Skip to content
Open
Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
17 commits
Select commit Hold shift + click to select a range
File filter

Filter by extension

Filter by extension

Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
Original file line number Diff line number Diff line change
Expand Up @@ -159,7 +159,7 @@ Relationship between rate and risk

Risk depends on both the incidence rate and on the duration of the at-risk period. In vivarium, we apply the incidence rate to each simulant at each time step to estimate the risk of developing disease where the duration of the period is the duration of the time-step:

Risk = :math:`1 e^\text{( –incidence rate × duration of the period at risk)}`
Risk = :math:`1 - e^{-( \text{incidence rate } \times \text{ duration of the period at risk})}`

For disease that have a low incidence rate or when the period at risk is short, the following approximation can be used:

Expand All @@ -169,13 +169,19 @@ Example:

* The incidence rate of a particular condition in a population is 50 per 100 000 person-years. The risk for an individual in this population of developing this condition during a five-year period (assuming no other causes of death) is given by

- 5-year risk = :math:`1 – e^\text{( –0.0005 per person-year × 5 years)}` = 0.25%
| The simplified equation can yield the same result
- 5-year risk = :math:`1 - e^{-(0.0005 \text{ per person-year }
\times\ 5 \text{ years})}` = 0.25%

| The simplified equation can yield the same result:

- 5-year risk=0.0005 per person-year X 5 years = 0.25%
* Consider now a common condition with an incidence rate of 300 per 1000 person-years

- 5-year risk = :math:`1 – e^\text{( –0.3 per person-year × 5 years)}` = 78%
| The simplified equation does not yield the same result
- 5-year risk = :math:`1 - e^{-(0.3 \text{ per person-year }
\times\ 5 \text{ years})}` = 78%

| The simplified equation does not yield the same result:

- 5-year risk = 0.3 per person-year X 5 years = 150%

Measures of effect
Expand Down
26 changes: 13 additions & 13 deletions docs/source/models/causes/afib/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -63,7 +63,7 @@ approach that combined DisMod-MR and CODEm models to generate fatal and nonfatal

3. We calculated the excess mortality rate (EMR) for the year 2019 according to the following formula:

Excess mortality rate = :math:`\frac{\text{\{cause-specific-mortality-rate\}_codem}}{\text{\{prevalence\}_dismod}}`
Excess mortality rate = :math:`\frac{\text{\{cause-specific-mortality-rate\}\_codem}}{\text{\{prevalence\}\_dismod}}`

We then selected 17 countries based on four conditions: 1) ranking of 4 or 5 stars on the system for assessing the quality of VR data; 2) prevalence data available from the literature were included in
the DisMod-MR estimation; 3) prevalence rate ≥ 0.005; and, 4) CSMR ≥ 0.00002. Using information from these countries as input data, we ran a MR-BRT model of logEMR on sex, a cubic spline of age, and
Expand Down Expand Up @@ -209,11 +209,11 @@ States Data
- Notes
* - All
- cause-specific mortality (CSMR)
- :math:`\frac{\text{deaths_c500}}{\text{population}}`
- :math:`\frac{\text{deaths\_c500}}{\text{population}}`
- Post CoDCorrect cause-level CSMR
* - S
- Prevalence
- :math:`1 - \text{prev_c500}`
- :math:`1 - \text{prev\_c500}`
-
* - A
- Prevalence
Expand All @@ -225,15 +225,15 @@ States Data
-
* - A
- excess mortality
- :math:`{emr}_m9366`
- emr_m9366
-
* - S
- disability weight
- 0
-
* - A
- disability weight
- :math:`\frac{1}{\text{{prevalence}_c500}} \times \sum\limits_{s \in \text{sequelae}} \text{disability_weight}_s \cdot \text{prevalence}_s`
- :math:`\frac{1}{\text{{prevalence}\_c500}} \times \sum\limits_{s \in \text{sequelae}} \text{disability\_weight}_s \cdot \text{prevalence}_s`
-


Expand All @@ -252,7 +252,7 @@ Transition Data
* - 1
- S
- A
- :math:`{incidence}_c500`
- incidence_c500
- This is cause-level incidence which is equivalent to the “population rate”


