Alzheimer’s disease with presymptomatic and MCI stages (GBD 2021)

Abbreviations

Abbreviation

Definition

AD

Alzheimer’s Disease

BBBM

Blood-Based Biomarker

CSU

Client Services Unit

DW

Disability Weight

FHS

Future Health Scenarios

MCI

Mild Cognitive Impairment

YLD

Years Lived with Disability

YLL

Years of Life Lost

Disease Overview

GBD 2021 Modeling Strategy

The IHME dementia modelers use DisMod to estimate the prevalence and incidence of a “dementia envelope” comprising all types of dementia combined, and then they estimate what proportion of the envelope corresponds to each subtype of dementia. The proportions of dementia due to stroke, Parkinson’s disease, Down’s syndrome, and traumatic brain injury are attributed to those GBD causes, and the remaining dementia in the envelope is attributed to the GBD cause “Alzheimer’s disease and other dementias” (cause ID 543).

For further information, see the methods appendices and HUB page:

Restrictions

The following table describes any restrictions in GBD 2021 on the effects of the cause “Alzheimer’s disease and other dementias” (such as being only fatal or only nonfatal), as well as restrictions on the ages and sexes to which the cause applies. We also list the implied age restriction on YLDs for the MCI-AD state of the cause model below.

GBD 2021 Cause Restrictions

Restriction Type

Value

Notes

Male only

False

Female only

False

YLL only

False

YLD only

False

YLL age group start

40 to 44

age_group_id = 13

YLL age group end

95 plus

age_group_id = 235

YLD age group start

  • 40 to 44 for AD-dementia cause state

  • No a priori age restriction for MCI-AD cause state

  • Restriction to age_group_id = 13 (40 to 44) for AD-dementia cause state is from GBD. However, due to simulation dynamics, it is possible for simulants to enter this state before age 40.

  • In practice, the age start for MCI-AD will be age_group_id = 10 (25 to 29) because we will be adding simulants at most 10.2 years before AD incidence (so 40 – 10.2 = 29.8, in the 25-29 age group)

YLD age group end

95 plus

age_group_id = 235

Vivarium Modeling Strategy

For Model 4 of the CSU Alzheimer’s simulation, we will add two pre-dementia states to the Alzheimer’s disease model. The model still functions similar to an SI model, but now there are multiple with-condition states, with unidirectional progression between them. In Model 4 we used the incidence and prevalence for GBD’s “Alzheimer’s disease and other dementias” (cause ID 543), so our numbers were inflated by the “other dementias” part.

In Model 5, we remove the “other dementias” from the disease model. To do this, the dementia modelers recommended not using the published GBD data directly, but to start with the GBD 2023 “dementia envelope” data from DisMod, and multiply by proportion of the envelope due to Alzheimer’s disease. The estimates of the proportions of the envelope due to each dementia subtype are unpublished as of September 2025, but the modelers shared a .csv file we can use as long as we don’t expose the raw numbers. See the Data Values and Sources section below for details.

Cause Model Diagram

digraph AlzheimersDisease { rankdir=LR; bbbm [label="BBBM-AD"] mci [label="MCI-AD"] ad [label="AD-dementia"] S -> bbbm [label="i_BBBM"] bbbm -> mci [label="i_MCI"] mci -> ad [label=i_AD] }

State Definitions

State

State Name

Definition

S

Susceptible

Simulant does not have Alzheimer’s disease or any of its precursors

BBBM-AD

Blood-Based-Biomarker-presymptomatic Alzheimer’s Disease

Simulant has presymptomatic Alzheimer’s disease that is detectable using blood-based biomarkers

MCI-AD

Mild Cognitive Impairment due to Alzheimer’s Disease

Simulant has mild cognitive impairment due to Alzheimer’s disease

AD-dementia

Alzheimer’s Disease dementia

Simulant has mild, moderate, or severe dementia due to Alzheimer’s disease

Death (not pictured)

