is also a row with H1 == H2.
-Return an informative error message if not.
-- Check that for any value of Analysis, and H1 = i1 < H2 = i2 specified that there is also a row with H1 = i1, H2 = i1 and another with
-H1 = i2, H2 = i2. Return an informative error message if not.
-
-
-Returned value from `compute_correlations()`.
-The returned value either a data frame (if `return_matrix = FALSE`) or a correlation matrix, otherwise.
-The data frame has the following columns.
- H1 - hypothesis i1
- H2 - hypothesis i2 >= i1
- Analysis1 - k1.
- Analysis2 - k2 >= k1.
- Correlation - correlation between Z[i1, k1] and Z[i2, k2].
-
-Correlation is computed as
-Event for i1, i2 and k1 divided by square root of the product of
-Event for H1 = i1, H2 = i1, Analysis = min(k1, k2) times
-Event for H1 = i2, H2 = i2, Analysis = k2.
-
-If `return_ matrix = TRUE` (default) then a symmetric matrix should be returned as follows.
-Columns should be named `H1_A1`, `H1_A2`, ..., `H1_AK`, `H2_A1`, `H2_A2`, ..., `H2_AK`, ..., `HM_A1`, `HM_A2`, ..., `HM_AK` where
-M and K are as computed from `event`.
-Rows should be labeled the same way.
-Diagonal elements are all 1.
-Off-diagonal elements are filled with the computed correlations.
-Only cells included should be where `Event` value was provided for the combination of Analysis, H1 and H2.
-
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/s7 prompts.md b/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/s7 prompts.md
deleted file mode 100644
index 69bae54..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/aiprompts/s7 prompts.md
+++ /dev/null
@@ -1,101 +0,0 @@
-## Prompt for s7 Class conversion
-
-We want to convert the wpgsd R package to operate with s7 classes throughout.
-Please check for exported functions in the R directory suggest what s7 classes need to be developed.
-
-## Suggested S7 Classes for wpgsd Package Conversion
-
-Based on the exported functions and their data structures, here are the key S7 classes that should be developed:
-
-### 1. **EventTable Class**
-- **Purpose**: Represents event count data structure used in `generate_corr()` and `generate_event_table()`
-- **Key Fields**:
- - `H1`, `H2`: Hypothesis indices
- - `Analysis`: Analysis number
- - `Event`: Event count
-- **Methods**: Validation, printing, subsetting
-
-### 2. **CorrelationMatrix Class**
-- **Purpose**: Represents correlation matrices returned by `generate_corr()`
-- **Key Fields**:
- - `matrix`: The correlation matrix
- - `n_hypotheses`: Number of hypotheses
- - `n_analyses`: Number of analyses
- - `column_names`: Named columns (e.g., "H1_A1", "H2_A1", etc.)
-- **Methods**: Validation (positive definite), printing, subsetting
-
-### 3. **TransitionMatrix Class**
-- **Purpose**: Represents transition matrices used in graphical procedures
-- **Key Fields**:
- - `matrix`: The transition matrix
- - `n_hypotheses`: Number of hypotheses
-- **Methods**: Validation (row sums ≤ 1), printing
-
-### 4. **Bounds Class**
-- **Purpose**: Represents p-value boundaries from `generate_bounds()`
-- **Key Fields**:
- - `data`: Tibble with Analysis, Hypotheses, H1, H2, etc., xi columns
- - `type`: Boundary type (0, 1, 2, or 3)
- - `alpha`: Overall alpha level
- - `n_hypotheses`: Number of hypotheses
- - `n_analyses`: Number of analyses
-- **Methods**: Validation, printing, plotting
-
-### 5. **ObservedPValues Class**
-- **Purpose**: Represents observed p-values for `closed_test()`
-- **Key Fields**:
- - `data`: Tibble with Analysis, H1, H2, etc. columns
- - `n_hypotheses`: Number of hypotheses
- - `n_analyses`: Number of analyses
-- **Methods**: Validation, printing
-
-### 6. **ClosedTestResult Class**
-- **Purpose**: Represents results from `closed_test()`
-- **Key Fields**:
- - `outcome_matrix`: Matrix summarizing testing results
- - `bounds`: Associated bounds used
- - `p_obs`: Observed p-values used
- - `rejected_hypotheses`: List of rejected hypotheses by analysis
-- **Methods**: Validation, printing, summary
-
-### 7. **StudyDesign Class**
-- **Purpose**: High-level class to encapsulate entire study design
-- **Key Fields**:
- - `initial_weights`: Vector of initial hypothesis weights
- - `transition_matrix`: TransitionMatrix object
- - `n_hypotheses`: Number of hypotheses
- - `n_analyses`: Number of planned analyses
