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‎docs/source/models/causes/alzheimers/index.rst‎

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..
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Section title decorators for this document:
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==============
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Document Title
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==============
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Section Level 1 (#.0)
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+++++++++++++++++++++
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Section Level 2 (#.#)
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---------------------
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Section Level 3 (#.#.#)
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~~~~~~~~~~~~~~~~~~~~~~~
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Section Level 4
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^^^^^^^^^^^^^^^
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Section Level 5
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'''''''''''''''
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The depth of each section level is determined by the order in which each
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decorator is encountered below. If you need an even deeper section level, just
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choose a new decorator symbol from the list here:
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https://docutils.sourceforge.io/docs/ref/rst/restructuredtext.html#sections
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And then add it to the list of decorators above.
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.. _2021_cause_alzheimers_disease:
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==============================
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Alzheimer's Disease (GBD 2021)
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==============================
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.. contents::
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:local:
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.. list-table:: Abbreviations
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:widths: 15 15 15
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:header-rows: 1
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* - Abbreviation
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- Definition
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- Note
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* - AD
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- Alzheimer's Disease
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-
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* - YLD
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- Years Lived with Disability
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-
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* - YLL
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- Years of Life Lost
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-
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Disease Overview
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++++++++++++++++
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GBD 2021 Modeling Strategy
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++++++++++++++++++++++++++
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Restrictions
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------------
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The following table describes any restrictions in GBD 2021 on the
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effects of this cause (such as being only fatal or only nonfatal), as
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well as restrictions on the ages and sexes to which the cause applies.
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.. list-table:: GBD 2021 Cause Restrictions
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:widths: 15 15 20
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:header-rows: 1
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* - Restriction Type
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- Value
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- Notes
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* - Male only
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- False
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-
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* - Female only
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- False
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-
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* - YLL only
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- False
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-
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* - YLD only
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- False
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-
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* - YLL age group start
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- 40 to 44
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- age_group_id = 13
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* - YLL age group end
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- 95 plus
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- age_group_id = 235
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* - YLD age group start
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- 40 to 44
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- age_group_id = 13
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* - YLD age group end
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- 95 plus
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- age_group_id = 235
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Vivarium Modeling Strategy
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++++++++++++++++++++++++++
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For :ref:`Model 1 <2025_alzheimers_model_runs_table>` of the
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:ref:`Alzheimer's simulation <2025_concept_model_vivarium_alzheimers>`,
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we will model Alzheimer's disease as a simple SI model using GBD data
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for the cause "Alzheimer's disease and other dementias" (cause ID 543).
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Cause Model Diagram
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-------------------
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.. graphviz::
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digraph AlzheimersDisease {
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rankdir=LR;
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S -> AD [label=i_alz]
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}
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.. list-table:: State Definitions
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:widths: 5 5 20
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:header-rows: 1
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* - State
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- State Name
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- Definition
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* - S
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- Susceptible
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- Simulant does not have Alzheimer's disease or another dementia
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* - AD
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- Alzheimer's Disease
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- Simulant has Alzheimer's disease or another dementia
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.. list-table:: Transition Definitions
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:widths: 5 5 20
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:header-rows: 1
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* - Transition
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- Transition Name
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- Definition
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* - i_alz
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- Alzheimer's Incidence
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- Incidence rate of Alzheimer's disease and other dementias
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(incident cases per susceptible person-year)
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Data Tables
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-----------
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All data values are defined for a specified year, location, age group,
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and sex.
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.. list-table:: Data Sources
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:widths: 20 30 25 25
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:header-rows: 1
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* - Variable
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- Definition
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- Source or value
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- Notes
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* - prevalence_c543
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- Prevalence of Alzheimer's disease and other dementias
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- como
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-
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* - deaths_c543
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- Deaths from Alzheimer's disease and other dementias
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- codcorrect
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-
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* - population
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- Average population during specified year
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- get_population
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- Numerically equal to person-years. Often interpreted as population
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at year's midpoint (which is approximately equal to person-years
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if we think the midpoint rule with a single rectangle gives a good
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estimate of the area under the population curve).
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* - incidence_rate_c543
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- GBD's "total population incidence rate" for Alzheimer's disease
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and other dementias
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- como
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- Raw GBD value, different from "susceptible incidence rate"
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automatically calculated by Vivarium Inputs
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* - csmr_c543
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- Cause-specific mortality rate for Alzheimer's disease and other
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dementias
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- :math:`\frac{\text{deaths_c543}}{(\text{population}) \cdot (\text{1 year})}`
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- Calculated automatically by Vivarium Inputs
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* - emr_c543
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- Excess mortality rate for Alzheimer's disease and other dementias
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- :math:`\frac{\text{csmr_c543}}{\text{prevalence_c543}}`
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- Calculated automatically by Vivarium Inputs
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* - sequelae_c543
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- Sequelae of Alzheimer's disease and other dementias
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- Set of 3 sequelae: s452, s453, s454
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- Obtained from gbd_mapping.
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Sequela names are "Mild," "Moderate," or "Severe Alzheimer's
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disease and other dementias," respectively.
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* - :math:`\text{disability_weight}_s`
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- Disability weight of sequela :math:`s`
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- YLD Appendix
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- For reference, the values are:
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- s452: 0.069 (0.046-0.099)
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- s453: 0.377 (0.252-0.508)
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- s454: 0.449 (0.304-0.595)
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* - :math:`\text{prevalence}_s`
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- Prevalence of sequela :math:`s`
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- como
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-
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The following two tables describe the data needed for the cause model
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drawn in the previous section in terms of the data values in the above
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table.
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.. list-table:: State Data
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:widths: 20 25 30 30
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:header-rows: 1
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* - State
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- Measure
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- Value
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- Notes
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* - S
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- prevalence
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- 1 - prevalence_c543
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- Used for initial population at start of simulation
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* - S
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- birth prevalence
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- 1
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- Used for simulants born into the simulation
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* - S
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- excess mortality rate
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- 0
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- Added onto mortality hazard for susceptible simulants
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* - S
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- disability weight
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- 0
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- Used to calculate YLDs
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* - AD
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- prevalence
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- prevalence_c543
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- Used for initial population at start of simulation
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* - AD
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- birth prevalence
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- 0
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- Used for simulants born into the simulation
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* - AD
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- excess mortality rate
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- emr_c543
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- Added onto mortality hazard for simulants with AD
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* - AD
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- disability weight
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- :math:`\sum_\limits{s\in \text{sequelae_c543}}
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\text{disability_weight}_s \cdot \text{prevalence}_s`
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- Prevalence-weighted average disability weight over sequelae,
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computed automatically by Vivarium Inputs. Used to calculate
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YLDs.
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* - ALL
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- cause specific mortality rate
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- csmr_c543
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- Subtracted from all-cause mortality hazard to get cause-deleted
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mortality hazard in all cause states
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.. list-table:: Transition Data
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:widths: 10 10 10 20 30
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:header-rows: 1
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* - Transition
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- Source State
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- Sink State
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- Value
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- Notes
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* - i_alz
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- S
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- AD
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- :math:`\frac{\text{incidence_rate_c543}}{\text{1 - prevalence_c543}}`
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- Compute susceptible population incidence rate from GBD's "total
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population incidence rate." Conversion is automatic when using
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the get_measure function in Vivarium Inputs.

