การวิเคราะห์ความไวแบบอาศัยความน่าจะเป็น: จากการแจกแจงพารามิเตอร์สู่ CEAC

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")

# Uncertain inputs as curves, many runs of a stand-in model, and the share of wins at each price
# Give each uncertain input of the fund's decision a curve, rerun a stand-in model 1,000 times.
# ให้ข้อมูลนำเข้าที่ไม่แน่นอนแต่ละตัวมีเส้นโค้งของตัวเอง แล้วรันแบบจำลองแทน 1,000 ครั้ง
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# ggplot2 4.0.3 (stable)
# install.packages(c("ggplot2"))
# update.packages(oldPkgs = c("ggplot2"))
# remotes::install_version("ggplot2", "4.0.3")
library(ggplot2)  # Display the shares across prices without saving files.
stopifnot(getRversion() >= "4.5.2")

#%%@note 1. Define the illustrative inputs
# Every input is synthetic and written out once, in the order the article uses it.
# ค่าตั้งต้นทั้งหมดเป็นข้อมูลสมมติ เขียนไว้ครั้งเดียวตามลำดับที่บทความใช้
extra_cost <- 150000
extra_health <- 1.00
price <- 160000
events <- c(8, 13)
patients <- c(66, 60)
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
ratio <- c(0.25, 0.56, 1.26)
z95 <- 1.96
rate_mean <- 0.30
rate_se <- 0.05
cost_mean <- 10000
cost_se <- 2000
counts <- c(80, 15, 5)
cohort <- 1000
health_avg_sd <- c(1.00, 0.20)
cost_avg_sd <- c(150000, 24000)
wtp <- 160000
draws <- 1000
prices <- c(100000, 150000, 160000, 200000, 300000)
health_c <- c(1.00, 0.20)
cost_c <- c(150000, 24000)

#%%@note 2. Move the trial's ratio to the log scale
# On the log scale the interval is symmetric, so its half width over 1.96 gives the spread.
# บนสเกลลอการิทึม ช่วงความเชื่อมั่นสมมาตร ครึ่งความกว้างหารด้วย 1.96 จึงได้ค่าการกระจาย
logs <- log(ratio)
half_width <- (logs[3] - logs[1]) / 2
spread <- half_width / z95
ends <- logs[2] + c(-1, 1) * z95 * spread

#%%@note 3. Turn a mean and a standard error into curve shapes
# A rate needs a curve between 0 and 1, a cost needs one above zero.
# อัตราต้องใช้เส้นโค้งระหว่าง 0 ถึง 1 ส่วนต้นทุนต้องใช้เส้นโค้งที่อยู่เหนือศูนย์
se_squared <- rate_se^2
patients_worth <- rate_mean * (1 - rate_mean) / se_squared - 1
shapes <- c(rate_mean, 1 - rate_mean) * patients_worth
cost_shape <- (cost_mean / cost_se)^2
cost_scale <- cost_se^2 / cost_mean
cost_ends <- stats::qgamma(c(0.025, 0.975), cost_shape, scale = cost_scale)

#%%@note 4. Draw whole rows of yearly chances
# Rows drawn together always add up to 1, rows drawn one share at a time do not.
# แถวที่สุ่มพร้อมกันรวมได้ 1 เสมอ ส่วนแถวที่สุ่มทีละค่าไม่รวมได้ 1
set.seed(20261028)
together <- matrix(stats::rgamma(9, shape = rep(counts, 3)), nrow = 3)
together <- together / rep(colSums(together), each = 3)
apart <- matrix(stats::rbeta(9, rep(counts, 3), rep(sum(counts) - counts, 3)), nrow = 3)

#%%@note 5. Combine the two uncertain results into one net gain
# Net gain is price x extra health - extra cost, and independent spreads add as squares.
# ผลได้สุทธิคือราคา x สุขภาพที่เพิ่ม - ต้นทุนที่เพิ่ม ค่าการกระจายที่อิสระต่อกันรวมกันแบบกำลังสอง
gain_mean <- wtp * health_avg_sd[1] - cost_avg_sd[1]
parts <- c(wtp * health_avg_sd[2], cost_avg_sd[2]) / 1000
gain_sd <- sqrt(sum(parts^2)) * 1000
above <- stats::pnorm(gain_mean / gain_sd)

#%%@note 6. Run the stand-in model 1,000 times
# Each run draws extra health and extra cost afresh, then records whether C comes out ahead.
# แต่ละครั้งสุ่มสุขภาพที่เพิ่มและต้นทุนที่เพิ่มใหม่ แล้วบันทึกว่า C ชนะหรือไม่
set.seed(20261028)
gain_draws <- 160000 * stats::rnorm(draws, 1.00, 0.20) - stats::rnorm(draws, 150000, 24000)
running <- cumsum(gain_draws > 0) / seq_len(draws)
mc_se <- sqrt(0.60 * 0.40 / draws)

