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Diabetes model for the NCD Module
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appendix-3 diabetes model

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The Diabetes Model, and its Scenarios

This document describes the Diabetes state-transition model, and the scenarios which are run using it. If you are uncertain about the general appendix 3 methodologies, or have general queries, please refer to the README.

Link to Models

The Diabetes Model and its design

Diabetes Models creates several scenarios: Null_Diabetes, D1, D2, D3, D4, D5

The Diabetes 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 Diabetes model is used to run two scenarios of treatment coverage: D1, D2, D3, D4 and D5 In addition, the Diabetes model is also used to run a "Null Scenario": Called Diabetes_Null. We will explain the Null Scenario later.

Structure of the Diabetes Model

Diabetes has several key states, DsFreeSus, DiabetesEpsd, DiabeticRetinopathy, LowerExtrmAmpt, DiabeticNephropathy and Deceased. DsFreeSus means "Disease free, susceptible", and this refers to the majority of the population. DiabetesEpsd means "Diabetes Episode", and generally refers to people who have been diagnosed with diabetes. DiabeticRetinopathy means "Diabetic Retinopathy" and refers to people who have retinopathy caused by diabetes. LowerExtrmAmpt means "Lower Extremity Amputation" and refers to people who have had a lower limb, or part of that lower limb (e.g. a foot) amputated because of diabetes. DiabeticNephropathy means "Diabetic Nephropathy", and refers to people who have nephropathy caused by diabetes. Deceased refers to the people in the model who have died, either through background mortality (DsFreeSus -> Deceased) or through the Diabetes episode (DiabetesEpsd -> 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 key states 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 modelled treatments for Diabetes

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

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

Treatment Impacts

NOTE - These figures imply a modification of effect sizes. E.g. StdGlycControl reduces the CFR of DiabeticRetpathy by 75% (-0.75).

Population in Need

NOTE - Refers to the proportion of people in DiabetesEpsd who are "in need" of this treatment. e.g. 90% of DiabetesEpsd are "in need" of StdGlycControl

The Model has two key components

The Diabetes model is large, but can be broken down into two components. Both Components Together

The main component moves people between states

The Main Component

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

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 Calculation Component The "Surrogate Nodes" mentioned above, are set by a series of calculations in the model. We will explain these in detail below in the section "The Order of Operations".

The Diabetes model scenarios

The Diabetes_Null scenario

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

Scenario D1 - Foot care to prevent amputation in people with diabetes (including educational programmes, access to appropriate footwear, multidisciplinary clinics)

In D1:

Scenario D2 - Diabetic retinopathy screening for all diabetes patients and laser photocoagulation for prevention of blindness

In D2:

Scenario D3 - Glycaemic control for people with diabetes, along with standard home glucose monitoring for people treated with insulin to reduce diabetes complications

In D3:

Scenario D5 - Control of blood pressure in people with diabetes

In D5:

Missing Diabetes Scenarios

Other diabetes scenarios involve the Cardiovascular Disease model, and will be introduced once that is built.

The Diabetes Model and its key 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/diabetes.csv as a reference guide for some assumptions. Values for disability weights have come from ./data/Diabetes.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 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.

What is the order of operations?

What do we mean by the order of operations?

When you "run a model" you are telling the model to, for example:

However, the ordering of these can be important. Therefore, the order of operations describes the order in which steps are taken each year the model runs.

The order of operations

It may look complicated at first, but we can simplify it by working through one example. We will use the example of LowDoseBeclom to show this affects disability and mortality. Importantly, for all these calculations, do not imagine these are people being transferred between states. Rather, imagine this is an alternative to using Microsoft Excel, for calculating some values that will become a transition rate.

1. Generate the population of the country in 2019

We do this using the UNDP World Population Prospects Data, for country, year. The data that is returned is the number of people for sex, age (through 100). Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/CSV_FILES/WPP2022_Population1JanuaryBySingleAgeSex_Medium_1950-2021.zip Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/CSV_FILES/WPP2022_Population1JanuaryBySingleAgeSex_Medium_2022-2100.zip

2. Generate values for constants in the Calculation Component

We need to load the constants which are used to calculate the effects on disability and mortality. This is the second step of the model.

3. Calculate the Coverage Rate

The coverage rate is calculated by Coverage - Starting Coverage. For example, RetinopathyScrn_Coverage - RetinopathyScrn_StartingCoverage. The result of this calculation is stored in, e.g. RetinopathyScrn_Calculated_Coverage

4. Calculate Incidence Effects

Disability effects are calculated by: PIN * Incidence Impact * Coverage Therefore, using RetinopathyScrn as an example, we multiply RetinopathyScrn_PIN, RetinopathyScrn_DiabeticRetinopathy_Incidence_Impact and RetinopathyScrn_Calculated_Coverage We store this value in RetinopathyScrn_Incidence_Effect.