- - `alpha`: Overall alpha level
- - `spending_functions`: List of spending functions
-- **Methods**: Validation, printing, summary
-
-### 8. **SequentialPValue Class**
-- **Purpose**: Represents sequential p-values from `calc_seq_p()`
-- **Key Fields**:
- - `value`: The sequential p-value
- - `test_analysis`: Analysis index
- - `test_hypothesis`: Hypothesis being tested
- - `method_type`: Alpha spending type used
-- **Methods**: Validation, printing
-
-## Implementation Benefits
-
-1. **Type Safety**: S7 classes provide strong typing and validation
-2. **Method Dispatch**: Can implement specialized methods for each class
-3. **Consistency**: Standardized data structures across the package
-4. **User Experience**: Better error messages and documentation
-5. **Extensibility**: Easy to add new methods and functionality
-
-## Migration Strategy
-
-1. Start with core data structures (`EventTable`, `CorrelationMatrix`)
-2. Update `generate_corr()` to return `CorrelationMatrix` objects
-3. Update `generate_bounds()` to return `Bounds` objects
-4. Progressively convert other functions
-5. Ensure backward compatibility during transition
-6. Update documentation and vignettes
-
-This S7 class structure would provide a solid foundation for the wpgsd package while maintaining the existing functionality and improving the user experience with better type safety and method dispatch.
-
-Claude Sonnet 4 running under VSCode returned the following:
-
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.R b/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.R
deleted file mode 100644
index 63d7cc2..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.R
+++ /dev/null
@@ -1,739 +0,0 @@
-## ----message = FALSE, warning = FALSE-----------------------------------------
-library(wpgsd)
-library(gsDesign)
-library(tibble)
-library(gt)
-library(dplyr)
-
-## -----------------------------------------------------------------------------
-event_tbl <- tribble(
- ~population, ~analysis, ~event,
- "A positive", 1, 100,
- "B positive", 1, 110,
- "AB positive", 1, 80,
- "overall", 1, 225,
- "A positive", 2, 200,
- "B positive", 2, 220,
- "AB positive", 2, 160,
- "overall", 2, 450,
-)
-
-## -----------------------------------------------------------------------------
-obs_tbl <- tribble(
- ~hypothesis, ~analysis, ~obs_p,
- "H1", 1, 0.02,
- "H2", 1, 0.01,
- "H3", 1, 0.012,
- "H1", 2, 0.015,
- "H2", 2, 0.012,
- "H3", 2, 0.010
-) %>%
- mutate(obs_Z = -qnorm(obs_p))
-
-obs_tbl %>%
- gt() %>%
- tab_header(title = "Nominal p-values")
-
-p_obs_IA <- (obs_tbl %>% filter(analysis == 1))$obs_p
-p_obs_FA <- (obs_tbl %>% filter(analysis == 2))$obs_p
-
-## -----------------------------------------------------------------------------
-IF_IA <- c(
- ((event_tbl %>% filter(analysis == 1, population == "A positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "A positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event),
- ((event_tbl %>% filter(analysis == 1, population == "B positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "B positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event),
- ((event_tbl %>% filter(analysis == 1, population == "AB positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "AB positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event)
-)
-
-IF_IA
-
-## -----------------------------------------------------------------------------
-# Transition matrix in Figure A1
-m <- matrix(c(
- 0, 3 / 7, 4 / 7,
- 3 / 7, 0, 4 / 7,
- 0.5, 0.5, 0
-), nrow = 3, byrow = TRUE)
-# Initial weights
-w <- c(0.3, 0.3, 0.4)
-
-## -----------------------------------------------------------------------------
-name_hypotheses <- c("H1: Biomarker A positive", "H2: Biomarker B positive", "H3: Overall Population")
-
-hplot <- gMCPLite::hGraph(
- 3,
- alphaHypotheses = w, m = m,
- nameHypotheses = name_hypotheses, trhw = .2, trhh = .1,
- digits = 5, trdigits = 3, size = 5, halfWid = 1, halfHgt = 0.5,
- offset = 0.2, trprop = 0.4,
- fill = as.factor(c(2, 3, 1)),
- palette = c("#BDBDBD", "#E0E0E0", "#EEEEEE"),
- wchar = "w"
-)
-hplot
-
-## -----------------------------------------------------------------------------
-# Event count of intersection of paired hypotheses - Table 2
-# H1, H2: Hypotheses intersected.
