Calibrate COPD Prevalence

Overview

This document outlines the calibration process undertaken to align the model’s outputs with U.S.-based validation targets for COPD prevalence, using NHANES data in which COPD was defined according to the Lower Limit of Normal (LLN) definition. The calibration was conducted over a 25-year simulation time horizon.

Validation Reference:
Tilert et al. 2013 (DOI: 10.1186/1465-9921-14-103)

Validation Target (Age-Specific Prevalence):
- 40–59 years: 8.1%
- 60–79 years: 14.4%

Validation Target (Sex-Specific Prevalence):
- Males: 12.0%
- Females: 8.6%

It is important to note that the EPIC model simulates individuals aged 40 and older, including those ≥80 years, whereas Tilert et al. 2013 included only individuals aged 40–79.

Given this limitation, the calibration emphasized preserving the sex-specific prevalence ratio observed in Tilert et al. 2013 (1.4:1; 12.0% males vs. 8.6% females) as the validation target. The model was deemed adequately calibrated if this ratio was maintained, even if absolute prevalence values by sex differed slightly due to inclusion of older age groups.

Evolution of LLN Reference Equations and Impact on COPD Prevalence Estimation

Reference equations used to define the LLN for spirometry to diagnose COPD have evolved over time, moving from race-specific models toward more inclusive, race-neutral approaches. Tilert et al. 2013 defined COPD using LLN values derived from the Hankinson equation, a race-specific model widely used in earlier guidelines. In contrast, current guidelines recommend using the Global Lung Function Initiative (GLI) race-neutral reference equations. A recent analysis by Cadham et al. 2024 (DOI: 10.1186/s12931-024-02841-y) compared COPD prevalence estimates based on the Hankinson and GLI race-neutral equations and found no significant differences between the two approaches.

Step 1: Load libraries and setup

Here, we load the necessary libraries. We also set the default simulation settings and specify the time horizon for the simulation (25 years).

library(epicUS)
library(tidyverse)
library(ggplot2)
library(dplyr)
library(knitr)

# Load EPIC general settings
settings <- get_default_settings()
settings$record_mode <- 0
settings$n_base_agents <- 1e6
init_session(settings = settings)
## [1] 0
input <- get_input()
time_horizon <- 26
input$values$global_parameters$time_horizon <- time_horizon

Step 2: Modify intercept value to calibrate proportion of COPD prevalence by age group and sex

The sex-specific intercepts were adjusted to match the age-specific prevalence targets (age groups: 40–59 and 60–79 years) while maintaining a 1.4:1 male-to-female ratio.

input$COPD$logit_p_COPD_betas_by_sex <- cbind(male = c(intercept = -4.30190, age = 0.033070, age2 = 0, pack_years = 0.025049   ,
                                                       current_smoking = 0, year = 0, asthma = 0),
                                              female = c(intercept = -4.40202, age = 0.027359   , age2 = 0, pack_years=0.030399,                                                         current_smoking = 0, year = 0, asthma = 0))

Step 3: Run EPIC 

# Run EPIC simulation
run(input = input$values)
## [1] 0
## Terminating the session
## [1] 0

Step 4: Create data tables by age category 

# Determine overall COPD prevalence

COPDprevalence_ctime_age<-output$n_COPD_by_ctime_age
COPDprevalence_ctime_age<-as.data.frame(output$n_COPD_by_ctime_age)
totalpopulation<-output$n_alive_by_ctime_age

# Overall prevalence of COPD

alive_age_all <- rowSums(output$n_alive_by_ctime_age[1:26, 40:111])
COPD_age_all <- rowSums (output$n_COPD_by_ctime_age[1:26, 40:111])
prevalenceCOPD_age_all <- COPD_age_all / alive_age_all

# Prevalence by age 40-59 

alive_age_40to59 <- rowSums(output$n_alive_by_ctime_age[1:26, 40:59])
COPD_age_40to59 <-rowSums(output$n_COPD_by_ctime_age[1:26, 40:59])
prevalenceCOPD_age_40to59 <- COPD_age_40to59 / alive_age_40to59

# Prevalence by age 60-79

alive_age_60to79 <- rowSums(output$n_alive_by_ctime_age[1:26, 60:79])
COPD_age_60to79 <-rowSums(output$n_COPD_by_ctime_age[1:26, 60:79])
prevalenceCOPD_age_60to79 <- COPD_age_60to79 / alive_age_60to79