5. Transform the Incidence Effects

Here, we transform a value to its inverse by subtractring it from one. E.g. 1 - 0.05 = 0.95. Therefore, the sequence might be: 1 - 0.05 - 0.03 - 0.02 - 0.00 = 0.90 We store this value in the variable referring to the state of interest: DiabeticRetinopathy_Transform, LowerExtrmAmpt_Transform,DiabeticNeprhopathy_Transform

6. We calculate the "Blended Disability" for DiabetesEpsd, DiabeticRetinopathy, LowerExtrmAmpt and DiabeticNephropathy

(We'll use DiabetesEpsd as an example in this section)

The default disability weight for DiabetesEpsd is not a static value. Instead, it is determined by the following equation: dw = 1 - ((1 - healthy_disability) * (1 - DiabetesEpsd_disability)) We call this a "blended disability".

We calculate this in our model through the following:

7. Calculate the Surrogate Values

In Diabetes, we have surrogates for incidence, disability, and mortality. In this step, we calculate the surrogate values. As a reminder, "surrogate values" really mean "the final transition rates between a source and a target".

For incidence, we:

  1. Add the incidence rates to their respective surrogate (e.g. DiabeticRetinopathy_Incidence_Rate to DiabeticRetinopathy Incidence)
  2. Multiply the transformed effect against the surrogate (e.g. DiabeticRetinopathy_Transform to DiabeticRetinopathy Incidence)

For disability, we:

  1. Move the value from Blended_Disability_Transform into DiabetesEpsd Disability
  2. Multiply Disability_Effect_Transform against the value in DiabetesEpsd Disability

For mortality:

  1. Add the mortality rates to their respective surrogate

Once this is set in the surrogate, it is propagated to the edges surrounding it.

8. Calculate the DsFreeSus Disability Surrogate

The disability weight for DsFreeSus is simply just the Healthy_Disability value. Therefore, we just move this value to the DsFreeSus Disability state

9. Record the number of births that will occur

For states DsFreeSus, DiabetesEpsd, DiabeticRetinopathy, LowerExtrmAmpt and DiabeticNephropathy we multiply the number of fertile women, against their age specific fertility rates (UNDP Statistics), to calculate the number of births. NOTE - These women don't given birth yet, but we calculate births now, before people move states or die, or age or migrate. Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/CSV_FILES/WPP2022_Fertility_by_Age1.zip

10 - Movement around the main states

DsFreeSus move to DiabetesEpsd (if this is the first year, the prevalent population is moved first). DiabetesEpsd move to DiabeticRetinopathy, LowerExtrmAmpt and DiabeticNephropathy (if this is the first year, the prevalent population is moved first). Note - there is no remission from these states.

12 - Disability is Recorded

DsFree -> Disability, DiabetesEpsd -> Disability, DiabeticRetinopathy -> Disability, LowerExtrmAmpt -> Disability, DiabeticNephropathy -> Disability and Deceased -> Disability are recorded. Using DiabetesEpsd as an example, let's explain this. First, the stock of persons in DiabetesEpsd is counted e.g. 3,000. Then, this stock is multiplied against the disability weight calculated and stored in DiabetesEpsd Disability e.g. 0.1 Then, disability is calculated as 3000 * 0.1 = 300. This value is sent and stored into Disability.

The disability weight for DiabetesEpsd, DiabeticRetinopathy, LowerExtrmAmpt, and DiabeticNephropathy is taken from Spectrum by Avenir Health. In particular, they are taken from the Diabetes.xlsx file in the Spectrum repository. The disability weight for DsFreeSus is taken from the Spectrum repository but is originally from GBD we believe.

13 - Populations migrate

Migration rates calculated using the UNDP World Population Projections are used to increase or decrease the current populations of people in DsFreeSus, DiabetesEpsd, DiabeticRetinopathy, LowerExtrmAmpt and DiabeticNephropathy. Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/EXCEL_FILES/1_General/WPP2022_GEN_F01_DEMOGRAPHIC_INDICATORS_COMPACT_REV1.xlsx

14 - People get older

People get older by 1 year. If a person was 100, they are removed from the model at this point.

15 - People die

People move to the Deceased state via: DsFreeSus -> Deceased The background mortality rate for DsFreeSus -> Deceased is taken from the UNDP World Population Projections lifetables (we use the rate "qx"). Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/CSV_FILES/WPP2022_Life_Table_Complete_Medium_Male_1950-2021.zip Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/CSV_FILES/WPP2022_Life_Table_Complete_Medium_Male_2022-2100.zip

People move to the Deceased state via: DiabetesEpsd -> Deceased This mortality rate was taken from GBD_Country_Data.xlsx in the Spectrum repository.

People move to the Deceased state via: DiabeticRetinopathy -> Deceased, LowerExtrmAmpt -> ... and DiabeticNephropathy -> ... This mortality rate was taken from Diabetes.xlsx in the Spectrum repository.

16 - Women give birth

The births that were stored in the Births state are transmitted to DsFreeSus. The number of males and females are governed by the sex ratio from the UNDP World Population Projections database.

Reference: https://population.un.org/wpp/Download/Files/1_Indicators%20(Standard)/EXCEL_FILES/1_General/WPP2022_GEN_F01_DEMOGRAPHIC_INDICATORS_COMPACT_REV1.xlsx

17 - Constants are cleared

Any constants or intermediate values that were calculated are cleared from the model, so they don't contribute to calculations in the next year.

18 - The timestep is incremented.

If the year was 2019, it is now 2020. If the year was 2020, it is now 2021. If the year was 2119, the model simulation ends.

Outstanding Issues / Clarifications / Questions

Link to Results