## ===== Packages =====
suppressPackageStartupMessages({
library(MASS)
library(Matrix)
library(dplyr)
library(tidyr)
library(ggplot2)
library(forcats)
library(scales)
})
## Warning: package 'forcats' was built under R version 4.4.3
set.seed(12345)
## ===== Global config =====
nsim <- 10000
n_per_arm <- 225
alpha_tot <- 0.05
sided <- "two"
pC <- 0.50
endpts <- c("H1","H2","H3","H4","H5","H6")
## ===== Correlation (fixed) =====
Sigma <- matrix(c(
1.0, 0.1, 0.5, 0.1, 0.1, 0.1,
0.1, 1.0, 0.1, 0.8, 0.5, 0.5,
0.5, 0.1, 1.0, 0.1, 0.1, 0.1,
0.1, 0.8, 0.1, 1.0, 0.5, 0.5,
0.1, 0.5, 0.1, 0.5, 1.0, 0.5,
0.1, 0.5, 0.1, 0.5, 0.5, 1.0
), 6, 6, byrow=TRUE, dimnames=list(endpts,endpts))
if (min(eigen(Sigma, symmetric=TRUE, only.values=TRUE)$values) < 1e-8) {
Sigma <- as.matrix(nearPD(Sigma)$mat)
}
Sigma <- (Sigma + t(Sigma))/2
## ===== Graphs for D1–D6 =====
G13 <- rbind(
H1 = c(0,0,1,0,0,0),
H2 = c(0,0,1,0,0,0),
H3 = c(0,0,0,1,0,0),
H4 = c(0,0,0,0,1,0),
H5 = c(0,0,0,0,0,1),
H6 = c(0,0,0,0,0,0)
); colnames(G13) <- rownames(G13) <- endpts
G4 <- rbind(
H1 = c(0,0,1,0,0,0),
H2 = c(0,0,0,1,0,0),
H3 = c(0,1,0,0,0,0),
H4 = c(0,0,0,0,1,0),
H5 = c(1,0,0,0,0,0),
H6 = c(0,0,0,0,0,0)
); colnames(G4) <- rownames(G4) <- endpts
G5 <- rbind(
H1 = c(0, 2/3, 1/3, 0, 0, 0),
H2 = c(0, 0, 1, 0, 0, 0),
H3 = c(0, 0, 0, 1, 0, 0),
H4 = c(0, 0, 0, 0, 1, 0),
H5 = c(0, 0, 0, 0, 0, 1),
H6 = c(1, 0, 0, 0, 0, 0)
); colnames(G5) <- rownames(G5) <- endpts
G6 <- rbind(
H1 = c(0,0,1,0,0,0),
H2 = c(0,0,0,1,0,0),
H3 = c(0,0,0,0,1,0),
H4 = c(1,0,0,0,0,0),
H5 = c(0,1,0,0,0,0),
H6 = c(0,0,0,0,0,0)
); colnames(G6) <- rownames(G6) <- endpts
# Initial weights
w_D1 <- c(H1=1/2, H2=1/2, H3=0, H4=0, H5=0, H6=0)
w_D2 <- c(H1=4/5, H2=1/5, H3=0, H4=0, H5=0, H6=0)
w_D3 <- c(H1=2/3, H2=1/3, H3=0, H4=0, H5=0, H6=0)
w_D4 <- c(H1=1/2, H2=1/2, H3=0, H4=0, H5=0, H6=0)
w_D5 <- c(H1=4/5, H2=1/5, H3=0, H4=0, H5=0, H6=0)
w_D6 <- c(H1=4/5, H2=1/5, H3=0, H4=0, H5=0, H6=0)
## ===== Colors =====
cols <- c("D1"="#1f77b4","D2"="#ff7f0e","D3"="#2ca02c",
"D4"="#9467bd","D5"="#8c564b","D6"="#17becf")
## ===== Engines & helpers =====
axis_limits <- function(mx) {
if (is.na(mx) || mx <= 0) return(c(0, 0.25))
if (mx < 0.25) c(0, 0.25)
else if (mx < 0.50) c(0, 0.50)
else if (mx < 0.75) c(0, 0.75)
else c(0, 1.00)
}
breaks_for_limits <- function(ylim) {
top <- ylim[2]
if (abs(top-0.25) < 1e-12) c(0, 0.25)
else if (abs(top-0.50) < 1e-12) seq(0, 0.50, by=0.25)
else if (abs(top-0.75) < 1e-12) seq(0, 0.75, by=0.25)
