suppressPackageStartupMessages({
library(MASS)
library(Matrix)
library(dplyr)
library(tidyr)
library(ggplot2)
library(forcats)
library(scales)
library(tibble)
})
## 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 =====
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, D5, D6, D7 =====
# D1 (G13)
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
# D5 (G5)
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
# D6 (G6)
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
# D7 (G7): like D5 but remove H6 from recycling; recycle when H5 rejects within H1–H5;
# H6 is tested at alpha=0.05 only if H1–H5 all reject (AND-gate).
G7 <- 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(1, 0, 0, 0, 0, 0), # recycle to H1; no flow to H6
H6 = c(0, 0, 0, 0, 0, 0)
); colnames(G7) <- rownames(G7) <- endpts
## ===== Initial weights (D4 removed) =====
w_D1 <- 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)
w_D7 <- c(H1=4/5, H2=1/5, H3=0, H4=0, H5=0, H6=0)
## ===== Colors (D1, D5, D6, D7) =====
cols <- c("D1"="#1f77b4","D5"="#8c564b","D6"="#17becf","D7"="#e377c2")
## ===== Helpers (dynamic 25/50/75/100 top, ticks every 5%) =====
axis_cap_25_50_75 <- function(mx) {
if (is.na(mx) || mx <= 0) return(0.25)
if (mx <= 0.25) return(0.25)
if (mx <= 0.50) return(0.50)
if (mx <= 0.75) return(0.75)
1.00
}
axis_breaks_5pct <- function(top) seq(0, top, by = 0.05)
## ===== Alpha flow helpers =====
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)
}
## AND-gate for H6 only (used by D6 & D7)
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 generation & 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 (Scenario 1 added back) =====
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=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 2" = list(H1=list(diff=5.00, sd=15), H2=list(diff=0.75, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 3" = list(H1=list(diff=5.00, sd=15), H2=list(diff=0.54, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 4" = list(H1=list(diff=5.00, sd=15), H2=list(diff=0.30, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 5" = list(H1=list(diff=3.75, sd=15), H2=list(diff=1.00, sd=3), H3=0.2, H4=list(diff=0.25, 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=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 7" = list(H1=list(diff=3.75, sd=15), H2=list(diff=0.54, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 8" = list(H1=list(diff=3.75, sd=15), H2=list(diff=0.30, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 9" = list(H1=list(diff=2.70, sd=15), H2=list(diff=1.00, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 