-# (1, 1) represents counts for hypothesis 1
-# (1, 2) for counts for the intersection of hypotheses 1 and 2
-event <- tribble(
- ~H1, ~H2, ~Analysis, ~Event,
- 1, 1, 1, event_tbl %>% filter(analysis == 1, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 2, 1, event_tbl %>% filter(analysis == 1, population == "B positive") %>% select(event) %>% as.numeric(),
- 3, 3, 1, event_tbl %>% filter(analysis == 1, population == "overall") %>% select(event) %>% as.numeric(),
- 1, 2, 1, event_tbl %>% filter(analysis == 1, population == "AB positive") %>% select(event) %>% as.numeric(),
- 1, 3, 1, event_tbl %>% filter(analysis == 1, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 3, 1, event_tbl %>% filter(analysis == 1, population == "B positive") %>% select(event) %>% as.numeric(),
- 1, 1, 2, event_tbl %>% filter(analysis == 2, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 2, 2, event_tbl %>% filter(analysis == 2, population == "B positive") %>% select(event) %>% as.numeric(),
- 3, 3, 2, event_tbl %>% filter(analysis == 2, population == "overall") %>% select(event) %>% as.numeric(),
- 1, 2, 2, event_tbl %>% filter(analysis == 2, population == "AB positive") %>% select(event) %>% as.numeric(),
- 1, 3, 2, event_tbl %>% filter(analysis == 2, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 3, 2, event_tbl %>% filter(analysis == 2, population == "B positive") %>% select(event) %>% as.numeric()
-)
-event
-
-# Generate correlation from events
-gs_corr <- wpgsd::generate_corr(event)
-gs_corr %>% round(2)
-
-## ----wpgsdSeqIA, message=FALSE------------------------------------------------
-seq_p_IA_H123 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H12 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H13 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H23 <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H1 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H2 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H3 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-## ----weightedBonferroniSeqIA, message=FALSE-----------------------------------
-seq_p_IA_H123_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H12_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H13_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H23_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H1_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H2_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H3_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-## ----wpgsdSeqFA, message=FALSE------------------------------------------------
-seq_p_FA_H123 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H12 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H13 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H23 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H1 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H2 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H3 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-## ----weightedBonferroniSeqFA, message=FALSE-----------------------------------
-seq_p_FA_H123_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H12_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H13_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H23_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H1_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H2_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H3_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-## ----wpgsdAdjSeqIA------------------------------------------------------------