else seq(0, 1.00, by=0.25)
}
has_path_to_nonrejected <- function(start, rejected, G) {
q <- which(names(rejected)==start)
visited <- setNames(rep(FALSE, length(rejected)), names(rejected))
while (length(q)) {
i <- q[1]; q <- q[-1]
if (visited[i]) next
visited[i] <- TRUE
nbrs <- names(which(G[i,] > 0))
for (jname in nbrs) {
j <- which(names(rejected)==jname)
if (!rejected[j]) return(TRUE)
if (!visited[j]) q <- c(q, j)
}
}
FALSE
}
push_alpha_through_rejected <- function(a, rejected, G) {
repeat {
moved <- FALSE
for (i in seq_along(a)) {
if (rejected[i] && a[i] > 0) {
if (has_path_to_nonrejected(names(a)[i], rejected, G)) {
ai <- a[i]; a <- a + ai * G[i, ]; a[i] <- 0; moved <- TRUE
} else { a[i] <- 0; moved <- TRUE }
}
}
if (!moved) break
}
a
}
run_graph <- function(p, w, G, alpha_tot=0.05) {
stopifnot(abs(sum(w)-1) < 1e-12, identical(names(w), colnames(G)))
a <- alpha_tot * w
tested <- setNames(rep(FALSE, 6), names(w))
rejected <- setNames(rep(FALSE, 6), names(w))
tested[a > 0] <- TRUE
repeat {
can_reject <- (!rejected) & (p <= a)
if (!any(can_reject)) break
rej_nodes <- names(which(can_reject))
for (i in rej_nodes) {
ai <- a[i]
if (ai > 0) { a <- a + ai * G[i, ]; a[i] <- 0 }
rejected[i] <- TRUE
}
a <- push_alpha_through_rejected(a, rejected, G)
tested[a > 0] <- TRUE
}
list(tested=tested, rejected=rejected)
}
run_andgate_H6 <- function(p, w, G, alpha_tot=0.05) {
a <- alpha_tot * w
tested <- setNames(rep(FALSE, 6), names(w))
rejected <- setNames(rep(FALSE, 6), names(w))
tested[a > 0] <- TRUE
repeat {
can_reject <- (!rejected[1:5]) & (p[1:5] <= a[1:5])
if (!any(can_reject)) break
rej_nodes <- names(which(can_reject))
for (i in rej_nodes) {
ai <- a[i]
if (ai > 0) { a <- a + ai * G[i, ]; a[i] <- 0 }
rejected[i] <- TRUE
}
a <- push_alpha_through_rejected(a, rejected, G)
tested[a > 0] <- TRUE
}
if (all(rejected[1:5])) {
tested["H6"] <- TRUE
rejected["H6"] <- (p["H6"] <= 0.05)
}
list(tested=tested, rejected=rejected)
}
## ===== Data & p-values =====
gen_arm <- function(trt, n, Sigma, Delta, SD, pC) {
Z <- mvrnorm(n, mu=rep(0,6), Sigma=Sigma); colnames(Z) <- endpts
means <- setNames(rep(0,6), endpts)
if (trt==1) means[c("H1","H2","H4","H5","H6")] <- Delta[c("H1","H2","H4","H5","H6")]
dat <- data.frame(
kccq = means["H1"] + SD["H1"] * Z[,"H1"],
pvo2 = means["H2"] + SD["H2"] * Z[,"H2"],
zscore = means["H4"] + SD["H4"] * Z[,"H4"],
ntprob = means["H5"] + SD["H5"] * Z[,"H5"],
lavi = means["H6"] + SD["H6"] * Z[,"H6"],
