การเลือกแบบจำลองเพื่อการตัดสินใจ: ให้เส้นทางทางคลินิกกำหนดโครงสร้าง

# Choosing a Decision-Analytic Model: Let the Clinical Pathway Decide
# Follow one leg cellulitis case from a two-week tree to monthly states with memory.
# ติดตามผู้ป่วยเซลลูไลติสที่ขาจากต้นไม้สองสัปดาห์ ไปสู่ภาวะรายเดือนที่จำอดีตได้
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# tibble 3.3.1 (stable)
# dplyr 1.2.1 (stable)
# ggplot2 4.0.3 (stable)
# install.packages(c("tibble", "dplyr", "ggplot2"))
# update.packages(oldPkgs = c("tibble", "dplyr", "ggplot2"))
# remotes::install_version("tibble", "3.3.1")
# remotes::install_version("dplyr", "1.2.1")
# remotes::install_version("ggplot2", "4.0.3")
library(tibble)  # Write the model inputs as explicit tables.
library(dplyr)  # Calculate the weighted and split quantities.
library(ggplot2)  # Display the tree size against the reused states 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
p_success <- 0.8
value_success <- 10
value_failure <- 2
periods <- c(1, 2, 3, 10, 12)
states <- c("well", "active cellulitis")
cohort <- 1000
risk_month <- 0.03
well_first <- 750
well_again <- 250
risk_first <- 0.02
risk_again <- 0.06
prevent_cut <- 0.5
recovered <- 1000
risk_month1 <- 0.10
risk_month2 <- 0.05

#%%@note 2. Roll back the two-week tree
# Weight each branch's symptom-free days by its chance, then add the two products.
# ถ่วงวันที่ไม่มีอาการของแต่ละกิ่งด้วยโอกาสของกิ่งนั้น แล้วรวมสองผลคูณ
branches <- tibble::tibble(
  branch = c("tablets work", "admitted"), probability = c(p_success, 1 - p_success),
  days = c(value_success, value_failure)
) |>
  dplyr::mutate(weighted_days = probability * days)
stopifnot(abs(sum(branches$probability) - 1) < 1e-9)
p_failure <- 1 - p_success
weighted_success <- branches$weighted_days[1]
weighted_failure <- branches$weighted_days[2]
expected_days <- weighted_success + weighted_failure

#%%@note 3. Count tree endpoints and take one monthly state step
# A tree doubles its endpoints every month; a state model reuses the same two states.
# ต้นไม้เพิ่มปลายกิ่งเป็นสองเท่าทุกเดือน ส่วนแบบจำลองภาวะใช้สองภาวะเดิมซ้ำ
endpoints <- 2^periods
comma_format <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
month_step <- cohort * c(1, risk_month, 1 - risk_month)
growth <- tibble::tibble(month = periods, tree_endpoints = endpoints,
  states_reused = length(states))

#%%@note 4. Split the well state by history and by time since recovery
# History states keep 0.02 and 0.06 apart; tunnel states keep the first two months apart.
# ภาวะที่เก็บประวัติแยกความเสี่ยง 0.02 กับ 0.06 ส่วนภาวะอุโมงค์แยกสองเดือนแรกหลังหาย
groups <- tibble::tibble(group = c("no recurrence", "after a recurrence"),
  people = c(well_first, well_again), risk = c(risk_first, risk_again)) |>
  dplyr::mutate(new_episodes = people * risk)
new_first <- groups$new_episodes[1]
new_again <- groups$new_episodes[2]
average_risk <- (new_first + new_again) / (well_first + well_again)
tunnel_free <- recovered * (1 - risk_month1) * (1 - risk_month2)
flat_free <- recovered * (1 - risk_month)^2
flat_returns <- recovered - flat_free
tunnel_returns <- recovered - tunnel_free
one_decimal <- function(value) formatC(value, format = "f", digits = 1)

#%%@note 5. Display the model
# Plot tree endpoints against the reused states on a log scale; no graphics file is saved.
# แสดงจำนวนปลายกิ่งเทียบกับภาวะที่ใช้ซ้ำบนสเกลลอการิทึม โดยไม่บันทึกไฟล์ภาพ
print(ggplot2::ggplot(growth, ggplot2::aes(x = month)) +
  ggplot2::geom_col(ggplot2::aes(y = tree_endpoints)) +
  ggplot2::geom_point(ggplot2::aes(y = states_reused)) +
  ggplot2::scale_y_log10() + ggplot2::labs(x = "Monthly periods", y = "Count (log scale)"))

