Alzheimers/calibration docs update by aflaxman · Pull Request #1871 · ihmeuw/vivarium_research

aflaxman · 2025-12-19T05:56:49Z

Update the Alz cause model docs, and add a section about using a system of ODEs to calibrate the model.

- Add "Calibrating Consistent Rates" section describing the NumPyro/JAX Bayesian calibration approach from consistent_rates.py - Update state data tables to use calibrated conditional prevalences (δ_BBBM, δ_MCI) instead of duration-based ratios - Update GBD references from 2021 to 2023 - Simplify Vivarium Modeling Strategy section, removing Model 4/5 references and explaining that BBBM-AD and MCI-AD require calibration - Fix LaTeX rendering (use arrow notation instead of escaped underscores) 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

- Rename "presymptomatic" to "pre-clinical" throughout - Clarify that excess mortality comes from dementia envelope but only incidence and prevalence are multiplied by AD proportion - Remove outdated MCI-AD age restriction notes - Update BBBM-AD state definition to note absence of cognitive impairment - Reorganize calibration reference for clarity 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

…d_2021/index.rst Co-authored-by: SylLutze <108029462+SylLutze@users.noreply.github.com>

NathanielBlairStahn · 2025-12-20T02:50:13Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

-      * 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)


What's the reason for deleting this? I think this is the only place where we documented how we computed 25-30 for the youngest age group we need to simulate.

Instead of approximating this with an algebraic expression based on the average durations of MCI, it is now being generated through the calibration optimization, so "10.2 years" years is no longer relevant. The optimization starts at age 30, though, so I could specify that here. (I could also include age group 25-30 in the optimization!)

Ok, I was confused because I thought the population model was still doing what the documentation says, which implies the 10.2-year duration. If the BBBM incidence rate is now 0 for age < 30, we shouldn't need the 25-30 age group anymore, so we should drop that from the sim. And it might be worth still noting here that the youngest possible age for MCI is 30 because that's now the youngest possible age for BBBM incidence.

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

NathanielBlairStahn · 2025-12-20T03:12:14Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+      see :math:`h_\text{MCI}(t)` in `Data Values and Sources`_
+  * - :math:`h_{\text{MCI} \to D}`
+    - Hazard rate of transitioning from MCI-AD to AD-dementia
+    - Constant hazard: :math:`1 / \Delta_\text{MCI}`


$\Delta_\text{MCI}$ has not yet been defined at this point, so if you want to write it here, maybe add a note that it's defined below.

NathanielBlairStahn · 2025-12-20T03:58:11Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

-      many simulants to add into the BBBM-AD state on each time step.
-  * - i_MCI
+    - From :ref:`rate calibration <cause_alzheimers_rate_calibration>`.
+      When modeling only AD simulants, this is used implicitly by the


Is the hazard rate you calculated actually used by the population model, or do we essentially recompute it using a different method? Should the population model just be using the rate you calculated instead of doing all the convoluted calculations we're doing to get $\lambda_{g,t}$?

The population model uses this rate, it is not actually used in the disease model. I will try to make that clearer here.

Ok, it sounds like you're saying that this calibrated rate is in fact being used by the population model. I was confused because this contradicts the documentation for the population model, which still says that we use approximations to back-calculate the simulant entrance rate from the Alzheimer's incidence rate. So how exactly are you using this new incidence rate instead? Did you just replace the artifact key that gets multiplied by the model scale and timestep? Presumably with $h_{S \to \text{BBBM}}$ times the forecasted population for the year? If that's what's happening, we need to update the population model documentation to specify this.

As discussed on 1/7, I will work on a PR to edit the population model documentation to reflect this change.

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

NathanielBlairStahn · 2025-12-20T04:06:57Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst


 ==================================================================
-Alzheimer's disease  with presymptomatic and MCI stages (GBD 2021)
+Alzheimer's disease  with pre-clinical and MCI stages (GBD 2023)


I think "preclinical" is usually written without a hyphen, but it's probably fine to leave it.

confirmed, I will change

NathanielBlairStahn · 2025-12-20T04:16:19Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

-  above formula applies to age groups 40+ since this is where
-  prevalence_AD and :math:`\Delta_\text{AD}` are nonzero. For ages
-  30--39, use the value of :math:`p_\text{(all AD states)}` for age
-  group 40--44; for ages <30, set :math:`p_\text{(all AD states)} = 0`.