Death

Simulant has died
Transition Definitions

Transition

Transition Name

Definition

Notes

i_BBBM

BBBM incidence hazard

Incidence hazard of BBBM-AD

This will be equal to GBD’s incidence rate of Alzheimer’s disease and other dementias, but with the age group and year shifted backward by the average duration of the BBBM-AD and MCI-AD states combined, and inflated to account for deaths in those two states

i_MCI

MCI incidence hazard

Incidence hazard of MCI due to AD

This will be a time-dependent hazard rate, depending on how long a simulant has been in the BBBM-AD state, not a constant hazard like we usually use

i_AD

AD dementia incidence hazard

Incidence hazard of Alzheimer’s disease dementia

We will define this as a constant hazard rate for simulants in MCI-AD

m_X (not pictured)

Mortality hazard in state X

Total mortality hazard for simulants in cause state X

X is a variable representing an arbitrary cause state

State and Transition Data

The tables in this section describe the data needed for the cause model drawn in the Cause Model Diagram section above. The variables in the tables are defined in the the Data Values and Sources section below.

The following tables describe the data for each state and transition if modeling only simulants with AD dementia or pre-dementia AD as described in the Alzheimer’s population model:

State data when modeling only simulants with AD dementia or pre-dementia AD

State

Initial prevalence

Entrance prevalence

Excess mortality rate

Disability weight

S

0

0

0

0

BBBM-AD

\(\Delta_\text{BBBM} / \Delta_\text{(all AD states)}\)

1

0

0

MCI-AD

\(\Delta_\text{MCI} / \Delta_\text{(all AD states)}\)

0

0

\(\text{DW}_\text{MCI}\)

AD-dementia

\(\Delta_\text{AD} / \Delta_\text{(all AD states)}\)

0

emr_c543

\(\text{DW}_\text{c543}\)

Note: The variable \(\Delta_\textsf{X}\) denotes the average duration in cause state X, as defined in the data values and sources table below.

Transition Data

Transition

Source State

Sink State

Value

i_BBBM

S

BBBM-AD

Not explicitly used because we’re not modeling susceptible simulants. Defined implicitly in the Alzheimer’s population model, which computes how many simulants to add into the BBBM-AD state on each time step.

i_MCI

BBBM-AD

MCI-AD

\(h_\text{MCI}(t - T_\text{BBBM})\), where \(t\) is the current time in the simulation, and \(T_\text{BBBM}\) is the time the simulant entered the BBBM-AD state. Adjusted in Hypothetical Alzheimer’s Treatment scenario.

i_AD

MCI-AD

AD

\(1 / \Delta_\text{MCI}\)

m_X

X

Death

acmr — csmr_c543 + emr_X

Note: \(h_\text{MCI}\) is the time-dependent hazard function for transitioning into MCI-AD, defined in the data values and sources table below.

Because i_MCI is defined in terms of a non-constant hazard function \(h_\text{MCI}\), simulants initialized into the BBBM-AD state will need to be assigned a value for \(T_\text{BBBM}\) to determine how long they have been in that state. For simulants in BBBM-AD at time \(t=0\), assign \(T_\text{BBBM}\) uniformly in the interval \([-\Delta_\text{BBBM},\, 0]\).

Attention

If we model the entire population including susceptible simulants, the state data should be modified as follows.

Define \(p_\textsf{X}\) to be the prevalence of cause state X in the total population including susceptible simulants, and define \(p_\text{(all AD states)}\) to be the sum of \(p_\textsf{X}\) for the three AD cause states X. Then multiplying the prevalence of each AD state in the above state data table by \(p_\text{(all AD states)}\) gives the prevalence of that state in the entire population. Since we know that

\[\begin{split}\begin{align*} p_\text{AD} &= \text{prevalence_AD} \\ &= \text{prevalence_m24351} \times \text{proportion_AD}, \end{align*}\end{split}\]

the prevalence of AD dementia computed from GBD’s dementia envelope (see data values and sources table below), we can solve to obtain

(1)\[p_\text{(all AD states)} = \frac{\Delta_\text{(all AD states)}}{\Delta_\text{AD}} \cdot \text{prevalence_AD} \quad\text{(for ages 40+)}.\]

Note that since the GBD prevalence applies to a given demographic group, so does the formula for \(p_\text{(all AD states)}\). The above formula applies to age groups 40+ since this is where prevalence_AD and \(\Delta_\text{AD}\) are nonzero. For ages 30–39, use the value of \(p_\text{(all AD states)}\) for age group 40–44; for ages <30, set \(p_\text{(all AD states)} = 0\). The following state data table shows the resulting initial prevalences when modeling the total population, as well as the birth prevalences, which replace the entrance prevalences. The excess mortality rate and disability weight of each state remain the same.