#%%@note 6. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Success, failure probability:", p_success, p_failure, "\n")
cat("Weighted days, success and failure:", weighted_success, weighted_failure, "\n")
cat("Expected symptom-free days:", expected_days, "\n")
cat("Monthly periods:", periods, "\n")
cat("Tree endpoints:", comma_format(endpoints), "\n")
cat("States reused every month:", length(states), "\n")
cat("Well now, new episodes, still well:", comma_format(month_step), "\n")
cat("New episodes next month, no recurrence and after one:", new_first, new_again, "\n")
cat("Average monthly risk in one well state:", average_risk, "\n")
cat("Episodes avoided a month, history states:", new_again * prevent_cut, "\n")
cat("Episodes avoided a month, one well state:", well_again * average_risk * prevent_cut, "\n")
cat("Free of a new episode after month 1, tunnel:", recovered * (1 - risk_month1), "\n")
cat("Free after month 2, tunnel and flat 0.03:", tunnel_free, one_decimal(flat_free), "\n")
cat("Returns within two months, tunnel and flat:", tunnel_returns, one_decimal(flat_returns), "\n")

# Choosing a Decision-Analytic Model: Let the Clinical Pathway Decide
# Follow one leg cellulitis case from a two-week tree to monthly states with memory.
# ติดตามผู้ป่วยเซลลูไลติสที่ขาจากต้นไม้สองสัปดาห์ ไปสู่ภาวะรายเดือนที่จำอดีตได้
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# tibble 3.3.1 (stable)
# dplyr 1.2.1 (stable)
# ggplot2 4.0.3 (stable)
# install.packages(c("tibble", "dplyr", "ggplot2"))
# update.packages(oldPkgs = c("tibble", "dplyr", "ggplot2"))
# remotes::install_version("tibble", "3.3.1")
# remotes::install_version("dplyr", "1.2.1")
# remotes::install_version("ggplot2", "4.0.3")
library(tibble)  # Write the model inputs as explicit tables.
library(dplyr)  # Calculate the weighted and split quantities.
library(ggplot2)  # Display the tree size against the reused states 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
p_success <- 0.8
value_success <- 10
value_failure <- 2
periods <- c(1, 2, 3, 10, 12)
states <- c("well", "active cellulitis")
cohort <- 1000
risk_month <- 0.03
well_first <- 750
well_again <- 250
risk_first <- 0.02
risk_again <- 0.06
prevent_cut <- 0.5
recovered <- 1000
risk_month1 <- 0.10
risk_month2 <- 0.05

#%%@note 2. Roll back the two-week tree
# Weight each branch's symptom-free days by its chance, then add the two products.
# ถ่วงวันที่ไม่มีอาการของแต่ละกิ่งด้วยโอกาสของกิ่งนั้น แล้วรวมสองผลคูณ
branches <- tibble::tibble(
  branch = c("tablets work", "admitted"), probability = c(p_success, 1 - p_success),
  days = c(value_success, value_failure)
) |>
  dplyr::mutate(weighted_days = probability * days)
stopifnot(abs(sum(branches$probability) - 1) < 1e-9)
p_failure <- 1 - p_success
weighted_success <- branches$weighted_days[1]
weighted_failure <- branches$weighted_days[2]
expected_days <- weighted_success + weighted_failure

#%%@note 3. Count tree endpoints and take one monthly state step
# A tree doubles its endpoints every month; a state model reuses the same two states.
# ต้นไม้เพิ่มปลายกิ่งเป็นสองเท่าทุกเดือน ส่วนแบบจำลองภาวะใช้สองภาวะเดิมซ้ำ
endpoints <- 2^periods
comma_format <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
month_step <- cohort * c(1, risk_month, 1 - risk_month)
growth <- tibble::tibble(month = periods, tree_endpoints = endpoints,
  states_reused = length(states))

#%%@note 4. Split the well state by history and by time since recovery
# History states keep 0.02 and 0.06 apart; tunnel states keep the first two months apart.
# ภาวะที่เก็บประวัติแยกความเสี่ยง 0.02 กับ 0.06 ส่วนภาวะอุโมงค์แยกสองเดือนแรกหลังหาย
groups <- tibble::tibble(group = c("no recurrence", "after a recurrence"),
  people = c(well_first, well_again), risk = c(risk_first, risk_again)) |>
  dplyr::mutate(new_episodes = people * risk)
new_first <- groups$new_episodes[1]
new_again <- groups$new_episodes[2]
average_risk <- (new_first + new_again) / (well_first + well_again)
tunnel_free <- recovered * (1 - risk_month1) * (1 - risk_month2)
flat_free <- recovered * (1 - risk_month)^2
flat_returns <- recovered - flat_free
tunnel_returns <- recovered - tunnel_free
one_decimal <- function(value) formatC(value, format = "f", digits = 1)