-adj_seq_IA_H1 <- max(seq_p_IA_H123, seq_p_IA_H12, seq_p_IA_H13, seq_p_IA_H1)
-adj_seq_IA_H2 <- max(seq_p_IA_H123, seq_p_IA_H12, seq_p_IA_H23, seq_p_IA_H2)
-adj_seq_IA_H3 <- max(seq_p_IA_H123, seq_p_IA_H13, seq_p_IA_H23, seq_p_IA_H3)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in IA via WPGSD is", adj_seq_IA_H1, adj_seq_IA_H2, adj_seq_IA_H3, "\n")
-
-## ----weightedBonferroniAdjSeqIA-----------------------------------------------
-adj_seq_IA_H1_B <- max(seq_p_IA_H123_B, seq_p_IA_H12_B, seq_p_IA_H13_B, seq_p_IA_H1_B)
-adj_seq_IA_H2_B <- max(seq_p_IA_H123_B, seq_p_IA_H12_B, seq_p_IA_H23_B, seq_p_IA_H2_B)
-adj_seq_IA_H3_B <- max(seq_p_IA_H123_B, seq_p_IA_H13_B, seq_p_IA_H23_B, seq_p_IA_H3_B)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via weighted Bonferroni is", adj_seq_IA_H1_B, adj_seq_IA_H2_B, adj_seq_IA_H3_B, "\n")
-
-## ----wpgsdAdjSeqFA------------------------------------------------------------
-adj_seq_FA_H1 <- max(seq_p_FA_H123, seq_p_FA_H12, seq_p_FA_H13, seq_p_FA_H1)
-adj_seq_FA_H2 <- max(seq_p_FA_H123, seq_p_FA_H12, seq_p_FA_H23, seq_p_FA_H2)
-adj_seq_FA_H3 <- max(seq_p_FA_H123, seq_p_FA_H13, seq_p_FA_H23, seq_p_FA_H3)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via WPGSD is", adj_seq_FA_H1, adj_seq_FA_H2, adj_seq_FA_H3, "\n")
-
-## ----weightedBonferroniAdjSeqFA-----------------------------------------------
-adj_seq_FA_H1_B <- max(seq_p_FA_H123_B, seq_p_FA_H12_B, seq_p_FA_H13_B, seq_p_FA_H1_B)
-adj_seq_FA_H2_B <- max(seq_p_FA_H123_B, seq_p_FA_H12_B, seq_p_FA_H23_B, seq_p_FA_H2_B)
-adj_seq_FA_H3_B <- max(seq_p_FA_H123_B, seq_p_FA_H13_B, seq_p_FA_H23_B, seq_p_FA_H3_B)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via weighted Bonferroni is", adj_seq_FA_H1_B, adj_seq_FA_H2_B, adj_seq_FA_H3_B, "\n")
-
-## -----------------------------------------------------------------------------
-ans <- tribble(
- ~Analysis, ~Hypothesis, ~`Sequential p-values of WPGSD`, ~`Sequential p-values of Weighted Bonferroni`, ~`Adjusted-sequential p-values of WPGSD`, ~`Adjusted-sequential p-values of Weighted Bonferroni`,
- "IA", "H123", seq_p_IA_H123, seq_p_IA_H123_B, NA, NA,
- "IA", "H12", seq_p_IA_H12, seq_p_IA_H12_B, NA, NA,
- "IA", "H13", seq_p_IA_H13, seq_p_IA_H13_B, NA, NA,
- "IA", "H23", seq_p_IA_H23, seq_p_IA_H23_B, NA, NA,
- "IA", "H1", seq_p_IA_H1, seq_p_IA_H1_B, adj_seq_IA_H1, adj_seq_IA_H1_B,
- "IA", "H2", seq_p_IA_H2, seq_p_IA_H2_B, adj_seq_IA_H2, adj_seq_IA_H2_B,
- "IA", "H3", seq_p_IA_H3, seq_p_IA_H3_B, adj_seq_IA_H3, adj_seq_IA_H3_B,
- "FA", "H123", seq_p_FA_H123, seq_p_FA_H123_B, NA, NA,
- "FA", "H12", seq_p_FA_H12, seq_p_FA_H12_B, NA, NA,
- "FA", "H13", seq_p_FA_H13, seq_p_FA_H13_B, NA, NA,
- "FA", "H23", seq_p_FA_H23, seq_p_FA_H23_B, NA, NA,
- "FA", "H1", seq_p_FA_H1, seq_p_FA_H1_B, adj_seq_FA_H1, adj_seq_FA_H1_B,
- "FA", "H2", seq_p_FA_H2, seq_p_FA_H2_B, adj_seq_FA_H2, adj_seq_FA_H2_B,
- "FA", "H3", seq_p_FA_H3, seq_p_FA_H3_B, adj_seq_FA_H3, adj_seq_FA_H3_B
-)
-
-ans %>%
- select(
- Analysis, Hypothesis,
- `Sequential p-values of Weighted Bonferroni`, `Adjusted-sequential p-values of Weighted Bonferroni`,
- `Sequential p-values of WPGSD`, `Adjusted-sequential p-values of WPGSD`
- ) %>%
- gt() %>%
- tab_spanner(
- label = "Weighted Bonferroni",
- columns = c(`Sequential p-values of Weighted Bonferroni`, `Adjusted-sequential p-values of Weighted Bonferroni`)
- ) %>%
- tab_spanner(
- label = "WPGSD",
- columns = c(`Sequential p-values of WPGSD`, `Adjusted-sequential p-values of WPGSD`)
- ) %>%
- tab_style_body(
- columns = where(is.numeric),