State data when modeling entire population including susceptible simulants

State

Initial prevalence

Birth prevalence

S

\(1 - p_\text{(all AD states)}\)

1

BBBM-AD

\(\frac{\Delta_\text{BBBM}}{\Delta_\text{(all AD states)}} \cdot p_\text{(all AD states)}\)

0

MCI-AD

\(\frac{\Delta_\text{MCI}}{\Delta_\text{(all AD states)}} \cdot p_\text{(all AD states)}\)

0

AD-dementia

\(\frac{\Delta_\text{AD}}{\Delta_\text{(all AD states)}} \cdot p_\text{(all AD states)}\)

0

Note

Although we will not need all the values in this table for Model 4, the value of \(p_\text{(all AD states)}\) defined in (1) will be needed in order to compute the model scale and initialize the correct number of simulants in each demographic subgroup. Note that in the notation on the Alzheimer’s population model page, \(p_\text{(all AD states)}\) refers to the prevalence within the entire population of a location, including all age groups and sexes. On the other hand, if we compute prevalence_AD for a specific demographic subgroup \(g\) (e.g., a single age group and sex) and year \(t\), then \(p_\text{(all AD states)}\) as computed in (1) corresponds to \(p_{g,t}\) on the Alzheimer’s population model page.

Data Values and Sources

Unless otherwise noted, all data values depend on year, location, age group, and sex, as defined by GBD.

The following paths on the cluster contain the data files listed in the table below:

  • population_agg.nc and mortality_all.nc from FHS team

  • squeezed_proportions_to_sim_sci.csv from dementia modelers

  • all.hdf disability weight file saved by Simulation Science team

# Data folder for Alzheimer's sim, including data from FHS team and
# dementia modelers (see README.txt for data provenance)
/mnt/team/simulation_science/pub/models/vivarium_csu_alzheimers/data

# Disability weights saved by Simscience team:
/mnt/team/simulation_science/costeffectiveness/auxiliary_data/GBD_2021/02_processed_data/disability_weight/sequela/all/all.hdf
Data values and sources

Variable

Definition

Source or value

Notes

proportion_AD

The proportion of the dementia envelope that is Alzheimer’s disease dementia

squeezed_proportions_to_sim_sci.csv

Point estimate stratified by age group and sex for ages 40+. Includes proportions for all subtypes of dementia — filter to type_label == “Alzheimer’s disease”.

Note: These estimates were provided by the dementia modelers and are not yet published, so they should not be stored directly in the Artifact or any other public location.

prevalence_m24351

Prevalence of GBD 2023 dementia envelope

get_draws( source=”epi”, gbd_id_type = “modelable_entity_id”, gbd_id=24351, release_id=16, year_id=2023, measure_id=5 )

The dementia envelope represents the combined prevalence all types of dementia. By contrast, the GBD cause “Alzheimer’s disease and other dementias” (c543) does not include certain dementias that result from other modeled GBD causes.

prevalence_AD

Prevalence of AD dementia in total population

prevalence_m24351 \(\times\) proportion_AD

\(p_\textsf{X}\)

Prevalence of cause state X in total population

Defined in the “Initial prevalence” column of the state data table in the Attention box above

By definition, \(p_\text{AD} =\) prevalence_AD, and \(p_\text{BBBM}\) and \(p_\text{MCI}\) are derived from this

\(p_\text{(all AD states)}\)

Prevalence of all stages of AD combined

Defined in (1) above

Equals \(p_\text{BBBM} + p_\text{MCI} + p_\text{AD}\)

incidence_m24351

Total-population incidence rate for GBD 2023 dementia envelope

get_draws( source=”epi”, gbd_id_type = “modelable_entity_id”, gbd_id=24351, release_id=16, year_id=2023, measure_id=6 )

