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Copy file name to clipboardExpand all lines: docs/source/models/other_models/alzheimers_proportional_multistate_life_table/index.rst
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@@ -94,28 +94,28 @@ Each blank cell represents a subpopulation with a stored count.
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- Negative (0 y ago)
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- Neg (1 y)
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- Neg (2 y)
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* - 65
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- Female
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- Male
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- Female
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- Male
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Initializing the Population
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+++++++++++++++++++++++++++
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We initialize the susceptible population using the 2021 year forecasted population data :math:`P_{2021}` and the
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We initialize the susceptible population using the 2023 year forecasted population data :math:`P_{2023}` and the
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initial simulation "all states" Alzheimer's prevalence :math:`prev_{all}`. Our MSLT initial population is
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:math:`P_{2021} * (1 - prev_{all})`. This equation represents the non-simulation population at the start of the
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:math:`P_{2023} * (1 - prev_{all})`. This equation represents the non-simulation population at the start of the
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simulation period.
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The only adjustment needed is to modify the age group sizes. The initial population data :math:`P_Y` is from
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GBD and age groups span five years, eg 60-64 year olds. To simplify our annual timesteps, we divide
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these age groups into single year ages, eg 60 year olds, 61 year olds. We divide the five-year GBD
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GBD and age groups span five years, eg 65-69 year olds. To simplify our annual timesteps, we divide
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these age groups into single year ages, eg 65 year olds, 66 year olds. We divide the five-year GBD
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age group populations by five to get single-year age group populations.
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Since BBBM testing doesn't begin until 2030, the entire susceptible population is initialized to the
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Since BBBM testing doesn't begin until 2027, the entire susceptible population is initialized to the
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untested state.
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Model Scale
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We use an annual time step in order to best reflect our annual test rate targets.
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On each time step, new simulants must be added to the MSLT. The only way to enter the MSLT is to turn
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60 years old, since it models all 60-80 year-olds who are not in the Vivarium simulation (see below for more details).
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65 years old, since it models all 65-80 year-olds who are not in the Vivarium simulation (see below for more details).
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The existing populations must be aged one year, and those who transition to preclinical AD or die must
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be removed.
@@ -207,45 +207,49 @@ in the following sections.
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* - Neg (1 y)
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- On the next time step simulants will move to the negative 2 years ago state.
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* - Neg (2 y)
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- On the next time step 33% of simulants will be tested and move to either the positive state or negative 0 years ago state. The remaining 67% will move to negative 3 years.
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* - Neg (3 y)
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- On the next time step 50% of simulants will be tested and move to either the positive state or negative 0 years ago state. The remaining 50% will move to negative 4 years.
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* - Neg (4 y)
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- On the next time step simulants will move to either the positive state or negative 0 years ago state.
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Adding New Simulants
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--------------------
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We add the new susceptible 60 year old population on each time step using the same data sources
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We add the new susceptible 65 year old population on each time step using the same data sources
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from initialization, for the year of the current MSLT time step. For time steps after 2050, when our forecasted
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population data ends, we continue to intitialize new 60 year olds using the 2050 data.
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population data ends, we continue to intitialize new 65 year olds using the 2050 data.
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In other words, the overall population is :math:`P_Y * (1 - prev_{all})`.
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We use the 60-64 year old subpopulation and divide it by 5 to get a 60 year old population.
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We use the 65-69 year old subpopulation and divide it by 5 to get a 65 year old population.
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The current time-specific test rate will determine the fraction of the incident 60 year old population which
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The current time-specific test rate will determine the fraction of the incident 65 year old population which
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will be tested - the rest will be initialized to the untested state.
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Updating Age Groups
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-------------------
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On each time step, the table rows corresponding to each age are copied to the next age, eg 60 year olds males become
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61 year olds. 80 year olds are removed from the table and no longer tracked.
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On each time step, the table rows corresponding to each age are copied to the next age, eg 65 year olds males become
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66 year olds. 80 year olds are removed from the table and no longer tracked.
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Mortality
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---------
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Some fraction of the susceptible, 60-79 year old population dies each year. We calculate an
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Some fraction of the susceptible, 65-79 year old population dies each year. We calculate an
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age, year, sex and location specific background mortality rate from the year-specific forecasted ACMR
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and 2021 CSMR from the artifact. ACMR forecasts end in 2050.
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and 2023 CSMR from the artifact. ACMR forecasts end in 2050.
On each time step we apply this background mortality rate to all
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subpopulations in our table of susceptible 60-79 year olds, without varying by test or treatment status.
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subpopulations in our table of susceptible 65-79 year olds, without varying by test or treatment status.
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Removing Simulants Incident to Alzheimer's
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------------------------------------------
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Some fraction of the susceptible, 60-79 year old population transitions from the susceptible state to the preclinical
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Some fraction of the susceptible, 65-79 year old population transitions from the susceptible state to the preclinical
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state each year. We use the ``cause.alzheimers.susceptible_to_bbbm_transition_count`` artifact key as our source for
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age, year, sex and location specific transition counts. We divide these counts (which uses GBD age groups) by 5 to get
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one-year age groups.
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Updating Testing States
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-----------------------
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On each time step, simulants in the negative test states are advanced to the next negative test state. A fraction of
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incident 60 year olds that are selected for testing based on the current test rate, along with all simulants in the
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negative 2 years ago state from the previous time step. Additionally, a number :math:`U` of the untested state simualants are also
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On each time step, simulants in the negative test states are advanced to the next negative test state or receive testing. Simulants get repeat testing uniformly between 3 and 5 years after their first test. To implement this, we have 33% of simulants in the negative 2 year group move to testing and the rest move to the negative 3 year bucket. Then 50% of people in the negative 3 year bucket are tested and the rest more to negative 4 years. All simulants in negative 4 years are tested.
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A fraction of
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incident 65 year olds that are selected for testing based on the current test rate. Additionally, a number :math:`U` of the untested state simualants are also
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selected for testing based on the increase in test rate compared to last year, :math:`\Delta_{\text{test_rates}}`:
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:math:`U = \Delta_{\text{test_rates}} * \text{total_age_pop}`, where :math:`\text{total_age_pop}` is the sum of all simulants
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--------------------------------
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Once the total number of people selected for testing on the time step is determined from the various sources
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(incident 60 year olds, negative 2 years ago and untested), tests are conducted.
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(incident 65 year olds, negative 2 years ago and untested), tests are conducted.
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Per the test parameters from the client, the BBBM test has a 90% specificity. We move 90% of the simulants to the negative
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0 years ago state and 10% to the positive state.
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Per the test parameters from the client, the BBBM test has a 99.8% specificity. We move 99.8% of the simulants to the negative
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0 years ago state and 0.2% to the positive state.
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Based on the location- and year-specific :ref:`treatment initiation rate <alzheimers_intervention_treatment_data_table>`,
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we observe the number of treatment initations.
@@ -305,7 +310,7 @@ The below table summarizes the variables, data values and sources.
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