trt = trt
)
p <- if (trt==1) pmin(pmax(pC + Delta["H3"], 1e-8), 1-1e-8) else pC
dat$imp <- as.integer(Z[,"H3"] <= qnorm(p))
dat
}
p_two_or_one <- function(tstat, sided=c("two","one"), delta_sign=1) {
sided <- match.arg(sided)
if (sided=="two") 2*pnorm(-abs(tstat)) else pnorm(-delta_sign*tstat)
}
pvals_from_data <- function(dt, Delta) {
pv <- setNames(rep(NA_real_,6), endpts)
pv["H1"] <- p_two_or_one(t.test(kccq ~ trt, data=dt, var.equal=FALSE)$statistic, sided=sided, delta_sign=sign(Delta["H1"]))
pv["H2"] <- p_two_or_one(t.test(pvo2 ~ trt, data=dt, var.equal=FALSE)$statistic, sided=sided, delta_sign=sign(Delta["H2"]))
pv["H3"] <- suppressWarnings(chisq.test(table(dt$trt, dt$imp), correct=FALSE)$p.value)
pv["H4"] <- p_two_or_one(t.test(zscore ~ trt, data=dt, var.equal=FALSE)$statistic, sided=sided, delta_sign=sign(Delta["H4"]))
pv["H5"] <- p_two_or_one(t.test(ntprob ~ trt, data=dt, var.equal=FALSE)$statistic, sided=sided, delta_sign=sign(Delta["H5"]))
pv["H6"] <- p_two_or_one(t.test(lavi ~ trt, data=dt, var.equal=FALSE)$statistic, sided=sided, delta_sign=sign(Delta["H6"]))
pv
}
## ===== Scenarios 1–8 =====
H5_fix <- list(diff=-1.0, sd=1.0)
H6_fix <- list(diff=-3.5, sd=10.0)
scenarios <- list(
"Scenario 1" = list(H1=list(diff=5.00, sd=15), H2=list(diff=1.00, sd=3),
H3=0.20, H4=list(diff=0.33, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 2" = list(H1=list(diff=3.75, sd=15), H2=list(diff=0.75, sd=3),
H3=0.20, H4=list(diff=0.33, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 3" = list(H1=list(diff=2.70, sd=15), H2=list(diff=0.54, sd=3),
H3=0.20, H4=list(diff=0.33, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 4" = list(H1=list(diff=1.50, sd=15), H2=list(diff=0.30, sd=3),
H3=0.20, H4=list(diff=0.33, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 5" = list(H1=list(diff=5.00, sd=15), H2=list(diff=1.00, sd=3),
H3=0.15, H4=list(diff=0.20, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 6" = list(H1=list(diff=3.75, sd=15), H2=list(diff=0.75, sd=3),
H3=0.15, H4=list(diff=0.20, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 7" = list(H1=list(diff=2.70, sd=15), H2=list(diff=0.54, sd=3),
H3=0.15, H4=list(diff=0.20, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 8" = list(H1=list(diff=1.50, sd=15), H2=list(diff=0.30, sd=3),
H3=0.15, H4=list(diff=0.20, sd=1), H5=H5_fix, H6=H6_fix)
)
## ===== Sim with shared datasets per scenario =====
simulate_designs_for_scenario <- function(sc) {