Presumably your consistent rates code will save zeros in the appropriate age groups, so we don't need to explicitly specify this anymore?

Oh, I wonder what is happening outside of the age groups I have saved; I bet that they are extrapolated from the age groups I do have, so they might be non-zero. I will add a TODO about that to my consistent rates with severity branch.

Could that explain the weird bump in incidence and prevalence that we were seeing in the younger ages?

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

NathanielBlairStahn · 2025-12-20T04:27:35Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

  * - :math:`\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.
  * - :math:`\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
    - :math:`\Delta_\text{BBBM} + \Delta_\text{MCI} + \Delta_\text{AD}`
    -


Are $\Delta_\text{AD}$ and $\Delta_\text{(all AD states)}$ even used anymore, since you directly defined the conditional probabilities instead?

NathanielBlairStahn · 2025-12-20T05:18:18Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+  m_\text{all}(a) = m(a) + f(a) \cdot p_\text{dementia}(a)
+
+**ODE Consistency Constraints.** The calibration enforces consistency by
+solving a 5-compartment ODE system from age :math:`a` to :math:`a + 5` and


I don't know what it means to solve an ODE system "from age $a$ to $a+5$"...

Yeah, I really have no idea how you're dealing with different age groups, so it would be good to explain that somewhere.

Does my modest edit help? I think we can probably make it clearer through discussion and then figure out how to write it.

NathanielBlairStahn · 2025-12-20T05:20:20Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+
+**ODE Consistency Constraints.** The calibration enforces consistency by
+solving a 5-compartment ODE system from age :math:`a` to :math:`a + 5` and
+penalizing deviations between ODE-predicted values and calibrated parameters.


What's the difference between an "ODE-predicted value" and a "calibrated parameter"? Are "calibrated parameters" the given data that you are trying to match, or did you have to use some additional process to calibrate the target values first?

It is basically the "method of multiple shootings", which is a cool hack I learned from Brad Bell. I will elaborate in the docs.

NathanielBlairStahn · 2025-12-20T05:27:05Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+- :math:`\delta_\text{BBBM}`, :math:`\delta_\text{MCI}`: Conditional
+  prevalences of BBBM and MCI states among AD cases
+- :math:`h_{S \to \text{BBBM}}`: Transition rate from susceptible to BBBM
+- :math:`i`: Population incidence rate of dementia


I don't see $i$ used anywhere below (unless I'm missing it). Is it the same as $h_{\text{MCI} \to D}$? Or is it the same as i_dementia in your input data table?

It is different than h_MCI->D, but related. But I made it a parameter and used consistency constraints to get the relationship instead of enforcing it deterministically (h_MCI->D has a denominator of MCI person years, while i has a denominator of any person years).

Ok, that makes sense. It might be better to call it the "total-population incidence rate" for extra clarity, since that's what we call it elsewhere in the docs.

NathanielBlairStahn · 2025-12-20T06:06:20Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+**Numerical Methods.** We solve the ODE using diffrax (Dopri5) and sample using
+NUTS with 500 warmup and 500 sample iterations.
+
+.. list-table:: Calibration Input Data


tl;dr: If these are the same as some of the values in the Data Values and Sources table above, you should rename things to be consistent (or at least explicitly specify a mapping from one to the other). And rename "f" so that the input EMR is not called the same thing as the output EMR.
...

Are these all values we get directly from GBD? It would be good to specify the sources more explicitly.

Is p_dementia the same as prevalence_AD in the Data Values and Sources table above? I.e., the total prevalence of the dementia envelope multiplied by the proportion Alzheimer's that we got from the dementia modelers?

Similarly, is i_dementia the same as incidence_AD from the Data Values and Sources table?

If so, we probably shouldn't have two different notations for the same thing -- if you like your notation better, you could rename the variables in the Data Values and Sources table. Except in that table it seems more important to distinguish AD from other types of dementia...

Is f the excess mortality rate from the dementia envelope? If so, it might be better to call it emr_m24351, following our usual naming convention for data. Especially because you are already using $f$ for the output of the calibration, so we should probably have a different notation for the input data.