# Prevalence by age 80+

alive_age_over80 <- rowSums(output$n_alive_by_ctime_age[1:26, 80:111])
COPD_age_over80 <-rowSums(output$n_COPD_by_ctime_age[1:26, 80:111])
prevalenceCOPD_age_over80 <- COPD_age_over80 / alive_age_over80

# Display summary of COPD prevalence by age group 

COPD_prevalence_summary <- data.frame(
  Year = 2015:2040,
  Prevalence_all = prevalenceCOPD_age_all,
  Prevalence_40to59 = prevalenceCOPD_age_40to59,
  Prevalence_60to79 = prevalenceCOPD_age_60to79,
  Prevalence_over80 = prevalenceCOPD_age_over80
  )

kable(COPD_prevalence_summary, 
      caption = "COPD Prevalence by Age Group Over Time",
      digits = 3)
COPD Prevalence by Age Group Over Time
Year Prevalence_all Prevalence_40to59 Prevalence_60to79 Prevalence_over80
2015 0.113 0.081 0.135 0.234
2016 0.112 0.082 0.134 0.227
2017 0.112 0.082 0.134 0.222
2018 0.112 0.082 0.134 0.218
2019 0.112 0.083 0.134 0.214
2020 0.113 0.083 0.134 0.211
2021 0.113 0.083 0.135 0.209
2022 0.113 0.083 0.135 0.206
2023 0.113 0.083 0.135 0.203
2024 0.114 0.083 0.136 0.201
2025 0.114 0.083 0.137 0.198
2026 0.114 0.083 0.137 0.197
2027 0.114 0.083 0.138 0.195
2028 0.114 0.083 0.138 0.193
2029 0.114 0.082 0.139 0.191
2030 0.115 0.082 0.140 0.191
2031 0.115 0.081 0.141 0.189
2032 0.115 0.080 0.142 0.188
2033 0.115 0.080 0.143 0.187
2034 0.115 0.079 0.144 0.187
2035 0.115 0.079 0.144 0.186
2036 0.115 0.078 0.145 0.186
2037 0.114 0.077 0.145 0.185
2038 0.114 0.076 0.145 0.184
2039 0.114 0.075 0.146 0.184
2040 0.113 0.074 0.145 0.183

Step 5: Visualize data by age category

COPD prevalence is projected to decline moderately between 2025 and 2050, as reported by Boers et al. 2023 (DOI: 10.1001/jamanetworkopen.2023.46598). A similar trend is observed in EPIC model projections of overall COPD prevalence. However, a limitation of EPIC include underestimating the size of the population aged 80 and older. As COPD prevalence increases with age, this results in a overestimation of overall COPD prevalence in the simulated population.

COPD prevalence all age groups

COPD prevalence from age 40 to 59

COPD prevalence from age 60 to 79

COPD prevalence from age 80+

Step 6: Create data tables by sex to check if gender distribution matches Tilert et al 2013 (doi:10.1186/1465-9921-14-103)) 

# Calculate COPD prevalence by sex over time

alive_sex <- output$n_alive_by_ctime_sex
COPD_sex <- output$n_COPD_by_ctime_sex
prevalenceCOPD_sex <- COPD_sex / alive_sex
prevalenceCOPD_sex<-as.data.frame (prevalenceCOPD_sex)

# Rename columns
colnames(prevalenceCOPD_sex) <- c("Male", "Female")
prevalenceCOPD_sex$Year <- 2015:2040


# Display summary of COPD prevalence by sex

kable(prevalenceCOPD_sex,
  caption = "COPD Prevalence by Sex Over Time",
  digits = 3
)
COPD Prevalence by Sex Over Time
Male Female Year
0.136 0.089 2015
0.135 0.090 2016
0.134 0.091 2017
0.134 0.092 2018
0.133 0.093 2019
0.132 0.094 2020
0.132 0.095 2021
0.131 0.096 2022
0.131 0.096 2023
0.131 0.098 2024
0.130 0.098 2025
0.130 0.099 2026
0.130 0.100 2027
0.129 0.101 2028
0.129 0.101 2029
0.129 0.102 2030
0.129 0.102 2031
0.129 0.103 2032
0.128 0.103 2033
0.128 0.103 2034
0.127 0.104 2035
0.127 0.104 2036
0.126 0.104 2037
0.126 0.104 2038
0.125 0.104 2039
0.124 0.104 2040