高校数学の質問スレ（医者・東大卒専用） Part438

高校数学の質問スレ（医者・東大卒専用） Part438 (883ﾚｽ)
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822: １３２人目の素数さん [sage] 2025/05/02(金) 10:48:45.43 ID:+8QO9mMm

set.seed(123)
library(fmsb)

alpha <- 0.05
N <- 1000

sim <- function() {
# 群ごとのサンプルサイズ（不均等で可）
n1 <- sample(250:350, 1)  # 低用量
n2 <- sample(250:350, 1)  # 高用量
n3 <- N - n1 - n2         # プラセボ

# 各群の成功率設定（ペアでは差なし、プラセボ vs 合算で差あり）
p1 <- 0.30  # 低用量
p2 <- 0.31  # 高用量
p3 <- 0.22  # プラセボ（低め）

x1 <- rbinom(1, n1, p1)
x2 <- rbinom(1, n2, p2)
x3 <- rbinom(1, n3, p3)

m <- rbind(success = c(x1, x2, x3), failure = c(n1 - x1, n2 - x2, n3 - x3))

bonf_p <- suppressWarnings(min(as.vector(pairwise.fisher.test(m[1,], colSums(m), p.adj="bonf")$p.value), na.rm=TRUE))

combined <- matrix(c(x1 + x2, n1 + n2 - x1 - x2, x3, n3 - x3), nrow=2)
comb_p <- fisher.test(combined)$p.value

list(m = m, bonf = bonf_p, combined_p = comb_p, sizes = c(n1, n2, n3))
}

# 条件を満たすデータが出るまでループ
res <- sim()
while (!(res$bonf > alpha && res$combined_p < alpha)) {
res <- sim()
}

# 結果出力
res$m
cat("Bonferroni-adjusted pairwise p-value (min):", res$bonf, "\n")
cat("Combined treatment vs placebo p-value:", res$combined_p, "\n")
cat("Sample sizes:", res$sizes, "\n")

http://rio2016.5ch.net/test/read.cgi/math/1723152147/822

823: １３２人目の素数さん [sage] 2025/05/02(金) 11:02:18.75 ID:+8QO9mMm

set.seed(123)
library(fmsb)

alpha <- 0.05
N <- 1000

# Simulation function
sim <- function() {
# Random group sizes
n1 <- sample(250:350, 1)     # Low-dose
n2 <- sample(250:350, 1)     # High-dose
n3 <- N - n1 - n2            # Placebo
if (n3 < 100) return(NULL)   # Skip too-small placebo

# Success rates from uniform distribution
p1 <- runif(1)
p2 <- runif(1)
p3 <- runif(1)

# Binomial draws
x1 <- rbinom(1, n1, p1)
x2 <- rbinom(1, n2, p2)
x3 <- rbinom(1, n3, p3)

# 3-group matrix
m3 <- rbind(success = c(x1, x2, x3),
failure = c(n1 - x1, n2 - x2, n3 - x3))
colnames(m3) <- c("Low", "High", "Placebo")

# Add 4th group = combined (low + high)
x4 <- x1 + x2
n4 <- n1 + n2
m4 <- cbind(m3, Combined = c(x4, n4 - x4))

# Perform pairwise Fisher's exact tests across 4 groups
pw <- suppressWarnings(pairwise.fisher.test(m4[1,], colSums(m4), p.adj="bonf")$p.value)
pw_vals <- as.vector(pw)
pw_vals <- pw_vals[!is.na(pw_vals)]
names_all <- names(pw_vals)

# Identify significant pairs
sig_idx <- which(pw_vals < alpha)
sig_names <- names(pw_vals)[sig_idx]

# Check if only Combined vs Placebo is significant
is_valid <- length(sig_idx) == 1 &&
any(grepl("Placebo-Combined|Combined-Placebo", sig_names))

if (is_valid) {
return(list(m = m4, probs = c(p1, p2, p3), sizes = c(n1, n2, n3), pvals = pw))
} else {
return(NULL)
}
}

# Run until condition met
res <- NULL
while (is.null(res)) {
res <- sim()
}

# Output results
print(res$m)
cat("Success probabilities (Low, High, Placebo):", round(res$probs, 3), "\n")
cat("Sample sizes (Low, High, Placebo):", res$sizes, "\n")
cat("Pairwise Bonferroni-adjusted p-values:\n")
print(res$pvals)

http://rio2016.5ch.net/test/read.cgi/math/1723152147/823

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