10" = list(H1=list(diff=2.70, sd=15), H2=list(diff=0.75, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 11" = list(H1=list(diff=2.70, sd=15), H2=list(diff=0.54, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 12" = list(H1=list(diff=2.70, sd=15), H2=list(diff=0.30, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 13" = list(H1=list(diff=1.50, sd=15), H2=list(diff=1.00, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 14" = list(H1=list(diff=1.50, sd=15), H2=list(diff=0.75, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 15" = list(H1=list(diff=1.50, sd=15), H2=list(diff=0.54, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix),
"Scenario 16" = list(H1=list(diff=1.50, sd=15), H2=list(diff=0.30, sd=3), H3=0.2, H4=list(diff=0.25, sd=1), H5=H5_fix, H6=H6_fix)
)
stopifnot(length(scenarios) >= 1)
## ===== Title helper: show ONLY diffs for H1–H4 =====
mk_title <- function(name, sc) {
paste0(
name, " — H1=", sc$H1$diff, "; ",
"H2=", sc$H2$diff, "; ",
"H3=", sc$H3, "; ",
"H4=", sc$H4$diff
)
}
## ===== Simulation per scenario (D4 removed; include D7; add H1_or_H2) =====
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$sd)
p_list <- vector("list", nsim)
for (b in seq_len(nsim)) {
trt <- gen_arm(1, n_per_arm, Sigma, Delta, SD, pC)
ctl <- gen_arm(0, n_per_arm, Sigma, Delta, SD, pC)
dt <- rbind(trt, ctl)
p_list[[b]] <- pvals_from_data(dt, Delta)
}
simulate_with_p <- function(label, w_init, Gmat, mode=c("generic","andgate")) {
mode <- match.arg(mode)
tested_acc <- matrix(0L, nsim, 6, dimnames=list(NULL,endpts))
reject_acc <- matrix(0L, nsim, 6, dimnames=list(NULL,endpts))
h1_rej <- logical(nsim); h2_rej <- logical(nsim)
for (b in seq_len(nsim)) {
p <- p_list[[b]]
out <- if (mode=="andgate") run_andgate_H6(p, w_init, Gmat, alpha_tot)
else run_graph (p, w_init, Gmat, alpha_tot)
tested_acc[b, ] <- as.integer(out$tested)
reject_acc[b, ] <- as.integer(out$rejected)
h1_rej[b] <- out$rejected["H1"]
h2_rej[b] <- out$rejected["H2"]
}
res_endpt <- tibble(endpoint=endpts,
prob_tested=colMeans(tested_acc),
power=colMeans(reject_acc),
design=label)
res_comb <- tibble(endpoint="H1_or_H2",
prob_tested=NA_real_,
power=mean(h1_rej | h2_rej),
design=label)
bind_rows(res_endpt, res_comb)
}
bind_rows(
simulate_with_p("D1", w_D1, G13, "generic"),
simulate_with_p("D5", w_D5, G5, "generic"),
simulate_with_p("D6", w_D6, G6, "andgate"),
simulate_with_p("D7", w_D7, G7, "andgate")
)
}
## ===== Run all scenarios and plot (no saving; titles show only diffs) =====
for (sc_name in names(scenarios)) {