Delta <- c(H1=sc$H1$diff, H2=sc$H2$diff, H3=sc$H3, H4=sc$H4$diff, H5=sc$H5$diff, H6=sc$H6$diff)
SD <- c(H1=sc$H1$sd, H2=sc$H2$sd, H4=sc$H4$sd, H5=sc$H5$sd, H6=sc$H6$sd)
p_list <- vector("list", nsim)
for (b in seq_len(nsim)) {
trt <- gen_arm(1, n_per_arm, Sigma, Delta, SD, pC)
ctl <- gen_arm(0, n_per_arm, Sigma, Delta, SD, pC)
dt <- rbind(trt, ctl)
p_list[[b]] <- pvals_from_data(dt, Delta)
}
simulate_with_p <- function(label, w_init, Gmat, mode=c("generic","andgate")) {
mode <- match.arg(mode)
tested_acc <- matrix(0L, nsim, 6, dimnames=list(NULL,endpts))
reject_acc <- matrix(0L, nsim, 6, dimnames=list(NULL,endpts))
for (b in seq_len(nsim)) {
p <- p_list[[b]]
out <- if (mode=="andgate") run_andgate_H6(p, w_init, Gmat, alpha_tot)
else run_graph (p, w_init, Gmat, alpha_tot)
tested_acc[b, ] <- as.integer(out$tested)
reject_acc[b, ] <- as.integer(out$rejected)
}
tibble(endpoint=endpts,
prob_tested=colMeans(tested_acc),
power=colMeans(reject_acc),
design=label)
}
bind_rows(
simulate_with_p("D1", w_D1, G13, "generic"),
simulate_with_p("D2", w_D2, G13, "generic"),
simulate_with_p("D3", w_D3, G13, "generic"),
simulate_with_p("D4", w_D4, G4, "andgate"),
simulate_with_p("D5", w_D5, G5, "generic"),
simulate_with_p("D6", w_D6, G6, "andgate")
)
}
## ===== Run all scenarios and plot (dynamic y-axis per figure) =====
for (sc_name in names(scenarios)) {
res <- simulate_designs_for_scenario(scenarios[[sc_name]])
## Probability of being tested: ONLY H3–H6
res_prob <- res %>%
filter(endpoint %in% paste0("H",3:6)) %>%
mutate(endpoint=factor(endpoint, levels=paste0("H",3:6)))
ylims_prob <- axis_limits(max(res_prob$prob_tested, na.rm=TRUE))
p_prob <- ggplot(res_prob, aes(endpoint, prob_tested, fill=design)) +
geom_col(position=position_dodge(width=0.82), width=0.72) +
labs(title=paste("Probability of Being Tested —", sc_name),
x="Endpoint", y="Probability tested") +
scale_y_continuous(limits=ylims_prob,
breaks = breaks_for_limits(ylims_prob),
labels = scales::percent_format(accuracy=1),
expand = expansion(mult=c(0,0))) +
theme_minimal(base_size=12) +
scale_fill_manual(values=cols)
print(p_prob)
## Power: H1–H6
ylims_pow <- axis_limits(max(res$power, na.rm=TRUE))
p_pow <- ggplot(res %>% mutate(endpoint=fct_inorder(endpoint)),
aes(endpoint, power, fill=design)) +
geom_col(position=position_dodge(width=0.82), width=0.72) +
labs(title=paste("Power by Endpoint —", sc_name),
x="Endpoint", y="Power") +
scale_y_continuous(limits=ylims_pow,