- style = cell_fill(color = "pink"),
- fn = function(x) x <= 0.025
- ) %>%
- fmt_number(columns = 3:6, decimals = 4) %>%
- tab_header(
- title = "(Adjusted-) sequential p-values",
- subtitle = "Multiple populations"
- ) # %>% as_latex()
-
diff --git a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.Rmd b/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.Rmd
deleted file mode 100644
index df94c1c..0000000
--- a/wpgsd.Rcheck/00_pkg_src/wpgsd/inst/doc/adj-seq-p.Rmd
+++ /dev/null
@@ -1,810 +0,0 @@
----
-title: "Adjusted sequential p-values"
-author: "Yujie Zhao, Qi Liu, Linda Sun, Keaven Anderson"
-output:
- rmarkdown::html_document:
- toc: true
- toc_float: true
- toc_depth: 2
- number_sections: true
- highlight: "textmate"
- css: "custom.css"
-# bibliography: "example.bib"
-vignette: >
- %\VignetteEngine{knitr::rmarkdown}
- %\VignetteIndexEntry{Adjusted sequential p-values}
----
-
-```{r, message = FALSE, warning = FALSE}
-library(wpgsd)
-library(gsDesign)
-library(tibble)
-library(gt)
-library(dplyr)
-```
-
-# Example overview
-
-In a 2-arm controlled clinical trial example with one primary endpoint, there are 3 patient populations defined by the status of two biomarkers A and B:
-
-- biomarker A positive,
-- biomarker B positive,
-- overall population.
-
-The 3 primary elementary hypotheses are:
-
-- $H_1$: the experimental treatment is superior to the control in the biomarker A positive population;
-- \item $H_2$: the experimental treatment is superior to the control in the biomarker B positive population;
-- \item $H_3$: the experimental treatment is superior to the control in the overall population.
-
-Assume an interim analysis and a final analysis are planned for the study and the number of events are listed as
-
-```{r}
-event_tbl <- tribble(
- ~population, ~analysis, ~event,
- "A positive", 1, 100,
- "B positive", 1, 110,
- "AB positive", 1, 80,
- "overall", 1, 225,
- "A positive", 2, 200,
- "B positive", 2, 220,
- "AB positive", 2, 160,
- "overall", 2, 450,
-)
-```
-
-The observed p-values are
-
-```{r}
-obs_tbl <- tribble(
- ~hypothesis, ~analysis, ~obs_p,
- "H1", 1, 0.02,
- "H2", 1, 0.01,
- "H3", 1, 0.012,
- "H1", 2, 0.015,
- "H2", 2, 0.012,
- "H3", 2, 0.010
-) %>%
- mutate(obs_Z = -qnorm(obs_p))
-
-obs_tbl %>%
- gt() %>%
- tab_header(title = "Nominal p-values")
-
-p_obs_IA <- (obs_tbl %>% filter(analysis == 1))$obs_p
-p_obs_FA <- (obs_tbl %>% filter(analysis == 2))$obs_p
-```
-
-The information fraction of $H_1, H_2, H_3$ at IA is
-
-```{r}
-IF_IA <- c(
- ((event_tbl %>% filter(analysis == 1, population == "A positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "A positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event),
- ((event_tbl %>% filter(analysis == 1, population == "B positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "B positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event),
- ((event_tbl %>% filter(analysis == 1, population == "AB positive"))$event + (event_tbl %>% filter(analysis == 1, population == "overall"))$event) /
- ((event_tbl %>% filter(analysis == 2, population == "AB positive"))$event + (event_tbl %>% filter(analysis == 2, population == "overall"))$event)
-)
-
-IF_IA
-```
-
-We assign the initial weights of $H_1, H_2, H_3$ as$\left(w_1(I), w_2(I), w_3(I) \right) = (0.3, 0.3, 0.4).$ And its multiplicity strategy is visualized in below. If $H_1$ is rejected, then $3/7$ local significance level $\alpha_1$ will be propagated to $H_2$, and $4/7$ will go to $H_3$. If $H_3$ is rejected, then half of $\alpha_3$ goes to $H_1$, and half goes to $H_2$.