#%%@note 5. Display the model
# Plot tree endpoints against the reused states on a log scale; no graphics file is saved.
# แสดงจำนวนปลายกิ่งเทียบกับภาวะที่ใช้ซ้ำบนสเกลลอการิทึม โดยไม่บันทึกไฟล์ภาพ
print(ggplot2::ggplot(growth, ggplot2::aes(x = month)) +
  ggplot2::geom_col(ggplot2::aes(y = tree_endpoints)) +
  ggplot2::geom_point(ggplot2::aes(y = states_reused)) +
  ggplot2::scale_y_log10() + ggplot2::labs(x = "Monthly periods", y = "Count (log scale)"))

#%%@note 6. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Success, failure probability:", p_success, p_failure, "\n")
cat("Weighted days, success and failure:", weighted_success, weighted_failure, "\n")
cat("Expected symptom-free days:", expected_days, "\n")
cat("Monthly periods:", periods, "\n")
cat("Tree endpoints:", comma_format(endpoints), "\n")
cat("States reused every month:", length(states), "\n")
cat("Well now, new episodes, still well:", comma_format(month_step), "\n")
cat("New episodes next month, no recurrence and after one:", new_first, new_again, "\n")
cat("Average monthly risk in one well state:", average_risk, "\n")
cat("Episodes avoided a month, history states:", new_again * prevent_cut, "\n")
cat("Episodes avoided a month, one well state:", well_again * average_risk * prevent_cut, "\n")
cat("Free of a new episode after month 1, tunnel:", recovered * (1 - risk_month1), "\n")
cat("Free after month 2, tunnel and flat 0.03:", tunnel_free, one_decimal(flat_free), "\n")
cat("Returns within two months, tunnel and flat:", tunnel_returns, one_decimal(flat_returns), "\n")

# Choosing a Decision-Analytic Model: Let the Clinical Pathway Decide
# Follow one leg cellulitis case from a two-week tree to monthly states with memory.
# ติดตามผู้ป่วยเซลลูไลติสที่ขาจากต้นไม้สองสัปดาห์ ไปสู่ภาวะรายเดือนที่จำอดีตได้
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# tibble 3.3.1 (stable)
# dplyr 1.2.1 (stable)
# ggplot2 4.0.3 (stable)
# install.packages(c("tibble", "dplyr", "ggplot2"))
# update.packages(oldPkgs = c("tibble", "dplyr", "ggplot2"))
# remotes::install_version("tibble", "3.3.1")
# remotes::install_version("dplyr", "1.2.1")
# remotes::install_version("ggplot2", "4.0.3")
library(tibble)  # Write the model inputs as explicit tables.
library(dplyr)  # Calculate the weighted and split quantities.
library(ggplot2)  # Display the tree size against the reused states 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
p_success <- 0.8
value_success <- 10
value_failure <- 2
periods <- c(1, 2, 3, 10, 12)
states <- c("well", "active cellulitis")
cohort <- 1000
risk_month <- 0.03
well_first <- 750
well_again <- 250
risk_first <- 0.02
risk_again <- 0.06
prevent_cut <- 0.5
recovered <- 1000
risk_month1 <- 0.10
risk_month2 <- 0.05

#%%@note 2. Roll back the two-week tree
# Weight each branch's symptom-free days by its chance, then add the two products.
# ถ่วงวันที่ไม่มีอาการของแต่ละกิ่งด้วยโอกาสของกิ่งนั้น แล้วรวมสองผลคูณ
branches <- tibble::tibble(
  branch = c("tablets work", "admitted"), probability = c(p_success, 1 - p_success),
  days = c(value_success, value_failure)
) |>
  dplyr::mutate(weighted_days = probability * days)
stopifnot(abs(sum(branches$probability) - 1) < 1e-9)
p_failure <- 1 - p_success
weighted_success <- branches$weighted_days[1]
weighted_failure <- branches$weighted_days[2]
expected_days <- weighted_success + weighted_failure