breaks = breaks_for_limits(ylims_pow),
labels = scales::percent_format(accuracy=1),
expand = expansion(mult=c(0,0))) +
theme_minimal(base_size=12) +
scale_fill_manual(values=cols)
print(p_pow)
cat("\n===== ", sc_name, " — Table =====\n", sep="")
print(res %>% arrange(endpoint, design), n=Inf)
}
##
## ===== Scenario 1 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.901 D1
## 2 H1 1 0.930 D2
## 3 H1 1 0.920 D3
## 4 H1 1 0.937 D4
## 5 H1 1 0.938 D5
## 6 H1 1 0.939 D6
## 7 H2 1 0.904 D1
## 8 H2 1 0.830 D2
## 9 H2 1 0.874 D3
## 10 H2 1 0.938 D4
## 11 H2 1 0.925 D5
## 12 H2 1 0.933 D6
## 13 H3 0.988 0.980 D1
## 14 H3 0.985 0.978 D2
## 15 H3 0.988 0.981 D3
## 16 H3 0.937 0.929 D4
## 17 H3 0.985 0.977 D5
## 18 H3 0.939 0.932 D6
## 19 H4 0.980 0.905 D1
## 20 H4 0.978 0.908 D2
## 21 H4 0.981 0.908 D3
## 22 H4 0.938 0.903 D4
## 23 H4 0.977 0.896 D5
## 24 H4 0.933 0.897 D6
## 25 H5 0.905 0.905 D1
## 26 H5 0.908 0.908 D2
## 27 H5 0.908 0.908 D3
## 28 H5 0.903 0.903 D4
## 29 H5 0.896 0.896 D5
## 30 H5 0.932 0.932 D6
## 31 H6 0.905 0.862 D1
## 32 H6 0.908 0.862 D2
## 33 H6 0.908 0.864 D3
## 34 H6 0.851 0.813 D4
## 35 H6 0.896 0.851 D5
## 36 H6 0.850 0.812 D6
##
## ===== Scenario 2 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.659 D1
## 2 H1 1 0.724 D2
## 3 H1 1 0.699 D3
## 4 H1 1 0.719 D4
## 5 H1 1 0.735 D5
## 6 H1 1 0.738 D6
## 7 H2 1 0.664 D1
## 8 H2 1 0.536 D2
## 9 H2 1 0.604 D3
## 10 H2 1 0.723 D4
## 11 H2 1 0.685 D5
## 12 H2 1 0.692 D6
## 13 H3 0.874 0.864 D1
## 14 H3 0.862 0.853 D2
## 15 H3 0.870 0.861 D3
## 16 H3 0.719 0.710 D4
## 17 H3 0.862 0.849 D5
## 18 H3 0.738 0.730 D6
## 19 H4 0.864 0.801 D1
## 20 H4 0.853 0.801 D2
## 21 H4 0.861 0.803 D3
## 22 H4 0.723 0.717 D4
## 23 H4 0.849 0.757 D5
## 24 H4 0.692 0.685 D6
## 25 H5 0.801 0.801 D1
## 26 H5 0.801 0.801 D2
## 27 H5 0.803 0.803 D3
## 28 H5 0.717 0.717 D4
## 29 H5 0.757 0.757 D5
## 30 H5 0.730 0.730 D6
## 31 H6 0.801 0.750 D1
## 32 H6 0.801 0.742 D2
## 33 H6 0.803 0.748 D3
## 34 H6 0.559 0.524 D4
## 35 H6 0.757 0.698 D5
## 36 H6 0.560 0.525 D6
##
## ===== Scenario 3 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.366 D1
## 2 H1 1 0.440 D2
## 3 H1 1 0.411 D3
## 4 H1 1 0.407 D4
## 5 H1 1 0.447 D5
## 6 H1 1 0.450 D6
## 7 H2 1 0.370 D1
## 8 H2 1 0.253 D2
## 9 H2 1 0.312 D3
## 10 H2 1 0.410 D4
## 11 H2 1 0.353 D5
## 12 H2 1 0.354 D6
## 13 H3 0.586 0.576 D1
## 14 H3 0.570 0.560 D2
## 15 H3 0.582 0.572 D3
## 16 H3 0.407 0.398 D4
## 