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Calibrate COPD Prevalence

Calibrate_COPD_Prevalence.Rmd

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(epicR)
library(ggplot2)
library(dplyr)
library(knitr)

# Load EPIC general settings
settings <- get_default_settings()
settings$record_mode <- 0
settings$n_base_agents <- 1e5
init_session(settings = settings)
## [1] 0
input <- get_input(jurisdiction = "us")
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$values$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)
## Using user config file from: /home/runner/.epicR/config/config_canada.json
## Running EPIC model (with custom input parameters)
## Record mode: record_mode_none (0)
## Note: No events will be recorded. Use record_mode_event (2) or record_mode_agent (1) to record events.
## Simulating 100000 base agents: 10% 20% 30% 40% 50%
## 60% 70% 80% 90% 100%
## [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 0.114 0.081 0.137 0.243
2016 0.114 0.081 0.137 0.238
2017 0.115 0.081 0.138 0.231
2018 0.115 0.081 0.137 0.230
2019 0.116 0.082 0.137 0.226
2020 0.116 0.082 0.137 0.221
2021 0.116 0.081 0.139 0.220
2022 0.117 0.082 0.139 0.217
2023 0.118 0.083 0.139 0.218
2024 0.119 0.083 0.139 0.216
2025 0.119 0.082 0.140 0.216
2026 0.120 0.083 0.141 0.212
2027 0.120 0.083 0.142 0.207
2028 0.121 0.082 0.143 0.202
2029 0.122 0.082 0.144 0.204
2030 0.122 0.082 0.145 0.203
2031 0.123 0.081 0.145 0.206
2032 0.123 0.081 0.147 0.203
2033 0.123 0.080 0.147 0.202
2034 0.123 0.079 0.147 0.199
2035 0.123 0.078 0.147 0.197
2036 0.123 0.077 0.149 0.194
2037 0.123 0.076 0.148 0.197
2038 0.123 0.075 0.148 0.196
2039 0.123 0.074 0.149 0.194
2040 0.122 0.074 0.148 0.196

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
0.137 0.091 2015
0.137 0.092 2016
0.137 0.093 2017
0.136 0.094 2018
0.136 0.095 2019
0.136 0.096 2020
0.137 0.096 2021
0.137 0.098 2022
0.138 0.099 2023
0.138 0.100 2024
0.138 0.101 2025
0.138 0.103 2026
0.139 0.103 2027
0.138 0.104 2028
0.139 0.105 2029
0.139 0.106 2030
0.140 0.107 2031
0.140 0.108 2032
0.140 0.108 2033
0.140 0.108 2034
0.139 0.108 2035
0.139 0.108 2036
0.139 0.109 2037
0.137 0.109 2038
0.137 0.109 2039
0.137 0.109 2040