sc <- scenarios[[sc_name]]
res <- simulate_designs_for_scenario(sc)
## Probability of being tested: ONLY H3–H6
res_prob <- res %>%
filter(endpoint %in% paste0("H",3:6)) %>%
mutate(endpoint=factor(endpoint, levels=paste0("H",3:6)))
top_prob <- axis_cap_25_50_75(max(res_prob$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 = mk_title(sc_name, sc),
subtitle = "Probability of being tested (H3–H6)",
x="Endpoint", y="Probability tested"
) +
scale_y_continuous(limits = c(0, top_prob),
breaks = axis_breaks_5pct(top_prob),
labels = percent_format(accuracy=1),
expand = expansion(mult=c(0,0))) +
theme_minimal(base_size=12) +
scale_fill_manual(values=cols) +
theme(plot.title = element_text(face="bold", size=14))
print(p_prob)
## Power: include H1_or_H2 + H1–H6
res_power <- res %>%
mutate(endpoint=factor(endpoint, levels=c("H1_or_H2", paste0("H",1:6))))
top_power <- axis_cap_25_50_75(max(res_power$power, na.rm = TRUE))
p_pow <- ggplot(res_power, aes(endpoint, power, fill=design)) +
geom_col(position=position_dodge(width=0.82), width=0.72) +
labs(
title = mk_title(sc_name, sc),
x="Endpoint", y="Power"
) +
scale_y_continuous(limits = c(0, top_power),
breaks = axis_breaks_5pct(top_power),
labels = percent_format(accuracy=1),
expand = expansion(mult=c(0,0))) +
theme_minimal(base_size=12) +
scale_fill_manual(values=cols) +
theme(plot.title = element_text(face="bold", size=14))
print(p_pow)
cat("\n===== ", sc_name, " — Table =====\n", sep = "")
print(res %>% arrange(match(endpoint, c("H1_or_H2", paste0("H",1:6))), design), n = Inf)
}
##
## ===== Scenario 1 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.988 D1
## 2 H1_or_H2 NA 0.985 D5
## 3 H1_or_H2 NA 0.985 D6
## 4 H1_or_H2 NA 0.985 D7
## 5 H1 1 0.901 D1
## 6 H1 1 0.935 D5
## 7 H1 1 0.936 D6
## 8 H1 1 0.936 D7
## 9 H2 1 0.904 D1
## 10 H2 1 0.921 D5
## 11 H2 1 0.933 D6
## 12 H2 1 0.921 D7
## 13 H3 0.988 0.980 D1
## 14 H3 0.985 0.977 D5
## 15 H3 0.936 0.927 D6
## 16 H3 0.985 0.977 D7
## 17 H4 0.980 0.733 D1
## 18 H4 0.977 0.729 D5
## 19 H4 0.933 0.733 D6
## 20 H4 0.977 0.729 D7
## 21 H5 0.733 0.733 D1
## 22 H5 0.729 0.729 D5
## 23 H5 0.927 0.927 D6
## 24 H5 0.729 0.729 D7
## 25 H6 0.733 0.692 D1
## 26 H6 0.729 0.686 D5
## 27 H6 0.702 0.665 D6
## 28 H6 0.701 0.664 D7
##
## ===== Scenario 2 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.963 D1
## 2 H1_or_H2 NA 0.964 D5
## 3 H1_or_H2 NA 0.964 D6
## 4 H1_or_H2 NA 0.964 D7
## 5 H1 1 0.905 D1
## 6 H1 1 0.937 D5
## 7 H1 1 0.938 D6
## 8 H1 1 0.938 D7
## 9 H2 1 0.664 D1
## 10 H2 1 0.712 D5
## 11 H2 1 0.737 D6
## 12 H2 1 0.713 