Presumably m_all is the mortality data from FHS? I.e., the same as acmr in the Data Values and Sources table above? If so, it seems like you can just rename "acmr" in that table to $m_\text{all}$ to be consistent with this section. Unless you want a different variable name here because it's referring specifically to one year of data (2025) instead of all years.

Also, how exactly is the input data used? E.g., are the values treated as constraints that must stay fixed throughout the calibration, or are they treated as initial values that then get updated to make things consistent?

It seems like maybe p_dementia, i_dementia, and the EMR are used as initial values, and m_all is a constraint that remains fixed, but I'm not sure.

There is probably a way to clean this up, I think I have some confusing redundancy here. These are the values to calibrate the ODE to (these are in addition to the consistency constraints described above)

NathanielBlairStahn · 2025-12-20T06:11:08Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+  :widths: 15 35 30 20
+  :header-rows: 1
+
+  * - Variable


If these are the same variables you're using in your equations above, you should use the same font. E.g., $p_\text{dementia}$ instead of p_dementia. Unless you want a different notation because they're fixed input values instead of variables that you're solving for -- I'm not sure exactly how they're being used.

Let's discuss before I make the change, because maybe something else will be clearer.

NathanielBlairStahn · 2025-12-20T06:19:20Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+enforcing ODE-based consistency constraints.
+
+The calibration is implemented in ``consistent_rates.py`` in the
+vivarium_csu_alzheimers repository. We fit separate models for males and


Might as well link to the repository (or the specific file) here.

NathanielBlairStahn · 2025-12-20T06:34:56Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+- :math:`f`: Excess mortality rate
+- :math:`m`: Background (non-AD) mortality rate
+
+**Key Relationships.** Dementia prevalence derives from total AD prevalence:


What exactly is "Key" about these relationships? How are they being used?

I'm struggling to figure out exactly what's going on. Are $p_\text{dementia}(a)$ and $m_\text{all}(a)$ fixed input values, or are you solving for them? Are you using these equations to implicitly define $m$, $f$, $p$, and/or the $\delta$'s?

I guess it would be more accurate to call these definitions, rather than key relationships.

NathanielBlairStahn · 2025-12-20T06:45:37Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+**ODE Consistency Constraints.** The calibration enforces consistency by
+solving a 5-compartment ODE system from age :math:`a` to :math:`a + 5` and
+penalizing deviations between ODE-predicted values and calibrated parameters.
+The state variables are S (susceptible), BBBM, MCI, D (dementia), and


Aha! I couldn't figure out how the $\delta$'s related to your differential equations, but I think I just realized you should have equations like:

$\delta_\text{BBBM} = \frac{\text{BBBM}}{\text{BBBM + MCI} + D}$

$\delta_\text{MCI} = \frac{\text{BBBM}}{\text{BBBM + MCI} + D}$

$p = \frac{\text{BBBM + MCI + D}}{S + \text{BBBM + MCI} + D}$

$p_\text{dementia} = \frac{D}{S + \text{BBBM + MCI} + D}$

You should probably explicitly write (some subset of) these somewhere to clarify how everything is related.

NathanielBlairStahn · 2025-12-20T06:47:32Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+  \frac{dD}{dt} &= h_{\text{MCI} \to D} \cdot \text{MCI} - (m + f) \cdot D \\
+  \frac{dD_\text{new}}{dt} &= h_{\text{MCI} \to D} \cdot \text{MCI}
+
+The transition rates :math:`h_{\text{BBBM} \to \text{MCI}} = 1 / \Delta_\text{BBBM}`


As I noted above, this constant hazard differs from our definition of the non-constant hazard function above, so you should probably note that this is an approximation of our Weibull hazard function.

NathanielBlairStahn · 2025-12-20T07:00:04Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+solving a 5-compartment ODE system from age :math:`a` to :math:`a + 5` and
+penalizing deviations between ODE-predicted values and calibrated parameters.
+The state variables are S (susceptible), BBBM, MCI, D (dementia), and
+:math:`D_\text{new}` (cumulative incident dementia). The ODE system is:


Why do you need $D_\text{new}$?

To calculate the dementia incidence rate for calibration; I will elaborate.