-
-```{r}
-# Transition matrix in Figure A1
-m <- matrix(c(
- 0, 3 / 7, 4 / 7,
- 3 / 7, 0, 4 / 7,
- 0.5, 0.5, 0
-), nrow = 3, byrow = TRUE)
-# Initial weights
-w <- c(0.3, 0.3, 0.4)
-```
-
-```{r}
-name_hypotheses <- c("H1: Biomarker A positive", "H2: Biomarker B positive", "H3: Overall Population")
-
-hplot <- gMCPLite::hGraph(
- 3,
- alphaHypotheses = w, m = m,
- nameHypotheses = name_hypotheses, trhw = .2, trhh = .1,
- digits = 5, trdigits = 3, size = 5, halfWid = 1, halfHgt = 0.5,
- offset = 0.2, trprop = 0.4,
- fill = as.factor(c(2, 3, 1)),
- palette = c("#BDBDBD", "#E0E0E0", "#EEEEEE"),
- wchar = "w"
-)
-hplot
-```
-
-The correlation of the 6 statistisc (2 analysis $\times$ 3 hypothesis) are
-
-```{r}
-# Event count of intersection of paired hypotheses - Table 2
-# H1, H2: Hypotheses intersected.
-# (1, 1) represents counts for hypothesis 1
-# (1, 2) for counts for the intersection of hypotheses 1 and 2
-event <- tribble(
- ~H1, ~H2, ~Analysis, ~Event,
- 1, 1, 1, event_tbl %>% filter(analysis == 1, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 2, 1, event_tbl %>% filter(analysis == 1, population == "B positive") %>% select(event) %>% as.numeric(),
- 3, 3, 1, event_tbl %>% filter(analysis == 1, population == "overall") %>% select(event) %>% as.numeric(),
- 1, 2, 1, event_tbl %>% filter(analysis == 1, population == "AB positive") %>% select(event) %>% as.numeric(),
- 1, 3, 1, event_tbl %>% filter(analysis == 1, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 3, 1, event_tbl %>% filter(analysis == 1, population == "B positive") %>% select(event) %>% as.numeric(),
- 1, 1, 2, event_tbl %>% filter(analysis == 2, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 2, 2, event_tbl %>% filter(analysis == 2, population == "B positive") %>% select(event) %>% as.numeric(),
- 3, 3, 2, event_tbl %>% filter(analysis == 2, population == "overall") %>% select(event) %>% as.numeric(),
- 1, 2, 2, event_tbl %>% filter(analysis == 2, population == "AB positive") %>% select(event) %>% as.numeric(),
- 1, 3, 2, event_tbl %>% filter(analysis == 2, population == "A positive") %>% select(event) %>% as.numeric(),
- 2, 3, 2, event_tbl %>% filter(analysis == 2, population == "B positive") %>% select(event) %>% as.numeric()
-)
-event
-
-# Generate correlation from events
-gs_corr <- wpgsd::generate_corr(event)
-gs_corr %>% round(2)
-```
-
-# Sequential p-value
-
-## IA
-
-```{r, wpgsdSeqIA, message=FALSE}
-seq_p_IA_H123 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H12 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H13 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H23 <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H1 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H2 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H3 <- calc_seq_p(
- test_analysis = 1,
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ),
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-```
-
-```{r, weightedBonferroniSeqIA, message=FALSE}