D7
## 13 H3 0.963 0.953 D1
## 14 H3 0.964 0.952 D5
## 15 H3 0.938 0.929 D6
## 16 H3 0.964 0.952 D7
## 17 H4 0.953 0.687 D1
## 18 H4 0.952 0.666 D5
## 19 H4 0.737 0.657 D6
## 20 H4 0.952 0.666 D7
## 21 H5 0.687 0.687 D1
## 22 H5 0.666 0.666 D5
## 23 H5 0.929 0.929 D6
## 24 H5 0.666 0.666 D7
## 25 H6 0.687 0.644 D1
## 26 H6 0.666 0.621 D5
## 27 H6 0.634 0.595 D6
## 28 H6 0.622 0.584 D7
##
## ===== Scenario 3 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.930 D1
## 2 H1_or_H2 NA 0.940 D5
## 3 H1_or_H2 NA 0.940 D6
## 4 H1_or_H2 NA 0.940 D7
## 5 H1 1 0.903 D1
## 6 H1 1 0.930 D5
## 7 H1 1 0.930 D6
## 8 H1 1 0.930 D7
## 9 H2 1 0.370 D1
## 10 H2 1 0.444 D5
## 11 H2 1 0.460 D6
## 12 H2 1 0.447 D7
## 13 H3 0.930 0.918 D1
## 14 H3 0.940 0.922 D5
## 15 H3 0.930 0.922 D6
## 16 H3 0.940 0.922 D7
## 17 H4 0.918 0.628 D1
## 18 H4 0.922 0.576 D5
## 19 H4 0.460 0.447 D6
## 20 H4 0.922 0.576 D7
## 21 H5 0.628 0.628 D1
## 22 H5 0.576 0.576 D5
## 23 H5 0.922 0.922 D6
## 24 H5 0.576 0.576 D7
## 25 H6 0.628 0.582 D1
## 26 H6 0.576 0.528 D5
## 27 H6 0.436 0.401 D6
## 28 H6 0.425 0.391 D7
##
## ===== Scenario 4 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.911 D1
## 2 H1_or_H2 NA 0.935 D5
## 3 H1_or_H2 NA 0.935 D6
## 4 H1_or_H2 NA 0.935 D7
## 5 H1 1 0.903 D1
## 6 H1 1 0.933 D5
## 7 H1 1 0.933 D6
## 8 H1 1 0.933 D7
## 9 H2 1 0.120 D1
## 10 H2 1 0.172 D5
## 11 H2 1 0.178 D6
## 12 H2 1 0.178 D7
## 13 H3 0.911 0.895 D1
## 14 H3 0.935 0.911 D5
## 15 H3 0.933 0.922 D6
## 16 H3 0.935 0.911 D7
## 17 H4 0.895 0.608 D1
## 18 H4 0.911 0.530 D5
## 19 H4 0.178 0.176 D6
## 20 H4 0.911 0.530 D7
## 21 H5 0.608 0.608 D1
## 22 H5 0.530 0.530 D5
## 23 H5 0.922 0.922 D6
## 24 H5 0.530 0.530 D7
## 25 H6 0.608 0.556 D1
## 26 H6 0.530 0.465 D5
## 27 H6 0.174 0.153 D6
## 28 H6 0.172 0.152 D7
##
## ===== Scenario 5 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.961 D1
## 2 H1_or_H2 NA 0.945 D5
## 3 H1_or_H2 NA 0.945 D6
## 4 H1_or_H2 NA 0.945 D7
## 5 H1 1 0.665 D1
## 6 H1 1 0.739 D5
## 7 H1 1 0.741 D6
## 8 H1 1 0.741 D7
## 9 H2 1 0.900 D1
## 10 H2 1 0.894 D5
## 11 H2 1 0.905 D6
## 12 H2 1 0.894 D7
## 13 H3 0.961 0.950 D1
## 14 H3 0.945 0.934 D5
## 15 H3 0.741 0.732 D6
## 16 H3 0.945 0.934 D7
## 17 H4 0.950 0.709 D1
## 18 H4 0.934 0.683 D5
## 19 H4 0.905 0.690 D6
## 20 H4 0.934 0.683 D7
## 21 H5 0.709 0.709 D1
## 22 H5 0.683 0.683 D5
## 23 H5 0.732 0.732 D6
## 24 H5 0.683 0.683 D7
## 25 H6 0.709 0.662 D1
## 26 H6 0.683 0.631 D5
## 27 H6 0.565 0.533 D6
## 28 H6 0.564 0.531 D7
##
## ===== Scenario 6 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.866 