‎docs/source/models/causes/neonatal/index.rst‎

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Modeling Strategy
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+++++++++++++++++
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The neonatal death model requires only the probability of death (aka "mortality risk") for the early and late neonatal time periods. Rather than using GBD mortality rates and converting them into probability of deaths, we will use mortality risk as direct input data into our model. We will calculate mortality risk input data as age-specific death counts divided by live birth counts from GBD.
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The neonatal death model requires only the probability of death (aka "mortality risk") for the early and late neonatal time periods.
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These mortality risks are age-group-, sex-, and location-specific.
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For brevity, sex and location subscripts are omitted in all equations.
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Rather than using GBD mortality rates and converting them into probability of deaths, we will use mortality risk as direct input data into our model. We will calculate mortality risk input data as age-specific death counts divided by live birth counts from GBD.
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Note that this strategy does not require any conversion between rates to probabilities NOR does it require any scaling to the duration of the age group. The mortality risk calculated as described below already represents the probability of dying within a neonatal age group and can be used directly as such in the simulation.
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Note that this strategy was updated in May of 2025 from a prior strategy of converting GBD mortality rates to probabilities. `The pull request that updated this strategy can be found here for reference. <https://github.com/ihmeuw/vivarium_research/pull/1654>`_ This strategy update was pursued following verification and validation issues in neonatal mortality and an exploration of potential solutions in model runs 6.1 through 6.4. Ultimately, a change from mortality rates to mortality risk was preferred given that it is the more policy relevant measure in the context of neonates, and accurately apportioning person time alive within the neonatal age group given the input data available to us was a challenge we judged to be unnecessary.
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The calculation of :math:`\text{ACMRisk}_i` (the all-cause mortality risk for a single simulant, :math:`i`) is a bit complicated, however. We begin with a population ACMRisk and use the LBWSG PAF to derive a risk-deleted ACMRisk to which we can then apply the relative risk of LBWSG matching any risk exposure level. Mathematically this is achieved by the following formula:
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The calculation of :math:`\text{ACMRisk}_i` (the all-cause mortality risk for a single simulant, :math:`i`) is a bit complicated, however. We begin with a population ACMRisk and use the LBWSG PAF to derive a risk-deleted ACMRisk to which we can then apply the relative risk of LBWSG matching any risk exposure level. Mathematically this is achieved by the following formula.
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Starting with this equation, we omit age group subscripts for brevity; all quantities are still age-, sex-, and location-specific.
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.. math::
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\begin{align*}
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and :math:`\text{CSMRisk}_{i}^{k}` is the cause-specific mortality risk for subcause :math:`k` for simulant :math:`i` (both detailed in the `Modeled Subcauses`_
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linked from this page).
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In addition to determining which simulants die due to any cause, we also need to determine which subcause is underlying the death. This is done by sampling from a categorical distribution obtained by renormalizing the CSMRisks:
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.. math::
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- GBD + assumption about relative risks + intervention model effects
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- see subcause models for details
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**Details of the** :math:`\text{PAF}_\text{LBWSG}` **calculation:**
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.. _details_of_the_lbwsg_paf_calculation:
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Details of the LBWSG PAF calculation
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++++++++++++++++++++++++++++++++++++
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As stated in the table above, :math:`\text{PAF}_\text{LBWSG}` is the population attributable fraction of all-cause mortality for low birth weight and short gestation. It is computed so that PAF = 1 - 1 / E(:math:`\text{RR}_{\text{BW},\text{GA}}`) from the capped interpolated relative risk function (with expectation taken over the distribution of LBWSG exposure).
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So,
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.. _details_of_the_lbwsg_paf_calculation_equation:
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.. math::
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E(\text{RR})_\text{population} = \frac{\sum_{\text{cat}} E(\text{RR})_\text{cat} \times p^\text{birth}_\text{cat} \times \frac{n_\text{cat} - n^\text{deaths}_\text{cat}}{n_\text{cat}}}{\sum_{\text{cat}} p^\text{birth}_\text{cat} \times \frac{n_\text{cat} - n^\text{deaths}_\text{cat}}{n_\text{cat}}}

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