สร้างแบบจำลองมาร์คอฟแบบกลุ่มประชากรทีละขั้น: ติดตามประชากรผ่านเวลา

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")

# Building a Markov Cohort Model Step by Step: Follow the Cohort Through Time
# Follow 1,000 people through Healthy, Sick and Dead for four years, then count health and cost.
# ติดตามคน 1,000 คนผ่านสถานะสุขภาพดี ป่วย และเสียชีวิต สี่รอบรายปี แล้วนับสุขภาพและต้นทุน
# 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 states and their yearly values as an explicit table.
library(dplyr)  # Add the per-cycle values to that table.
library(ggplot2)  # Display the trace 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
start <- c(1000, 0, 0)
transition <- c(0.80, 0.15, 0.05, 0, 0.85, 0.15, 0, 0, 1)
cycles <- 4
first_start <- c(1000, 0, 0)
first_end <- c(800, 150, 50)
health_value <- c(1, 0.6, 0)
yearly_cost <- c(100, 400, 0)
rate <- 0.03
average_by_year <- c(945, 839.25, 742.1625, 653.878125)
rate_per_year <- 0.12
cycle_years <- 0.25
years_in_state <- 10
state_value <- 0.70
future_cost <- 1834
cycle_length <- 1
big <- function(value) formatC(value, format = "f", digits = 0, big.mark = ",")
states <- tibble::tibble(state = c("Healthy", "Sick", "Dead"), health = health_value,
  cost = yearly_cost) |>
  dplyr::mutate(health_per_cycle = health * cycle_length, cost_per_cycle = cost * cycle_length)
moves <- matrix(transition, nrow = 3, byrow = TRUE)
stopifnot(all(abs(rowSums(moves) - 1) < 1e-9))

#%%@note 2. Move the cohort one year at a time
# Multiply the counts by the chances each year, and check that the total stays at 1,000.
# คูณจำนวนคนด้วยโอกาสย้ายสถานะทีละปี และตรวจว่ายอดรวมยังเท่ากับ 1,000
trace <- matrix(start, nrow = cycles + 1, ncol = 3, byrow = TRUE)
for (year in seq_len(cycles)) trace[year + 1, ] <- trace[year, ] %*% moves
stopifnot(all(abs(rowSums(trace) - sum(start)) < 1e-9))
flows <- trace[2, ] * moves
people <- trace

#%%@note 3. Count each year at its start, at its end and as the average
# The end count of one year is the start count of the next, so the same trace gives all three.
# จำนวนตอนท้ายปีหนึ่งคือจำนวนตอนต้นปีถัดไป trace เดียวจึงให้การนับได้ทั้งสามแบบ
counts <- rbind(first_start, first_end)
health <- c(counts %*% health_value, mean(counts %*% health_value))
spend <- c(counts %*% yearly_cost, mean(counts %*% yearly_cost))
health_edges <- people %*% health_value
at_start <- health_edges[1:4]
at_end <- health_edges[2:5]
average <- (at_start + at_end) / 2

#%%@note 4. Bring later years back to today
# Divide each year's value by 1.03 once for every year that has passed by its end.
# หารค่าของแต่ละปีด้วย 1.03 หนึ่งครั้งต่อทุกปีที่ผ่านไปเมื่อสิ้นปีนั้น
factors <- (1 + rate)^(1:4)
rewards <- cbind(health = states$health_per_cycle, cost = states$cost_per_cycle)
edges <- people %*% rewards
ways <- list(start = edges[1:4, ], end = edges[2:5, ], average = (edges[1:4, ] + edges[2:5, ]) / 2)
today <- cbind(start = colSums(ways$start / factors), end = colSums(ways$end / factors),
  average = colSums(ways$average / factors))

#%%@note 5. Rework the three foundation examples
# A yearly rate becomes a chance per cycle, a weight turns years into health, a later cost shrinks.
# อัตรารายปีกลายเป็นโอกาสต่อรอบ ค่าน้ำหนักเปลี่ยนปีเป็นสุขภาพ และต้นทุนในอนาคตมีค่าน้อยลงในวันนี้
cycle_chance <- signif(1 - exp(-rate_per_year * cycle_years), 3)
shortcut <- formatC(rate_per_year * cycle_years, format = "f", digits = 4)
weighted_years <- formatC(years_in_state * c(state_value, 1 - state_value), format = "f",
  digits = 1)

#%%@note 6. Display the trace
# Plot the number of people in each state at the end of each year, no graphics file is saved.
# แสดงจำนวนคนในแต่ละสถานะเมื่อสิ้นแต่ละปี โดยไม่บันทึกไฟล์ภาพ
trace_table <- tibble::tibble(year = rep(0:cycles, times = 3),
  state = rep(states$state, each = cycles + 1), people = as.vector(trace))
print(ggplot2::ggplot(trace_table, ggplot2::aes(x = year, y = people, colour = state)) +
  ggplot2::geom_line())

#%%@note 7. Numbers the article quotes
# Print exactly the short boxes in their reading order.
# พิมพ์ผลลัพธ์ตรงกับกล่องตัวอย่างตามลำดับในบทความ
cat("Row sums of the chances:", rowSums(moves), "| totals, years 0 to 4:", rowSums(trace), "\n")
cat("Year 2 flows from Healthy | Sick | Dead:", flows[1, ], "|", flows[2, ], "|", flows[3, ], "\n")
cat("Healthy, years 0 to 4:", round(trace[, 1], 3), "\n")
cat("Sick, years 0 to 4:", round(trace[, 2], 3), "\n")
cat("Dead, years 0 to 4:", round(trace[, 3], 3), "\n")
cat("Year 1 health, start | end | average:", health, "\n")
cat("Year 1 health per person:", sprintf("%.3f", health / 1000), "\n")
cat("Year 1 cost THB, start | end | average:", big(spend), "\n")
cat("Health by year, start:", at_start, "| total:", sum(at_start), "\n")
cat("Health by year, end:", round(at_end, 3), "| total:", round(sum(at_end), 3), "\n")
cat("Health by year, average:", round(average, 2), "| total:", round(sum(average), 2), "\n")
cat("Rate:", paste0(100 * rate, "%"), "| factors:",
  formatC(factors, format = "f", digits = 4), "\n")
cat("Average health by year, today's value:", round(average_by_year / factors, 1),
  "| total:", round(sum(average_by_year / factors), 3), "\n")
cat("Four-year health today, start | end | average:", sprintf("%.3f", today["health", ]), "\n")
cat("Four-year cost today THB, start | end | average:", round(today["cost", ]), "\n")
cat("Per person, average, health | cost THB:", sprintf("%.3f", today["health", "average"] / 1000),
  round(today["cost", "average"] / 1000), "\n")
cat("Rate 0.12, 0.25 years, chance | shortcut:", cycle_chance, shortcut, "\n")
cat("Ten years at 0.70 | gain from full health:", weighted_years, "\n")
cat("Cost due in year 3 at 3%, today THB:", round(future_cost / (1 + rate)^3), "\n")