D1
## 2 H1_or_H2 NA 0.849 D5
## 3 H1_or_H2 NA 0.849 D6
## 4 H1_or_H2 NA 0.849 D7
## 5 H1 1 0.660 D1
## 6 H1 1 0.732 D5
## 7 H1 1 0.735 D6
## 8 H1 1 0.735 D7
## 9 H2 1 0.661 D1
## 10 H2 1 0.666 D5
## 11 H2 1 0.687 D6
## 12 H2 1 0.666 D7
## 13 H3 0.866 0.855 D1
## 14 H3 0.849 0.836 D5
## 15 H3 0.735 0.725 D6
## 16 H3 0.849 0.836 D7
## 17 H4 0.855 0.650 D1
## 18 H4 0.836 0.606 D5
## 19 H4 0.687 0.602 D6
## 20 H4 0.836 0.606 D7
## 21 H5 0.650 0.650 D1
## 22 H5 0.606 0.606 D5
## 23 H5 0.725 0.725 D6
## 24 H5 0.606 0.606 D7
## 25 H6 0.650 0.605 D1
## 26 H6 0.606 0.554 D5
## 27 H6 0.511 0.480 D6
## 28 H6 0.501 0.470 D7
##
## ===== Scenario 7 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.776 D1
## 2 H1_or_H2 NA 0.786 D5
## 3 H1_or_H2 NA 0.786 D6
## 4 H1_or_H2 NA 0.786 D7
## 5 H1 1 0.662 D1
## 6 H1 1 0.731 D5
## 7 H1 1 0.732 D6
## 8 H1 1 0.732 D7
## 9 H2 1 0.373 D1
## 10 H2 1 0.402 D5
## 11 H2 1 0.414 D6
## 12 H2 1 0.404 D7
## 13 H3 0.776 0.761 D1
## 14 H3 0.786 0.766 D5
## 15 H3 0.732 0.721 D6
## 16 H3 0.786 0.766 D7
## 17 H4 0.761 0.550 D1
## 18 H4 0.766 0.495 D5
## 19 H4 0.414 0.398 D6
## 20 H4 0.766 0.495 D7
## 21 H5 0.550 0.550 D1
## 22 H5 0.495 0.495 D5
## 23 H5 0.721 0.721 D6
## 24 H5 0.495 0.495 D7
## 25 H6 0.550 0.504 D1
## 26 H6 0.495 0.445 D5
## 27 H6 0.347 0.320 D6
## 28 H6 0.339 0.312 D7
##
## ===== Scenario 8 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.687 D1
## 2 H1_or_H2 NA 0.733 D5
## 3 H1_or_H2 NA 0.733 D6
## 4 H1_or_H2 NA 0.733 D7
## 5 H1 1 0.653 D1
## 6 H1 1 0.721 D5
## 7 H1 1 0.722 D6
## 8 H1 1 0.722 D7
## 9 H2 1 0.120 D1
## 10 H2 1 0.148 D5
## 11 H2 1 0.154 D6
## 12 H2 1 0.153 D7
## 13 H3 0.687 0.675 D1
## 14 H3 0.733 0.714 D5
## 15 H3 0.722 0.715 D6
## 16 H3 0.733 0.714 D7
## 17 H4 0.675 0.460 D1
## 18 H4 0.714 0.425 D5
## 19 H4 0.154 0.153 D6
## 20 H4 0.714 0.425 D7
## 21 H5 0.460 0.460 D1
## 22 H5 0.425 0.425 D5
## 23 H5 0.715 0.715 D6
## 24 H5 0.425 0.425 D7
## 25 H6 0.460 0.412 D1
## 26 H6 0.425 0.365 D5
## 27 H6 0.141 0.122 D6
## 28 H6 0.140 0.120 D7
##
## ===== Scenario 9 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.932 D1
## 2 H1_or_H2 NA 0.895 D5
## 3 H1_or_H2 NA 0.895 D6
## 4 H1_or_H2 NA 0.895 D7
## 5 H1 1 0.372 D1
## 6 H1 1 0.458 D5
## 7 H1 1 0.463 D6
## 8 H1 1 0.463 D7
## 9 H2 1 0.902 D1
## 10 H2 1 0.867 D5
## 11 H2 1 0.871 D6
## 12 H2 1 0.867 D7
## 13 H3 0.932 0.920 D1
## 14 H3 0.895 0.880 D5
## 15 H3 0.463 0.454 D6
## 16 H3 0.895 0.880 D7
## 17 H4 0.920 0.668 D1
## 18 H4 0.880 0.599 D5
## 19 H4 0.871 0.608 D6
## 20 H4 0.880 0.599 D7
## 21 H5 0.668 0.668 D1
## 22 H5 0.599 