Expand All @@ -267,35 +267,35 @@ Data Sources
- Source
- Description
- Notes
* - :math:`{prevalence}_c500`
* - prevalence_c500
- como
- Prevalence of atrial fibrillation
-
* - :math:`{deaths}_c500`
* - deaths_c500
- codcorrect
- Deaths from atrial fibrillation
-
* - :math:`{incidence}_c500`
* - incidence_c500
- como
- Incidence of atrial fibrillation
- This is the population incidence rate for atrial fibrillation
* - population
- demography
- Mid-year population for given age/sex/year/location
-
* - :math:`{sequelae}_c500`
* - sequelae_c500
- gbd_mapping
- List of 2 sequelae for atrial fibrillation
-
* - :math:`prevalence_{s\{sid\}}`
* - :math:`\text{prevalence}_{s\{sid\}}`
- como
- Prevalence of sequela with id sid
-
* - :math:`disability-weight_{s\{sid\}}`
* - :math:`\text{disability-weight}_{s\{sid\}}`
- YLD appendix
- Disability weight of sequela with id sid
-
* - :math:`{emr}_m9366`
* - emr_m9366
- dismod-mr 2.1
- excess mortality rate of atrial fibrillation
-
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -188,19 +188,19 @@ team is located in the following folder:
* - csmr_c543
- Cause-specific mortality rate for Alzheimer's disease and other
dementias
- :math:`\frac{\text{deaths_c543}}{(\text{population}) \cdot (\text{1 year})}`
- :math:`\frac{\text{deaths\_c543}}{(\text{population}) \cdot (\text{1 year})}`
- Calculated automatically by Vivarium Inputs
* - emr_c543
- Excess mortality rate for Alzheimer's disease and other dementias
- :math:`\frac{\text{csmr_c543}}{\text{prevalence_c543}}`
- :math:`\frac{\text{csmr\_c543}}{\text{prevalence\_c543}}`
- Calculated automatically by Vivarium Inputs
* - 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.
* - :math:`\text{disability_weight}_s`
* - :math:`\text{disability\_weight}_s`
- Disability weight of sequela :math:`s`
- YLD Appendix
- For reference, the values are:
Expand Down Expand Up @@ -263,8 +263,8 @@ table.
- Added onto mortality hazard for simulants with AD
* - AD
- disability weight
- :math:`\sum_\limits{s\in \text{sequelae_c543}}
\text{disability_weight}_s \cdot \text{prevalence}_s`
- :math:`\sum\limits_{s\in \text{sequelae\_c543}}
\text{disability\_weight}_s \cdot \text{prevalence}_s`
- Prevalence-weighted average disability weight over sequelae,
computed automatically by Vivarium Inputs. Used to calculate
YLDs.
Expand All @@ -286,7 +286,7 @@ table.
* - i_AD
- S
- AD
- :math:`\frac{\text{incidence_rate_c543}}{\text{1 - prevalence_c543}}`
- :math:`\frac{\text{incidence\_rate\_c543}}{\text{1 - prevalence\_c543}}`
- Compute susceptible population incidence rate from GBD's "total
population incidence rate." Conversion is automatic when using
the get_measure function in Vivarium Inputs.
Original file line number Diff line number Diff line change
Expand Up @@ -495,7 +495,7 @@ table below:
artifact key
``cause.alzheimers_consistent.cause_specific_mortality_rate``
- Defined to be :math:`f \cdot p_\text{dementia}`, where :math:`f` and
:math:`p_\text{dementa}` are the calibrated excess mortality rate of AD
:math:`p_\text{dementia}` are the calibrated excess mortality rate of AD
and prevalence of AD dementia, respectively. Since :math:`f` is derived
from emr_m24351 from DisMod, this "CSMR" is **not** necessarily a true
"cause-specific" mortality rate, as it will include deaths *associated*
Expand Down Expand Up @@ -533,7 +533,7 @@ table below:
- s454: 0.449 (0.304-0.595)
* - :math:`\text{DW}_\text{c543}`
- Average disability weight of AD dementia
- :math:`\sum_\limits{s\in \text{sequelae\_c543}}
- :math:`\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
Expand Down
2 changes: 1 addition & 1 deletion docs/source/models/causes/aortic_aneurysm/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -125,7 +125,7 @@ States Data
- Notes
* - All
- cause-specific mortality (CSMR)
- :math:`\frac{\text{deaths_c501}}{\text{population}}`
- :math:`\frac{\text{deaths\_c501}}{\text{population}}`
- Post CoDCorrect cause-level CSMR


Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -165,7 +165,7 @@ State and Transition Data Tables
-
* - C
- excess mortality rate
- :math:`\frac{\text{deaths_c380}}{\text{population} \,\times\, \text{prevalence_c380}}`
- :math:`\frac{\text{deaths\_c380}}{\text{population} \,\times\, \text{prevalence\_c380}}`
- = (cause-specific mortality rate) / prevalence
* - C
- disability weight
Expand All @@ -189,7 +189,7 @@ State and Transition Data Tables
- this is a fatal-only model
* - All
- cause-specific mortality rate
- :math:`\frac{\text{deaths_c380}}{\text{population}}`
- :math:`\frac{\text{deaths\_c380}}{\text{population}}`
-