#%%@note 3. Count tree endpoints and take one monthly state step
# A tree doubles its endpoints every month; a state model reuses the same two states.
# ต้นไม้เพิ่มปลายกิ่งเป็นสองเท่าทุกเดือน ส่วนแบบจำลองภาวะใช้สองภาวะเดิมซ้ำ
endpoints <- 2^periods
comma_format <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
month_step <- cohort * c(1, risk_month, 1 - risk_month)
growth <- tibble::tibble(month = periods, tree_endpoints = endpoints,
  states_reused = length(states))

#%%@note 4. Split the well state by history and by time since recovery
# History states keep 0.02 and 0.06 apart; tunnel states keep the first two months apart.
# ภาวะที่เก็บประวัติแยกความเสี่ยง 0.02 กับ 0.06 ส่วนภาวะอุโมงค์แยกสองเดือนแรกหลังหาย
groups <- tibble::tibble(group = c("no recurrence", "after a recurrence"),
  people = c(well_first, well_again), risk = c(risk_first, risk_again)) |>
  dplyr::mutate(new_episodes = people * risk)
new_first <- groups$new_episodes[1]
new_again <- groups$new_episodes[2]
average_risk <- (new_first + new_again) / (well_first + well_again)
tunnel_free <- recovered * (1 - risk_month1) * (1 - risk_month2)
flat_free <- recovered * (1 - risk_month)^2
flat_returns <- recovered - flat_free
tunnel_returns <- recovered - tunnel_free
one_decimal <- function(value) formatC(value, format = "f", digits = 1)

#%%@note 5. Display the model
# Plot tree endpoints against the reused states on a log scale; no graphics file is saved.
# แสดงจำนวนปลายกิ่งเทียบกับภาวะที่ใช้ซ้ำบนสเกลลอการิทึม โดยไม่บันทึกไฟล์ภาพ
print(ggplot2::ggplot(growth, ggplot2::aes(x = month)) +
  ggplot2::geom_col(ggplot2::aes(y = tree_endpoints)) +
  ggplot2::geom_point(ggplot2::aes(y = states_reused)) +
  ggplot2::scale_y_log10() + ggplot2::labs(x = "Monthly periods", y = "Count (log scale)"))

#%%@note 6. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Success, failure probability:", p_success, p_failure, "\n")
cat("Weighted days, success and failure:", weighted_success, weighted_failure, "\n")
cat("Expected symptom-free days:", expected_days, "\n")
cat("Monthly periods:", periods, "\n")
cat("Tree endpoints:", comma_format(endpoints), "\n")
cat("States reused every month:", length(states), "\n")
cat("Well now, new episodes, still well:", comma_format(month_step), "\n")
cat("New episodes next month, no recurrence and after one:", new_first, new_again, "\n")
cat("Average monthly risk in one well state:", average_risk, "\n")
cat("Episodes avoided a month, history states:", new_again * prevent_cut, "\n")
cat("Episodes avoided a month, one well state:", well_again * average_risk * prevent_cut, "\n")
cat("Free of a new episode after month 1, tunnel:", recovered * (1 - risk_month1), "\n")
cat("Free after month 2, tunnel and flat 0.03:", tunnel_free, one_decimal(flat_free), "\n")
cat("Returns within two months, tunnel and flat:", tunnel_returns, one_decimal(flat_returns), "\n")

# Choosing a Decision-Analytic Model: Let the Clinical Pathway Decide
# Follow one leg cellulitis case from a two-week tree to monthly states with memory.
# ติดตามผู้ป่วยเซลลูไลติสที่ขาจากต้นไม้สองสัปดาห์ ไปสู่ภาวะรายเดือนที่จำอดีตได้
# Requires: R >= 4.5.2
# Tested: works in R 4.6.1
# tibble 3.3.1 (stable)
# dplyr 1.2.1 (stable)
# ggplot2 4.0.3 (stable)
# install.packages(c("tibble", "dplyr", "ggplot2"))
# update.packages(oldPkgs = c("tibble", "dplyr", "ggplot2"))
# remotes::install_version("tibble", "3.3.1")
# remotes::install_version("dplyr", "1.2.1")
# remotes::install_version("ggplot2", "4.0.3")
library(tibble)  # Write the model inputs as explicit tables.
library(dplyr)  # Calculate the weighted and split quantities.
library(ggplot2)  # Display the tree size against the reused states 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
p_success <- 0.8
value_success <- 10
value_failure <- 2
periods <- c(1, 2, 3, 10, 12)
states <- c("well", "active cellulitis")
cohort <- 1000
risk_month <- 0.03
well_first <- 750
well_again <- 250
risk_first <- 0.02
risk_again <- 0.06
prevent_cut <- 0.5
recovered <- 1000
risk_month1 <- 0.10
risk_month2 <- 0.05