-seq_p_IA_H123_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H12_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_IA_H13_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H23_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H1_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H2_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-
-seq_p_IA_H3_B <- calc_seq_p(
- test_analysis = 1, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.3)
-)
-```
-
-## FA
-
-```{r, wpgsdSeqFA, message=FALSE}
-seq_p_FA_H123 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H12 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H13 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H23 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.15)
-)
-
-seq_p_FA_H1 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H2 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H3 <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 2,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = gsDesign::sfHSD,
- spending_fun_par = -4,
- info_frac = c(min(IF_IA), 1),
- interval = c(1e-4, 0.2)
-)
-```
-
-```{r, weightedBonferroniSeqFA, message=FALSE}
-seq_p_FA_H123_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H12_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H13_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H23_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2, H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H1_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H1",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H2_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H2",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-
-seq_p_FA_H3_B <- calc_seq_p(
- test_analysis = 2, # stage of interest
- test_hypothesis = "H3",
- p_obs = tibble(
- analysis = 1:2,
- H1 = c(p_obs_IA[1], p_obs_FA[1]),
- H2 = c(p_obs_IA[2], p_obs_FA[2]),
- H3 = c(p_obs_IA[3], p_obs_FA[3])
- ), # observed p-value
- alpha_spending_type = 0,
- n_analysis = 2,
- initial_weight = w,
- transition_mat = m,
- z_corr = gs_corr,
- spending_fun = list(gsDesign::sfHSD, gsDesign::sfHSD, gsDesign::sfHSD),
- spending_fun_par = list(-4, -4, -4),
- info_frac = list(c(IF_IA[1], 1), c(IF_IA[2], 1), c(IF_IA[2], 1)),
- interval = c(1e-4, 0.2)
-)
-```
-
-# Adjusted-Sequential p-value
-
-## IA
-
-```{r, wpgsdAdjSeqIA}
-adj_seq_IA_H1 <- max(seq_p_IA_H123, seq_p_IA_H12, seq_p_IA_H13, seq_p_IA_H1)
-adj_seq_IA_H2 <- max(seq_p_IA_H123, seq_p_IA_H12, seq_p_IA_H23, seq_p_IA_H2)
-adj_seq_IA_H3 <- max(seq_p_IA_H123, seq_p_IA_H13, seq_p_IA_H23, seq_p_IA_H3)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in IA via WPGSD is", adj_seq_IA_H1, adj_seq_IA_H2, adj_seq_IA_H3, "\n")
-```
-
-```{r, weightedBonferroniAdjSeqIA}
-adj_seq_IA_H1_B <- max(seq_p_IA_H123_B, seq_p_IA_H12_B, seq_p_IA_H13_B, seq_p_IA_H1_B)
-adj_seq_IA_H2_B <- max(seq_p_IA_H123_B, seq_p_IA_H12_B, seq_p_IA_H23_B, seq_p_IA_H2_B)