.. list-table:: Transition Data
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -89,11 +89,11 @@ State and Transition Data Tables
-
* - C
- excess mortality rate
- :math:`\frac{\text{deaths_c382}}{\text{population} \,\times\, \text{prevalence_c382}}`
- :math:`\frac{\text{deaths\_c382}}{\text{population} \,\times\, \text{prevalence\_c382}}`
- = (cause-specific mortality rate) / prevalence
* - C
- disability weight
- :math:`\displaystyle{\sum_{s\in \text{sequelae_c382}}} \scriptstyle{\text{disability_weight}_s \,\times\, \text{prevalence}_s}`
- :math:`\displaystyle{\sum_{s\in \text{sequelae\_c382}}} \scriptstyle{\text{disability\_weight}_s \,\times\, \text{prevalence}_s}`
- = average disability weight over all sequelae
* - F
- prevalence
Expand All @@ -113,7 +113,7 @@ State and Transition Data Tables
-
* - All
- cause-specific mortality rate
- :math:`\frac{\text{deaths_c382}}{\text{population}}`
- :math:`\frac{\text{deaths\_c382}}{\text{population}}`
-

.. list-table:: Transition Data
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -119,11 +119,11 @@ Data Descriptions
-
* - C
- excess mortality rate
- :math:`\frac{\text{deaths_c384}}{\text{population} \,\times\, \text{prevalence_c384}}`
- :math:`\frac{\text{deaths\_c384}}{\text{population} \,\times\, \text{prevalence\_c384}}`
-
* - C
- disability weight
- :math:`\displaystyle{\sum_{s\in \text{sequelae_c384}}} \scriptstyle{\text{disability_weight}_s \,\times\, \text{prevalence}_s}`
- :math:`\displaystyle{\sum_{s\in \text{sequelae\_c384}}} \scriptstyle{\text{disability\_weight}_s \,\times\, \text{prevalence}_s}`
-
* - F
- prevalence
Expand All @@ -143,7 +143,7 @@ Data Descriptions
-
* - All
- cause-specific mortality rate
- :math:`\frac{\text{deaths_c384}}{\text{population}}`
- :math:`\frac{\text{deaths\_c384}}{\text{population}}`
-


Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -124,15 +124,15 @@ Data Description
-
* - I
- excess mortality rate
- :math:`\frac{\text{deaths_c383}}{\text{population} \times \text{prevalence_c383}}`
- :math:`\frac{\text{deaths\_c383}}{\text{population} \times \text{prevalence\_c383}}`
- = (cause-specific mortality rate) / prevalence
* - I
- disability weights
- :math:`\displaystyle{\sum_{s\in \text{sequelae_c383}}} \scriptstyle{\text{disability_weight}_s \,\times\, \text{prevalence}_s}`
- :math:`\displaystyle{\sum_{s\in \text{sequelae\_c383}}} \scriptstyle{\text{disability\_weight}_s \,\times\, \text{prevalence}_s}`
- = average disability weight over all sequelae
* - ALL
- cause specific mortality rate
- :math:`\frac{\text{deaths_c383}}{\text{population}}`
- :math:`\frac{\text{deaths\_c383}}{\text{population}}`
-


Expand Down
6 changes: 3 additions & 3 deletions docs/source/models/causes/copd/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -180,11 +180,11 @@ States Data
- Notes
* - All
- cause-specific mortality (CSMR)
- :math:`\frac{\text{deaths_c509}}{\text{population}}`
- :math:`\frac{\text{deaths\_c509}}{\text{population}}`
- Post CoDCorrect cause-level CSMR
* - S
- prevalence
- :math:`1-\text{prevalence_c509}`
- :math:`1-\text{prevalence\_c509}`
-
* - C
- prevalence
Expand All @@ -204,7 +204,7 @@ States Data
-
* - C
- disability weight
- :math:`\frac{1}{\text{prevalence_c509}} \times \sum\limits_{s \in sequelae} \text{disability_weight}_s \times \text{prevalence}_s`
- :math:`\frac{1}{\text{prevalence\_c509}} \times \sum\limits_{s \in sequelae} \text{disability\_weight}_s \times \text{prevalence}_s`
-