17 H3 0.570 0.554 D5
## 18 H3 0.450 0.443 D6
## 19 H4 0.576 0.544 D1
## 20 H4 0.560 0.532 D2
## 21 H4 0.572 0.542 D3
## 22 H4 0.410 0.410 D4
## 23 H4 0.554 0.499 D5
## 24 H4 0.354 0.354 D6
## 25 H5 0.544 0.544 D1
## 26 H5 0.532 0.532 D2
## 27 H5 0.542 0.542 D3
## 28 H5 0.410 0.410 D4
## 29 H5 0.499 0.499 D5
## 30 H5 0.443 0.443 D6
## 31 H6 0.544 0.491 D1
## 32 H6 0.532 0.475 D2
## 33 H6 0.542 0.486 D3
## 34 H6 0.227 0.206 D4
## 35 H6 0.499 0.436 D5
## 36 H6 0.231 0.210 D6
##
## ===== Scenario 4 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.124 D1
## 2 H1 1 0.166 D2
## 3 H1 1 0.148 D3
## 4 H1 1 0.132 D4
## 5 H1 1 0.167 D5
## 6 H1 1 0.168 D6
## 7 H2 1 0.120 D1
## 8 H2 1 0.0647 D2
## 9 H2 1 0.0914 D3
## 10 H2 1 0.128 D4
## 11 H2 1 0.0874 D5
## 12 H2 1 0.0876 D6
## 13 H3 0.224 0.215 D1
## 14 H3 0.217 0.210 D2
## 15 H3 0.222 0.215 D3
## 16 H3 0.132 0.125 D4
## 17 H3 0.217 0.204 D5
## 18 H3 0.168 0.162 D6
## 19 H4 0.215 0.205 D1
## 20 H4 0.210 0.200 D2
## 21 H4 0.215 0.205 D3
## 22 H4 0.128 0.128 D4
## 23 H4 0.204 0.184 D5
## 24 H4 0.0876 0.0872 D6
## 25 H5 0.205 0.205 D1
## 26 H5 0.200 0.200 D2
## 27 H5 0.205 0.205 D3
## 28 H5 0.128 0.128 D4
## 29 H5 0.184 0.184 D5
## 30 H5 0.162 0.162 D6
## 31 H6 0.205 0.173 D1
## 32 H6 0.200 0.170 D2
## 33 H6 0.205 0.172 D3
## 34 H6 0.0354 0.0303 D4
## 35 H6 0.184 0.148 D5
## 36 H6 0.0373 0.0324 D6
##
## ===== Scenario 5 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.903 D1
## 2 H1 1 0.929 D2
## 3 H1 1 0.920 D3
## 4 H1 1 0.917 D4
## 5 H1 1 0.931 D5
## 6 H1 1 0.932 D6
## 7 H2 1 0.900 D1
## 8 H2 1 0.828 D2
## 9 H2 1 0.869 D3
## 10 H2 1 0.930 D4
## 11 H2 1 0.915 D5
## 12 H2 1 0.919 D6
## 13 H3 0.987 0.887 D1
## 14 H3 0.984 0.884 D2
## 15 H3 0.986 0.886 D3
## 16 H3 0.917 0.793 D4
## 17 H3 0.984 0.880 D5
## 18 H3 0.932 0.826 D6
## 19 H4 0.887 0.500 D1
## 20 H4 0.884 0.492 D2
## 21 H4 0.886 0.497 D3
## 22 H4 0.930 0.538 D4
## 23 H4 0.880 0.493 D5
## 24 H4 0.919 0.524 D6
## 25 H5 0.500 0.500 D1
## 26 H5 0.492 0.492 D2
## 27 H5 0.497 0.497 D3
## 28 H5 0.538 0.538 D4
## 29 H5 0.493 0.493 D5
## 30 H5 0.826 0.826 D6
## 31 H6 0.500 0.465 D1
## 32 H6 0.492 0.456 D2
## 33 H6 0.497 0.462 D3
## 34 H6 0.470 0.438 D4
## 35 H6 0.493 0.458 D5
## 36 H6 0.474 0.442 D6
##
## ===== Scenario 6 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.660 D1
## 2 H1 1 0.723 D2
## 3 H1 1 0.699 D3
## 4 H1 1 0.699 D4
## 5 H1 1 0.728 D5
## 6 H1 1 0.731 D6
## 7 H2 1 0.661 D1
## 8 H2 1 0.522 D2
## 