#%%@note 2. Roll back the two-week tree
# Weight each branch's symptom-free days by its chance, then add the two products.
# ถ่วงวันที่ไม่มีอาการของแต่ละกิ่งด้วยโอกาสของกิ่งนั้น แล้วรวมสองผลคูณ
branches <- tibble::tibble(
  branch = c("tablets work", "admitted"), probability = c(p_success, 1 - p_success),
  days = c(value_success, value_failure)
) |>
  dplyr::mutate(weighted_days = probability * days)
stopifnot(abs(sum(branches$probability) - 1) < 1e-9)
p_failure <- 1 - p_success
weighted_success <- branches$weighted_days[1]
weighted_failure <- branches$weighted_days[2]
expected_days <- weighted_success + weighted_failure

#%%@note 3. Count tree endpoints and take one monthly state step
# A tree doubles its endpoints every month; a state model reuses the same two states.
# ต้นไม้เพิ่มปลายกิ่งเป็นสองเท่าทุกเดือน ส่วนแบบจำลองภาวะใช้สองภาวะเดิมซ้ำ
endpoints <- 2^periods
comma_format <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
month_step <- cohort * c(1, risk_month, 1 - risk_month)
growth <- tibble::tibble(month = periods, tree_endpoints = endpoints,
  states_reused = length(states))

#%%@note 4. Split the well state by history and by time since recovery
# History states keep 0.02 and 0.06 apart; tunnel states keep the first two months apart.
# ภาวะที่เก็บประวัติแยกความเสี่ยง 0.02 กับ 0.06 ส่วนภาวะอุโมงค์แยกสองเดือนแรกหลังหาย
groups <- tibble::tibble(group = c("no recurrence", "after a recurrence"),
  people = c(well_first, well_again), risk = c(risk_first, risk_again)) |>
  dplyr::mutate(new_episodes = people * risk)
new_first <- groups$new_episodes[1]
new_again <- groups$new_episodes[2]
average_risk <- (new_first + new_again) / (well_first + well_again)
tunnel_free <- recovered * (1 - risk_month1) * (1 - risk_month2)
flat_free <- recovered * (1 - risk_month)^2
flat_returns <- recovered - flat_free
tunnel_returns <- recovered - tunnel_free
one_decimal <- function(value) formatC(value, format = "f", digits = 1)

#%%@note 5. Display the model
# Plot tree endpoints against the reused states on a log scale; no graphics file is saved.
# แสดงจำนวนปลายกิ่งเทียบกับภาวะที่ใช้ซ้ำบนสเกลลอการิทึม โดยไม่บันทึกไฟล์ภาพ
print(ggplot2::ggplot(growth, ggplot2::aes(x = month)) +
  ggplot2::geom_col(ggplot2::aes(y = tree_endpoints)) +
  ggplot2::geom_point(ggplot2::aes(y = states_reused)) +
  ggplot2::scale_y_log10() + ggplot2::labs(x = "Monthly periods", y = "Count (log scale)"))

#%%@note 6. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Success, failure probability:", p_success, p_failure, "\n")
cat("Weighted days, success and failure:", weighted_success, weighted_failure, "\n")
cat("Expected symptom-free days:", expected_days, "\n")
cat("Monthly periods:", periods, "\n")
cat("Tree endpoints:", comma_format(endpoints), "\n")
cat("States reused every month:", length(states), "\n")
cat("Well now, new episodes, still well:", comma_format(month_step), "\n")
cat("New episodes next month, no recurrence and after one:", new_first, new_again, "\n")
cat("Average monthly risk in one well state:", average_risk, "\n")
cat("Episodes avoided a month, history states:", new_again * prevent_cut, "\n")
cat("Episodes avoided a month, one well state:", well_again * average_risk * prevent_cut, "\n")
cat("Free of a new episode after month 1, tunnel:", recovered * (1 - risk_month1), "\n")
cat("Free after month 2, tunnel and flat 0.03:", tunnel_free, one_decimal(flat_free), "\n")
cat("Returns within two months, tunnel and flat:", tunnel_returns, one_decimal(flat_returns), "\n")