0.599 D5
## 23 H5 0.454 0.454 D6
## 24 H5 0.599 0.599 D7
## 25 H6 0.668 0.612 D1
## 26 H6 0.599 0.529 D5
## 27 H6 0.360 0.336 D6
## 28 H6 0.359 0.335 D7
##
## ===== Scenario 10 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.772 D1
## 2 H1_or_H2 NA 0.718 D5
## 3 H1_or_H2 NA 0.718 D6
## 4 H1_or_H2 NA 0.718 D7
## 5 H1 1 0.372 D1
## 6 H1 1 0.453 D5
## 7 H1 1 0.458 D6
## 8 H1 1 0.458 D7
## 9 H2 1 0.654 D1
## 10 H2 1 0.608 D5
## 11 H2 1 0.621 D6
## 12 H2 1 0.608 D7
## 13 H3 0.772 0.763 D1
## 14 H3 0.718 0.705 D5
## 15 H3 0.458 0.451 D6
## 16 H3 0.718 0.705 D7
## 17 H4 0.763 0.609 D1
## 18 H4 0.705 0.529 D5
## 19 H4 0.621 0.530 D6
## 20 H4 0.705 0.529 D7
## 21 H5 0.609 0.609 D1
## 22 H5 0.529 0.529 D5
## 23 H5 0.451 0.451 D6
## 24 H5 0.529 0.529 D7
## 25 H6 0.609 0.554 D1
## 26 H6 0.529 0.463 D5
## 27 H6 0.322 0.302 D6
## 28 H6 0.316 0.296 D7
##
## ===== Scenario 11 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.587 D1
## 2 H1_or_H2 NA 0.575 D5
## 3 H1_or_H2 NA 0.575 D6
## 4 H1_or_H2 NA 0.575 D7
## 5 H1 1 0.369 D1
## 6 H1 1 0.449 D5
## 7 H1 1 0.452 D6
## 8 H1 1 0.452 D7
## 9 H2 1 0.363 D1
## 10 H2 1 0.347 D5
## 11 H2 1 0.355 D6
## 12 H2 1 0.349 D7
## 13 H3 0.587 0.576 D1
## 14 H3 0.575 0.558 D5
## 15 H3 0.452 0.446 D6
## 16 H3 0.575 0.558 D7
## 17 H4 0.576 0.456 D1
## 18 H4 0.558 0.393 D5
## 19 H4 0.355 0.341 D6
## 20 H4 0.558 0.393 D7
## 21 H5 0.456 0.456 D1
## 22 H5 0.393 0.393 D5
## 23 H5 0.446 0.446 D6
## 24 H5 0.393 0.393 D7
## 25 H6 0.456 0.406 D1
## 26 H6 0.393 0.335 D5
## 27 H6 0.225 0.207 D6
## 28 H6 0.219 0.200 D7
##
## ===== Scenario 12 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.442 D1
## 2 H1_or_H2 NA 0.486 D5
## 3 H1_or_H2 NA 0.486 D6
## 4 H1_or_H2 NA 0.486 D7
## 5 H1 1 0.376 D1
## 6 H1 1 0.453 D5
## 7 H1 1 0.454 D6
## 8 H1 1 0.454 D7
## 9 H2 1 0.122 D1
## 10 H2 1 0.122 D5
## 11 H2 1 0.126 D6
## 12 H2 1 0.125 D7
## 13 H3 0.442 0.427 D1
## 14 H3 0.486 0.465 D5
## 15 H3 0.454 0.444 D6
## 16 H3 0.486 0.465 D7
## 17 H4 0.427 0.315 D1
## 18 H4 0.465 0.291 D5
## 19 H4 0.126 0.124 D6
## 20 H4 0.465 0.291 D7
## 21 H5 0.315 0.315 D1
## 22 H5 0.291 0.291 D5
## 23 H5 0.444 0.444 D6
## 24 H5 0.291 0.291 D7
## 25 H6 0.315 0.275 D1
## 26 H6 0.291 0.242 D5
## 27 H6 0.092 0.0776 D6
## 28 H6 0.0909 0.0767 D7
##
## ===== Scenario 13 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.911 D1
## 2 H1_or_H2 NA 0.851 D5
## 3 H1_or_H2 NA 0.851 D6
## 4 H1_or_H2 NA 0.851 D7
## 5 H1 1 0.117 D1
## 6 H1 1 0.168 D5
## 7 H1 1 0.172 D6
## 8 H1 1 0.171 D7
## 9 H2 1 0.903 D1
## 10 H2 1 0.843 D5
## 11 H2 1 0.845 D6
## 12 H2 1 