NathanielBlairStahn · 2025-12-20T08:03:57Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+    \left(\log \hat\delta_\text{BBBM} - \log \delta_\text{BBBM}(a+5)\right)^2 +
+    \left(\log \hat\delta_\text{MCI} - \log \delta_\text{MCI}(a+5)\right)^2 +
+    \left(\log \hat p_\text{dementia} - \log p_\text{dementia}(a+5)\right)^2 +
+    \left(\log \hat\imath - \log i(a+2.5)\right)^2


Why does $i$ have $a+2.5$ whereas all the other variables have $a+5$?

Also, as noted above, how does $i$ relate to the differential equations?

I don't remember! I think there is something different about incidence and prevalence that made me think incidence at the midpoint of the interval would be better than at the endpoint.

NathanielBlairStahn · 2025-12-20T09:30:51Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+.. math::
+
+  \epsilon(a) = \sqrt{
+    \left(\log \hat\delta_\text{BBBM} - \log \delta_\text{BBBM}(a+5)\right)^2 +


Are the "hat" variables supposed to be evaluated at $a$? What's the difference between the "hat" and "no-hat" variables?

hat is what the ODE implies, no-hat is the parameters being optimized

NathanielBlairStahn · 2025-12-21T05:17:58Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+
+where :math:`\hat\delta_\text{BBBM}`, :math:`\hat\delta_\text{MCI}`,
+:math:`\hat p_\text{dementia}`, and :math:`\hat\imath` are derived from the ODE
+solution. The calibration applies a normal penalty :math:`\epsilon(a) \sim


I'm not sure what a "normal penalty" means. Does this mean that you are including the error term $\epsilon(a)$ as one of the variables in the joint distribution you're sampling from, and you're specifying that its prior is $\mathcal{N}(0, \sigma)$ with $\sigma = 0.005$ to ensure that it stays close to 0?

yes, exactly.

NathanielBlairStahn · 2025-12-29T07:02:58Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+females.
+
+**Model Parameters.** The NumPyro model defines 7 age-varying parameters, each
+with truncated normal priors on :math:`[0, 1]`:


Why do the rates $h_{S \to \text{BBBM}}$, $i$, $f$, and $m$ use priors supported on $[0,1]$? Shouldn't these a priori be supported on $[0,\infty)$?

I did not try other priors, and [0, inf] would be a fine alternative for rates.

NathanielBlairStahn · 2025-12-29T09:24:58Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+includes presymptomatic states (BBBM-AD and MCI-AD) not directly measured by
+GBD. To derive internally consistent rates for these states, we use Bayesian
+inference with NumPyro/JAX to fit disease progression rates to GBD data while
+enforcing ODE-based consistency constraints.


I think the biggest thing missing from this section is an explanation of your overall strategy for finding the consistent rates. This one-sentence summary is good if you want to give someone an idea of what you did without actually explaining it, but it's not sufficient to actually understand how your approach works. If I had to guess, here's my best attempt to reconstruct what you did:

You're doing an optimization, presumably to find the best possible values of the seven parameters listed in the "model parameters" section, subject to the constraints imposed by the system of ODEs. However, as noted elsewhere, I'm still not sure what data is being used as a fixed constraint (maybe all-cause mortality?) vs. as an initial value for one of the parameters in the optimization (maybe some of the dementia envelope data from DisMod?). And I also don't know whether you're treating different age groups completely independently, or whether solutions for different age groups are somehow coupled together, or what.

You're using Bayesian inference with MCMC, which means you must be sampling from some joint distribution. My best guess at what distribution you're sampling is the 8-dimensional distribution of the seven model parameters together with the variable $\epsilon(a)$ representing the value of the loss function for the optimization. Is that right? And if you're doing Bayesian inference, what are the likelihood function and the evidence/data that go into the calculation of the posterior distribution? Presumably these are somehow related to the system of ODEs, but I'm unclear exactly how to formulate the inference problem.

This seems like a clever idea to use Bayesian inference to do an optimization, but I'm not sure if I'm understanding correctly -- I could be way off with my attempt to fill in the details. My point is that there are a lot of details that are left to the imagination, and it would be helpful if you filled more of them in.

I've tried to adapt your thoughts to give future readers a head start in figuring this out.