9 H2 1 0.596 D3
## 10 H2 1 0.711 D4
## 11 H2 1 0.659 D5
## 12 H2 1 0.667 D6
## 13 H3 0.866 0.751 D1
## 14 H3 0.849 0.737 D2
## 15 H3 0.859 0.745 D3
## 16 H3 0.699 0.584 D4
## 17 H3 0.849 0.718 D5
## 18 H3 0.731 0.627 D6
## 19 H4 0.751 0.435 D1
## 20 H4 0.737 0.414 D2
## 21 H4 0.745 0.424 D3
## 22 H4 0.711 0.489 D4
## 23 H4 0.718 0.406 D5
## 24 H4 0.667 0.450 D6
## 25 H5 0.435 0.435 D1
## 26 H5 0.414 0.414 D2
## 27 H5 0.424 0.424 D3
## 28 H5 0.489 0.489 D4
## 29 H5 0.406 0.406 D5
## 30 H5 0.627 0.627 D6
## 31 H6 0.435 0.399 D1
## 32 H6 0.414 0.375 D2
## 33 H6 0.424 0.385 D3
## 34 H6 0.352 0.327 D4
## 35 H6 0.406 0.368 D5
## 36 H6 0.355 0.331 D6
##
## ===== Scenario 7 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.367 D1
## 2 H1 1 0.438 D2
## 3 H1 1 0.408 D3
## 4 H1 1 0.401 D4
## 5 H1 1 0.443 D5
## 6 H1 1 0.446 D6
## 7 H2 1 0.373 D1
## 8 H2 1 0.257 D2
## 9 H2 1 0.317 D3
## 10 H2 1 0.402 D4
## 11 H2 1 0.338 D5
## 12 H2 1 0.337 D6
## 13 H3 0.590 0.486 D1
## 14 H3 0.570 0.470 D2
## 15 H3 0.583 0.480 D3
## 16 H3 0.401 0.315 D4
## 17 H3 0.570 0.442 D5
## 18 H3 0.446 0.367 D6
## 19 H4 0.486 0.317 D1
## 20 H4 0.470 0.290 D2
## 21 H4 0.480 0.301 D3
## 22 H4 0.402 0.337 D4
## 23 H4 0.442 0.259 D5
## 24 H4 0.337 0.278 D6
## 25 H5 0.317 0.317 D1
## 26 H5 0.290 0.290 D2
## 27 H5 0.301 0.301 D3
## 28 H5 0.337 0.337 D4
## 29 H5 0.259 0.259 D5
## 30 H5 0.367 0.367 D6
## 31 H6 0.317 0.279 D1
## 32 H6 0.290 0.248 D2
## 33 H6 0.301 0.264 D3
## 34 H6 0.163 0.149 D4
## 35 H6 0.259 0.217 D5
## 36 H6 0.167 0.154 D6
##
## ===== Scenario 8 — Table =====
## # A tibble: 36 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1 1 0.124 D1
## 2 H1 1 0.165 D2
## 3 H1 1 0.149 D3
## 4 H1 1 0.133 D4
## 5 H1 1 0.166 D5
## 6 H1 1 0.167 D6
## 7 H2 1 0.120 D1
## 8 H2 1 0.0662 D2
## 9 H2 1 0.0949 D3
## 10 H2 1 0.126 D4
## 11 H2 1 0.0852 D5
## 12 H2 1 0.0827 D6
## 13 H3 0.224 0.168 D1
## 14 H3 0.215 0.160 D2
## 15 H3 0.224 0.166 D3
## 16 H3 0.133 0.0906 D4
## 17 H3 0.215 0.139 D5
## 18 H3 0.167 0.124 D6
## 19 H4 0.168 0.125 D1
## 20 H4 0.160 0.107 D2
## 21 H4 0.166 0.118 D3
## 22 H4 0.126 0.121 D4
## 23 H4 0.139 0.0847 D5
## 24 H4 0.0827 0.079 D6
## 25 H5 0.125 0.125 D1
## 26 H5 0.107 0.107 D2
## 27 H5 0.118 0.118 D3
## 28 H5 0.121 0.121 D4
## 29 H5 0.0847 0.0847 D5
## 30 H5 0.124 0.124 D6
## 31 H6 0.125 0.100 D1
## 32 H6 0.107 0.0843 D2
## 33 H6 0.118 0.0916 D3
## 34 H6 0.0275 0.0233 D4
## 35 H6 0.0847 0.0606 D5
## 36 H6 0.0293 0.0251 D6