The COPD Model, and its Scenarios

The COPD Model

Model Structure

COPD Models creates three scenarios: Null_COPD, CR2, and CR4

The COPD Model refers to a "Model architecture": A structure of states and transitions, which can be used to run different scenarios. A scenario is when the structure has a different set of transition rates between the states.

The COPD model is used to run two scenarios of treatment coverage: CR2 and CR4. In addition, the COPD model is also used to run a "Null Scenario": Called COPD_Null. We will explain the Null Scenario later.

Structure of the COPD Model

COPD has three key states, DsFreeSus, COPDEpsd, and Deceased. DsFreeSus means "Disease free, susceptible", and this refers to the majority of the population. COPDEpsd means "COPD Episode", and generally refers to people who have asthma and will experience an episode that year. Deceased refers to the people in the model who have died, either through background mortality (DsFreeSus -> Deceased) or through the COPD episode (COPDEpsd -> Deceased).

In addition to these states, there are other "states" which are used to perform calculations, or collect useful statistics about the model. This is something we have chosen to do in our model structure, so it's visible to users, but it is not strictly necessary. For example, we have states for Disability, which collects information about the stock of DsFreeSus, COPDEpsd and Deceased and multiplies them against some disability weight. We also have states to calculate births, migration, and the effects of interventions on disability and mortality. Once again, we made these design decisions so that users can see how these work, but they aren't strictly necessary. They can be done elsewhere, and simply rendered as a transition rate.

The Model has two key components

The COPD model is large, but can be broken down into two components.

The main component moves people between states

The main component has the states we've introduced: DsFreeSus, COPDEpsd, Deceased, Disability, Births. Importantly there are some other states which sit between states:

• DsFreeSus Disability sits between DsFreeSus and Disability
• COPDEpsd Disability sits between COPDEpsd and Disability
• COPDEpsd Mortality sits between COPDEpsd and Deceased

These states aren't really states in a true sense. Rather, these states set the value of the transition rates around them. So, for example, DsFreeSus Disability is really the transition rate for DsFreeSus -> Disability. In the nomenclature of the Botech protocol, we call this a "Surrogate node". This is a structural decision we have made, but it doesn't change the results. Rather, we do this, so we can show how the calculations work to determine the disability and mortality effects.

The calculation component sets the transition rates

The "Surrogate Nodes" mentioned above, are set by a series of calculations in the model. These calculations follow the common order of operations described in the introduction.

Order of Operations

The COPD model follows the common order of operations used by all disease models. The key COPD-specific variations are:

Treatment Effect Calculations (Steps 4-7)

The model calculates effects for three treatments: InhaledSalbutamol, IpratropiumInhaler, and OralPrednisolone.

Step 4 example: InhaledSalbutamol_PIN × InhaledSalbutamol_Disability_Impact × InhaledSalbutamol_Calculated_Coverage

Step 6: Blended disability for COPDEpsd uses: dw = 1 - ((1 - healthy_disability) * (1 - copd_disability))

Note: No treatments have mortality effects in the COPD model.

Main State Transitions (Step 10)

• DsFreeSus ↔ COPDEpsd (incidence and remission of COPD)
• COPDEpsd → Deceased (COPD-related mortality)

Interventions

Interventions Table

The modelled treatments for COPD

For COPD, there are four treatments. An intervention is something that has an effect on the main components of the model, such as disability, or mortality.

• InhaledSalbutamol
  • Name in Spectrum: Inhaled Salbutamol
• IpratropiumInhaler
  • Name in Spectrum: Ipratropium Inhaler
• OralPrednisolone
  • Name in Spectrum: Oral Prednisolone

While treatments are always present in the structure of the COPD model, their coverage differs depending on the scenario.

Treatment Impacts

NOTE - These figures imply a modification of effect sizes. E.g. InhaledSalbutamol reduces the Disability of COPDEpsd by 14.8% (-0.148).

Population in Need (PIN)

NOTE - Refers to the proportion of people in COPDEpsd who are "in need" of this treatment. e.g. 30% of COPDEpsd are "in need" of OralPrednisolone

The COPD model scenarios

The COPD_Null scenario

In the COPD_Null, the coverage of all treatments is set to its baseline in the first year of the projection, then 0% afterwards.

Scenario CR2 - Acute treatment of COPD exacerbations with inhaled bronchodilators and oral steroids

In CR2:

• InhaledSalbutamol continues at its baseline coverage for the entirety of the run
• IpratropiumInhaler continues at its baseline coverage for the entirety of the run
• OralPrednisolone is set at its baseline coverage for the first year (2019) of the projection, and then to 95% coverage for the rest of the projection.

Scenario CR4 - Long-term management of COPD with inhaled bronchodilator

In CR4:

• InhaledSalbutamol is set at its baseline coverage for the first year (2019) of the projection, and then to 95% coverage for the rest of the projection.
• IpratropiumInhaler is set at its baseline coverage for the first year (2019) of the projection, and then to 95% coverage for the rest of the projection.
• OralPrednisolone continues at its baseline coverage for the entirety of the run

Assumptions

NOTE - A document is a difficult place to put entire lists of assumptions, as many of the assumptions we have change over time, and many of the assumptions are arrays of values, which apply to males and females differently, as well as different ages.

Therefore, please look at ./data/copd.csv as a reference guide for some assumptions. Values for disability weights have come from ./data/COPD.xlsx which is taken from Spectrum. Furthermore, even though measures of incidence, prevalence, and mortality may appear in this document, the final values were taken from ./data/GBD_Country_DATA.xlsx.

The baseline scenario is the default scenario

The baseline scenario has a coverage rate that is static, and continues from the start year to the end year. This is important, because it completely removes the effect of the Calculation Component. This is because, in essence, the effect of treatments is governed by the calculation: effect = impact * coverage * population in need. However, coverage is no the current coverage, but the difference between the current coverage, and the starting coverage. Therefore: effect = impact * (current_coverage - starting_coverage) * population in need. Because current_coverage - starting_coverage = 0, there is no effect to add to the default values for disability and mortality.

The null scenario reduces the coverage, and therefore the impacts

In the null scenario, all treatments are reduced from the baseline coverage to zero. For example, in Afghanistan, it is assumed that the baseline coverage rate is 5%. Therefore: effect = impact * (0 - 0.05) * population in need = impact * -0.05 * population in need. Therefore, in this country, the null scenario implies a 5% reduction in the impact of the four treatments.

The scale-up scenario increases the coverage, and therefor the impacts

In the scale-up scenario, select treatments (one treatment in CR2, three treatments in CR4) are increased from baseline to 95% for the projection, starting in the second year. For the treatments that aren't selected, they are left at the baseline level, and thus do not contribute to effect calculations. Therefore, for a select treatment in Afghanistan: effect = impact * (0.95 - 0.05) * population in need = impact * 0.9 * population in need.