Raw value from get_draws, different from susceptible-population incidence rate automatically calculated by Vivarium Inputs

incidence_AD

Total-population incidence rate of AD dementia

incidence_m24351 \(\times\) proportion_AD

Used in AD population model to calculate BBBM-AD incidence. We are assuming the prevalence proportions can be applied to incidence. We are assuming the AD-dementia incidence rate is constant over time in each demographic group.

acmr

All-cause mortality rate

mortality_all.nc

Draw-level, age-specific forecasts from GBD 2021 Forecasting Capstone. See Abie’s population and mortality forecasts notebook for a demonstration of how to load and transform the .nc file

population_forecast

Forecasted average population during specified year

population_agg.nc

Draw-level, age-specific forecasts from GBD 2021 Forecasting Capstone. Numerically equal to person-years. Used in AD population model to calculate BBBM-AD incidence counts. See Abie’s population and mortality forecasts notebook for a demonstration of how to load and transform the .nc file.

\(\text{population}_{2021}\)

Average population during the year 2021

get_population

Point estimate. Used only for the calculation of csmr_c543 by Vivarium Inputs

\(\text{deaths_c543}_{2021}\)

Deaths from Alzheimer’s disease and other dementias in 2021

codcorrect

Used only for the calculation of csmr_c543 by Vivarium Inputs

csmr_c543

Cause-specific mortality rate for Alzheimer’s disease and other dementias

\(\frac{\text{deaths_c543}_{2021}}{(\text{population}_{2021}) \cdot (\text{1 year})}\)

Calculated automatically by Vivarium Inputs. Assumed to remain constant over time in each demographic group.

\(\text{prevalence_c543}_{2021}\)

Prevalence of Alzheimer’s disease and other dementias in 2021

como

Used only for calculation of emr_c543 by Vivarium Inputs

emr_c543

Excess mortality rate for Alzheimer’s disease and other dementias

\(\frac{\text{csmr_c543}}{\text{prevalence_c543}_{2021}}\)

Calculated automatically by Vivarium Inputs. Assumed to remain constant over time in each demographic group.

emr_X

Excess mortality rate in cause state X

Values listed in “Excess mortality rate” column of state data table above

  • emr_S, emr_BBBM, emr_MCI, emr_AD

m_X

Mortality hazard in cause state X

acmr — csmr_c543 + emr_X

sequelae_c543

Sequelae of Alzheimer’s disease and other dementias

Set of 3 sequelae: s452, s453, s454

Obtained from gbd_mapping. Sequela names are “Mild,” “Moderate,” or “Severe Alzheimer’s disease and other dementias,” respectively. Same for all years, locations, age groups, and sexes.

\(\text{prevalence}_s\)

Prevalence of sequela \(s\)

como

\(\text{DW}_s\)

Disability weight of sequela \(s\)

all.hdf disability weight file in our team’s auxiliary data

Disability weights are stored as draws and do not vary by year, location, age group, or sex. For reference, the values are:

  • s452: 0.069 (0.046-0.099)

  • s453: 0.377 (0.252-0.508)

  • s454: 0.449 (0.304-0.595)

\(\text{DW}_\text{c543}\)

Average disability weight of AD-dementia

\(\sum_\limits{s\in \text{sequelae_c543}} \text{DW}_s \cdot \text{prevalence}_s\)

Prevalence-weighted average disability weight over sequelae, computed automatically by Vivarium Inputs. Used to calculate YLDs.

\(\text{DW}_\text{motor}\)

Disability weight for health state “motor impairment, mild”

all.hdf disability weight file in our team’s auxiliary data

Disability weights are stored as draws and do not vary by year, location, age group, or sex. See Abie’s disability weight notebook for details on pulling the correct value.

\(\text{DW}_\text{motor+cog}\)

Disability weight for health state “motor plus cognitive impairments, mild”

all.hdf disability weight file in our team’s auxiliary data

Disability weights are stored as draws and do not vary by year, location, age group, or sex. See Abie’s disability weight notebook for details on pulling the correct value.

\(\text{DW}_\text{MCI}\)

Disability weight of mild cognitive impairment

\(\frac{\text{DW}_\text{motor+cog} - \text{DW}_\text{motor}} {1 - \text{DW}_\text{motor}}\)

Disability weights are stored as draws and do not vary by location, age group, or sex. For reference, the value is

  • 0.021 (0.013, 0.032)

Obtained by removing DW of “motor impairment, mild” from DW of “motor plus cognitive impairments, mild,” at the draw level. See Abie’s disability weight notebook for details, and see the derivation below for further explanation.