-adj_seq_IA_H3_B <- max(seq_p_IA_H123_B, seq_p_IA_H13_B, seq_p_IA_H23_B, seq_p_IA_H3_B)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via weighted Bonferroni is", adj_seq_IA_H1_B, adj_seq_IA_H2_B, adj_seq_IA_H3_B, "\n")
-```
-
-## FA
-
-### WPGSD
-```{r, wpgsdAdjSeqFA}
-adj_seq_FA_H1 <- max(seq_p_FA_H123, seq_p_FA_H12, seq_p_FA_H13, seq_p_FA_H1)
-adj_seq_FA_H2 <- max(seq_p_FA_H123, seq_p_FA_H12, seq_p_FA_H23, seq_p_FA_H2)
-adj_seq_FA_H3 <- max(seq_p_FA_H123, seq_p_FA_H13, seq_p_FA_H23, seq_p_FA_H3)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via WPGSD is", adj_seq_FA_H1, adj_seq_FA_H2, adj_seq_FA_H3, "\n")
-```
-
-```{r, weightedBonferroniAdjSeqFA}
-adj_seq_FA_H1_B <- max(seq_p_FA_H123_B, seq_p_FA_H12_B, seq_p_FA_H13_B, seq_p_FA_H1_B)
-adj_seq_FA_H2_B <- max(seq_p_FA_H123_B, seq_p_FA_H12_B, seq_p_FA_H23_B, seq_p_FA_H2_B)
-adj_seq_FA_H3_B <- max(seq_p_FA_H123_B, seq_p_FA_H13_B, seq_p_FA_H23_B, seq_p_FA_H3_B)
-
-cat("The adjusted-sequential p-value of H1, H2, H3 in FA via weighted Bonferroni is", adj_seq_FA_H1_B, adj_seq_FA_H2_B, adj_seq_FA_H3_B, "\n")
-```
-
-# Summary
-
-```{r}
-ans <- tribble(
- ~Analysis, ~Hypothesis, ~`Sequential p-values of WPGSD`, ~`Sequential p-values of Weighted Bonferroni`, ~`Adjusted-sequential p-values of WPGSD`, ~`Adjusted-sequential p-values of Weighted Bonferroni`,
- "IA", "H123", seq_p_IA_H123, seq_p_IA_H123_B, NA, NA,
- "IA", "H12", seq_p_IA_H12, seq_p_IA_H12_B, NA, NA,
- "IA", "H13", seq_p_IA_H13, seq_p_IA_H13_B, NA, NA,
- "IA", "H23", seq_p_IA_H23, seq_p_IA_H23_B, NA, NA,
- "IA", "H1", seq_p_IA_H1, seq_p_IA_H1_B, adj_seq_IA_H1, adj_seq_IA_H1_B,
- "IA", "H2", seq_p_IA_H2, seq_p_IA_H2_B, adj_seq_IA_H2, adj_seq_IA_H2_B,
- "IA", "H3", seq_p_IA_H3, seq_p_IA_H3_B, adj_seq_IA_H3, adj_seq_IA_H3_B,
- "FA", "H123", seq_p_FA_H123, seq_p_FA_H123_B, NA, NA,
- "FA", "H12", seq_p_FA_H12, seq_p_FA_H12_B, NA, NA,
- "FA", "H13", seq_p_FA_H13, seq_p_FA_H13_B, NA, NA,
- "FA", "H23", seq_p_FA_H23, seq_p_FA_H23_B, NA, NA,
- "FA", "H1", seq_p_FA_H1, seq_p_FA_H1_B, adj_seq_FA_H1, adj_seq_FA_H1_B,
- "FA", "H2", seq_p_FA_H2, seq_p_FA_H2_B, adj_seq_FA_H2, adj_seq_FA_H2_B,
- "FA", "H3", seq_p_FA_H3, seq_p_FA_H3_B, adj_seq_FA_H3, adj_seq_FA_H3_B
-)
-
-ans %>%
- select(
- Analysis, Hypothesis,
- `Sequential p-values of Weighted Bonferroni`, `Adjusted-sequential p-values of Weighted Bonferroni`,
- `Sequential p-values of WPGSD`, `Adjusted-sequential p-values of WPGSD`
- ) %>%
- gt() %>%
- tab_spanner(
- label = "Weighted Bonferroni",
- columns = c(`Sequential p-values of Weighted Bonferroni`, `Adjusted-sequential p-values of Weighted Bonferroni`)
- ) %>%
- tab_spanner(
- label = "WPGSD",
- columns = c(`Sequential p-values of WPGSD`, `Adjusted-sequential p-values of WPGSD`)
- ) %>%
- tab_style_body(
- columns = where(is.numeric),
- style = cell_fill(color = "pink"),
- fn = function(x) x <= 0.025
- ) %>%
- fmt_number(columns = 3:6, decimals = 4) %>%
- tab_header(
- title = "(Adjusted-) sequential p-values",
- subtitle = "Multiple populations"
- ) # %>% as_latex()
-```
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