0.843 D7
## 13 H3 0.911 0.898 D1
## 14 H3 0.851 0.828 D5
## 15 H3 0.172 0.167 D6
## 16 H3 0.851 0.828 D7
## 17 H4 0.898 0.661 D1
## 18 H4 0.828 0.548 D5
## 19 H4 0.845 0.563 D6
## 20 H4 0.828 0.548 D7
## 21 H5 0.661 0.661 D1
## 22 H5 0.548 0.548 D5
## 23 H5 0.167 0.167 D6
## 24 H5 0.548 0.548 D7
## 25 H6 0.661 0.598 D1
## 26 H6 0.548 0.457 D5
## 27 H6 0.135 0.127 D6
## 28 H6 0.134 0.126 D7
##
## ===== Scenario 14 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.695 D1
## 2 H1_or_H2 NA 0.598 D5
## 3 H1_or_H2 NA 0.598 D6
## 4 H1_or_H2 NA 0.598 D7
## 5 H1 1 0.123 D1
## 6 H1 1 0.175 D5
## 7 H1 1 0.179 D6
## 8 H1 1 0.177 D7
## 9 H2 1 0.662 D1
## 10 H2 1 0.562 D5
## 11 H2 1 0.565 D6
## 12 H2 1 0.562 D7
## 13 H3 0.695 0.684 D1
## 14 H3 0.598 0.579 D5
## 15 H3 0.179 0.174 D6
## 16 H3 0.598 0.579 D7
## 17 H4 0.684 0.577 D1
## 18 H4 0.579 0.457 D5
## 19 H4 0.565 0.468 D6
## 20 H4 0.579 0.457 D7
## 21 H5 0.577 0.577 D1
## 22 H5 0.457 0.457 D5
## 23 H5 0.174 0.174 D6
## 24 H5 0.457 0.457 D7
## 25 H6 0.577 0.518 D1
## 26 H6 0.457 0.374 D5
## 27 H6 0.133 0.123 D6
## 28 H6 0.130 0.120 D7
##
## ===== Scenario 15 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.436 D1
## 2 H1_or_H2 NA 0.363 D5
## 3 H1_or_H2 NA 0.363 D6
## 4 H1_or_H2 NA 0.363 D7
## 5 H1 1 0.119 D1
## 6 H1 1 0.163 D5
## 7 H1 1 0.165 D6
## 8 H1 1 0.164 D7
## 9 H2 1 0.366 D1
## 10 H2 1 0.286 D5
## 11 H2 1 0.290 D6
## 12 H2 1 0.288 D7
## 13 H3 0.436 0.425 D1
## 14 H3 0.363 0.348 D5
## 15 H3 0.165 0.16 D6
## 16 H3 0.363 0.348 D7
## 17 H4 0.425 0.383 D1
## 18 H4 0.348 0.290 D5
## 19 H4 0.290 0.278 D6
## 20 H4 0.348 0.290 D7
## 21 H5 0.383 0.383 D1
## 22 H5 0.290 0.290 D5
## 23 H5 0.16 0.16 D6
## 24 H5 0.290 0.290 D7
## 25 H6 0.383 0.333 D1
## 26 H6 0.290 0.225 D5
## 27 H6 0.0886 0.0815 D6
## 28 H6 0.0854 0.0785 D7
##
## ===== Scenario 16 — Table =====
## # A tibble: 28 × 4
## endpoint prob_tested power design
## <chr> <dbl> <dbl> <chr>
## 1 H1_or_H2 NA 0.216 D1
## 2 H1_or_H2 NA 0.208 D5
## 3 H1_or_H2 NA 0.208 D6
## 4 H1_or_H2 NA 0.208 D7
## 5 H1 1 0.114 D1
## 6 H1 1 0.158 D5
## 7 H1 1 0.158 D6
## 8 H1 1 0.158 D7
## 9 H2 1 0.120 D1
## 10 H2 1 0.0834 D5
## 11 H2 1 0.0844 D6
## 12 H2 1 0.0843 D7
## 13 H3 0.216 0.208 D1
## 14 H3 0.208 0.194 D5
## 15 H3 0.158 0.153 D6
## 16 H3 0.208 0.194 D7
## 17 H4 0.208 0.176 D1
## 18 H4 0.194 0.140 D5
## 19 H4 0.0844 0.0837 D6
## 20 H4 0.194 0.140 D7
## 21 H5 0.176 0.176 D1
## 22 H5 0.140 0.140 D5
## 23 H5 0.153 0.153 D6
## 24 H5 0.140 0.140 D7
## 25 H6 0.176 0.146 D1
## 26 H6 0.140 0.107 D5
## 27 H6 0.0333 0.0285 D6
## 28 H6 0.0328 0.028 D7