Transition Data
Expand Down
6 changes: 3 additions & 3 deletions docs/source/models/causes/diabetes/index.rst
Original file line number Diff line number Diff line change
Expand Up @@ -218,7 +218,7 @@ States Data
- Notes
* - All
- cause-specific mortality rate (CSMR)
- :math:`\frac{\text{deaths_c976}}{\text{population}}`
- :math:`\frac{\text{deaths\_c976}}{\text{population}}`
- Post CoDCorrect cause-level CSMR, type 2 only
* - S
- prevalence
Expand All @@ -234,15 +234,15 @@ States Data
-
* - P
- excess mortality rate
- :math:`\frac{\text{csmr_976}}{\text{prevalence_976}}`
- :math:`\frac{\text{csmr\_976}}{\text{prevalence\_976}}`
- Cannot use EMR from overall DM model as it represents combination of risk for type 1 and type 2
* - S
- disabilty weights
- 0
-
* - P
- disability weights
- :math:`\frac{1}{\text{prevalence_c976}} \times \sum\limits_{s \in sequelae} \text{disability_weight}_s \times \text{prevalence}_s`
- :math:`\frac{1}{\text{prevalence\_c976}} \times \sum\limits_{s \in sequelae} \text{disability\_weight}_s \times \text{prevalence}_s`
-

Transition Data
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -128,11 +128,11 @@ Data Description
-
* - I
- excess mortality rate
- :math:`\frac{\text{deaths_c302}}{\text{population} \,\times\, \text{prevalence_c302}}`
- :math:`\frac{\text{deaths\_c302}}{\text{population} \,\times\, \text{prevalence\_c302}}`
-
* - I
- disability weight
- :math:`\displaystyle{\sum_{s\in \text{sequelae_c302}}} \scriptstyle{\text{disability_weight}_s \,\times\, \text{prevalence}_s}`
- :math:`\displaystyle{\sum_{s\in \text{sequelae\_c302}}} \scriptstyle{\text{disability\_weight}_s \,\times\, \text{prevalence}_s}`
-
* - S
- prevalence
Expand All @@ -152,7 +152,7 @@ Data Description
-
* - All
- cause-specific mortality rate
- :math:`\frac{\text{deaths_c302}}{\text{population}}`
- :math:`\frac{\text{deaths\_c302}}{\text{population}}`
-

.. list-table:: Transition Data
Expand All @@ -167,7 +167,7 @@ Data Description
* - i
- S
- I
- :math:`\frac{\text{incidence_rate_c302}}{1-\text{prevalence_c302}}`
- :math:`\frac{\text{incidence\_rate\_c302}}{1-\text{prevalence\_c302}}`
- We transform incidence to be a rate within the susceptible population.
* - r
- I
Expand Down
Original file line number Diff line number Diff line change
Expand Up @@ -181,11 +181,11 @@ Data Descriptions
-
* - I
- excess mortality rate
- :math:`\frac{\text{deaths_c302}}{\text{population} \,\times\, \text{prevalence_I}}`
- :math:`\frac{\text{deaths\_c302}}{\text{population} \,\times\, \text{prevalence\_I}}`
- Use prevalence calculated for the I state in the row above
* - I
- disability weight
- :math:`\displaystyle{\sum_{s\in \text{sequelae_c302}}} \scriptstyle{\text{disability_weight}_s \,\times\, \text{prevalence}_s}`
- :math:`\displaystyle{\sum_{s\in \text{sequelae\_c302}}} \scriptstyle{\text{disability\_weight}_s \,\times\, \text{prevalence}_s}`
-
* - S
- prevalence
Expand All @@ -205,7 +205,7 @@ Data Descriptions
-
* - All
- cause-specific mortality rate
- :math:`\frac{\text{deaths_c302}}{\text{population}}`
- :math:`\frac{\text{deaths\_c302}}{\text{population}}`
-

.. list-table:: Transition Data
Expand All @@ -220,7 +220,7 @@ Data Descriptions
* - i
- S
- I
- :math:`\frac{\text{incidence_rate_c302}}{1-\text{incidence_rate_c302}*(\text{duration_c302} / 365)}`
- :math:`\frac{\text{incidence\_rate\_c302}}{1-\text{incidence\_rate\_c302}*(\text{duration\_c302} / 365)}`
- We transform incidence to be a rate within the susceptible population under the assumption that prevalence ~= incidence * duration.
* - r: USED IN CIFF AND IV IRON SIMULATIONS AS WELL AS MODELS 1-11 OF NUTRITION OPTIMIZATION SIMULATION
- I
Expand Down
Loading
Loading