#%%@note 7. Repeat the count at five prices
# The share of runs where C is ahead, price by price.
# สัดส่วนของการรันที่ C ชนะ ทีละระดับราคา
centre <- prices * health_c[1] - cost_c[1]
width <- sqrt((prices * health_c[2])^2 + cost_c[2]^2)
curve_table <- data.frame(price = prices, share_c = stats::pnorm(centre / width))
print(ggplot2::ggplot(curve_table, ggplot2::aes(x = price, y = share_c)) +
  ggplot2::geom_line() + ggplot2::geom_point())

#%%@note 8. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Extra cost THB:", big(extra_cost), "| extra health:", sprintf("%.2f", extra_health),
  "| price THB:", big(price), "| net gain THB:", big(price * extra_health - extra_cost), "\n")
cat("Trial risks:", paste0(sprintf("%.2f", 100 * events / patients), "%"), "| risk ratio:",
  round((events[1] / patients[1]) / (events[2] / patients[2]), 2), "\n")
cat("Weight 1 = full health, 0 = death | 10 years at 0.70 | gain from full health:",
  sprintf("%.1f", 10 * c(0.70, 1 - 0.70)), "\n")
cat("Below | above 0.56:", sprintf("%.2f", diff(ratio)), "| logs:", sprintf("%.3f", logs), "\n")
cat("Half width:", sprintf("%.3f", half_width), "| / 1.96, the spread:", sprintf("%.3f", spread),
  "| rounded centre and spread:", sprintf("%.2f", c(logs[2], spread)), "\n")
cat("Centre -/+ 1.96 spreads:", sprintf("%.3f", ends), "| rounded:", sprintf("%.2f", ends), "\n")
cat("Back as ratios:", sprintf("%.3f", exp(ends)), "| rounded:", sprintf("%.2f", exp(ends)), "\n")
cat("Draws above 1 (%):", sprintf("%.1f", 100 * stats::pnorm(logs[2] / spread)), "\n")
cat("0.30 x 0.70:", rate_mean * (1 - rate_mean), "| 0.05 x 0.05:",
  formatC(se_squared, format = "f", digits = 4), "\n")
cat("Divided:", rate_mean * (1 - rate_mean) / se_squared, "| minus 1:", patients_worth, "\n")
cat("Shapes, responders | non-responders:", shapes, "| their mean:", shapes[1] / sum(shapes), "\n")
cat("Middle 95%:", round(stats::qbeta(c(0.025, 0.975), shapes[1], shapes[2]), 2), "\n")
cat("Mean / standard error:", cost_mean / cost_se, "| squared, the shape:", cost_shape, "\n")
cat("2,000 x 2,000:", big(cost_se^2), "| / 10,000, the scale THB:", cost_scale,
  "| shape x scale:", big(cost_shape * cost_scale), "\n")
cat("Middle 95% THB:", big(cost_ends), "| peak THB:", big((cost_shape - 1) * cost_scale), "\n")
cat("Below | above mean THB:", big(cost_mean - cost_ends[1]), big(cost_ends[2] - cost_mean), "\n")
cat("Average row:", sprintf("%.2f", counts / sum(counts)), "| 1,000 healthy, one year on:",
  cohort * counts / sum(counts), "\n")
cat("Rows drawn together:", sprintf("%.3f", together), "| sums:", colSums(together), "\n")
cat("Rows drawn one share at a time:", sprintf("%.3f", apart), "\n")
cat("Their sums:", sprintf("%.3f", colSums(apart)), "\n")
cat("Average net gain THB:", gain_mean, "| spread parts THB:", 1000 * parts, "\n")
cat("In thousands:", parts, "| squared:", parts^2, "| sum:", sum(parts^2), "| root:",
  sqrt(sum(parts^2)), "| spread THB:", gain_sd, "\n")
cat("Average / spread:", gain_mean / gain_sd, "| share above zero:", round(above, 3), "| rounded:",
  round(above, 2), "| runs of 1,000:", round(1000 * above), "\n")
cat("Runs ahead of 1,000:", sum(gain_draws > 0), "| average, spread THB:", round(mean(gain_draws)),
  round(stats::sd(gain_draws)), "\n")
cat("Share ahead after 10, 25, 50, 100, 250, 500, 1000 runs:",
  sprintf("%.3f", running[c(10, 25, 50, 100, 250, 500, 1000)]), "\n")
cat("Share (%):", 60, "| 0.60 x 0.40:", 0.60 * 0.40, "\n")
cat("One standard error:", formatC(mc_se, format = "f", digits = 4), "| x 1.96, in points:",
  sprintf("%.1f", 196 * mc_se), "| range:", sprintf("%.2f", 0.60 + c(-1, 1) * 1.96 * mc_se), "\n")
cat("Prices THB:", formatC(prices, format = "d", big.mark = ","), "\n")
cat("Average net gain THB:", formatC(centre, format = "d", big.mark = ","), "\n")
cat("Spread THB:", formatC(round(width), format = "d", big.mark = ","), "\n")
cat("Average / spread:", sprintf("%.2f", centre / width), "\n")
cat("Share of runs where C is ahead:", sprintf("%.3f", stats::pnorm(centre / width)), "\n")
cat("Share where A is ahead:", sprintf("%.3f", 1 - stats::pnorm(centre / width)), "\n")