\(T_X\)

The time at which a simulant enters the cause state \(X\)

Determined within the simulation

Random variable for each simulant. \(T_\text{BBBM}\) is used to determine how long a simulant has been in the BBBM-AD state, in order to compute the hazard rate of transitioning to MCI-AD at a given simulation time \(t\).

\(D_\text{BBBM}\)

Dwell time in cause state BBBM-AD

\(T_\text{MCI} - T_\text{BBBM}\)

Random variable for each simulant, constructed implicitly through simulation dynamics to have approximately a Weibull distribution with shape parameter \(k\) and scale parameter \(\lambda\)

\(k\), \(\lambda\)

Shape and scale parameters, respectively, of Weibull distribution for \(D_\text{BBBM}\)

  • \(k = 1.22\)

  • \(\lambda = 6.76\)

Chosen to match client’s specification for \(D_\text{BBBM}\): The probability of progression from BBBM-AD to MCI-AD is about 50% at 5 years and 80% at 10 years, corresponding to an average annual rate of progression of approximately 15% . Use the same parameters for all years, locations, age groups, and sexes.

bbbm_dist

Python object representing the Weibull distribution for \(D_\text{BBBM}\)

scipy.stats.weibull_min(k, scale=λ)

An instance of SciPy’s Weibull distribution class.

\(h_\text{MCI}(t)\)

Hazard function for transitioning into the MCI-AD state from BBBM-AD

  • bbbm_dist.pdf(t) / bbbm_dist.sf(t), or

  • exp( bbbm_dist.logpdf(t) — bbbm_dist.logsf(t) ), an equivalent expression that may help avoid underflow

Equal to \(\frac{k}{\lambda} \left(\frac{t}{\lambda}\right)^{k-1}\), but can also be computed as the ratio of the probability density function to the survival function, using the methods defined in SciPy’s Weibull distribution class

\(\Delta_\text{BBBM}\)

Average duration of BBBM-presymptomatic AD in the absence of mortality

bbbm_dist.mean()

Equal to \(\lambda \Gamma(1 + 1/k)\), where \(\Gamma\) is the gamma function. Can be computed using scipy.special.gamma, but using bbbm_dist.mean() is more general if we update the underlying distribution. Does not vary by year, location, age group, or sex.

\(\Delta_\text{MCI}\)

Average duration of MCI due to AD in the absence of mortality

3.85 years

Obtained from Table 3 in Potashman et al., assuming a constant hazard rate of transitioning to AD-dementia. Corresponds to an annual conditional probability of 0.771 of staying in MCI-AD given that you don’t die within one year, since \(\exp(-1 / 3.85) \approx 0.771\). Does not vary by year, location, age group, or sex.

Note: The paper reports a 68.2% chance of staying in MCI and a 5.3% chance of returning to asymptomatic—these probabilities have been combined to get an annual probability of 73.5% of staying in MCI since our model assumes that a backwards transition is not possible. The conditional probability above is computed as \(0.771 = 0.735 / (1 - 0.047)\) since the paper reports a 4.7% chance of dying within a year when starting in the MCI state.

\(\Delta_\text{AD}\)

Average duration of AD-dementia

  • prevalence_AD / incidence_AD for ages 40+

  • 0 for ages under 40

Follows from the steady-state equation (prevalent cases) = (incident cases) x (average duration). Note that the denominator is the raw total-population incidence rate from GBD, not the susceptible-population incidence rate usually returned by Vivarium Inputs. This is because we want the total-population person-time in the denominators of prevalence and incidence to cancel out, leaving a ratio of counts.

\(\Delta_\text{(all AD states)}\)

Average duration of all stages of AD combined if there is no mortality in the BBBM-AD and MCI-AD stages

\(\Delta_\text{BBBM} + \Delta_\text{MCI} + \Delta_\text{AD}\)

Deriving a disability weight for MCI

Todo

Derive the formula for the disability weight of MCI, and include Abie’s plot comparing DWs of various relevant health states.