NathanielBlairStahn · 2025-12-29T09:28:36Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+
+**Loss Function.** After solving the ODE from age :math:`a` to :math:`a + 5`,
+the calibration computes the root-sum-squared log-difference between ODE
+predictions and parameter values:


Maybe this is a small thing, but in what sense are the values from the ODEs "predictions"?

Perhaps it is more precise to say "After solving the ODE with initial values for age :math:a to find the ODE-implied values at :math:a + 5, the calibration computes the root-sum-squared log-difference between ODE-impled values and parameter values"

NathanielBlairStahn · 2025-12-29T09:33:45Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+    - ``cause.all_causes.cause_specific_mortality_rate``
+    - 2025
+
+.. list-table:: Calibrated Outputs (written to artifact for year 2025)


It looks like the values in this table correspond to the 7 variables in the "model parameters" section, except that you've added the ODE errors ($\epsilon(a)$, presumably), which makes sense, and the variable $m$ (background mortality rate) is missing. Why is $m$ missing?

I did not use m in the sim (it is calculated by the mortality component as m_all - CSMR); I did save CSMR, though, which I did not include in this table.

Then why does the data table list $m$ as one of the keys in the artifact?

Also, how did you calculate CSMR in your calibration? I don't see that explained anywhere.

NathanielBlairStahn · 2025-12-29T10:16:37Z

There are a few references to data values in the Data Sources table on the Alzheimer's Population page that will need to get updated based on the changes in this PR (e.g., $p_\text{(All AD states)}$, incidence_AD, and m_BBBM and m_MCI).

…d_2021/index.rst Co-authored-by: Nathaniel Blair-Stahn <ndbs@uw.edu>

NathanielBlairStahn · 2026-01-06T00:40:59Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+
+The transition rates :math:`h_{\text{BBBM} \to \text{MCI}} = 1 / \Delta_\text{BBBM}`
+and :math:`h_{\text{MCI} \to D} = 1 / \Delta_\text{MCI}` are fixed based on
+literature values in the data values table above and the assumption that the Weibull distribution is approximated acceptably by a constant for calibration purposes.


It's confusing to say the distribution can be approximated by a constant...

Suggested change

literature values in the data values table above and the assumption that the Weibull distribution is approximated acceptably by a constant for calibration purposes.

literature values in the data values table above and the assumption that the Weibull distribution is approximated acceptably by a constant hazard for calibration purposes.

NathanielBlairStahn · 2026-01-07T19:07:54Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+    - Background mortality rate (non-AD mortality)
+    - From :ref:`rate calibration <cause_alzheimers_rate_calibration>`,
+      artifact key ``cause.alzheimers_consistent.background_mortality_rate``
+    - Applies to all states. Derived from forecasts of all-cause mortality.


Is it possible to specify how this is derived from all-cause mortality together with the calibration? Currently, this data table lists ACMR as one of the needed data inputs for the model, but doesn't show it being used anywhere.

NathanielBlairStahn · 2026-01-07T19:14:38Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+  p\_\text{dementia} = \frac{D}{S + \text{BBBM + MCI} + D}
+
+
+**ODE Consistency Constraints.** The calibration produces consistent parameters by


I think this section should probably go before the non-ODE constraints, in order to introduce all the notation.

NathanielBlairStahn · 2026-01-07T19:24:24Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+solving a 5-compartment ODE system starting with initial conditions at from age :math:`a` to find the implied values at :math:`a + 5`; we include the squared difference between these implied values and the parameter values in the MCMC objective.  
+
+The state variables are S (susceptible), BBBM, MCI, D (dementia), and
+:math:`D_\text{new}` (cumulative incident dementia, which is used to calibrate the incidence rate of AD dementia). The ODE system is:


I still don't understand why $D_\text{new}$ is needed. Are you saying you need it to calculate $i$? Is it that the calculation of $i$ is done like this?

$$ \begin{align} i(a) &= h_{\text{MCI} \to D} \cdot \text{MCI} / (S + BBBM + MCI + D) \\ &= (dD_\text{new}/ dt) / (S + BBBM + MCI + D) \end{align} $$

If so, you should explicitly write that in the equation for $i$, which would make more sense if you re-order the sections as I suggested above. Or is it something else?

I guess I'm confused because if you have $m$, $f$, and $D$, then $D_\text{new}$ seems redundant based on your equations. Is it just a convenience to include it, or is there something you fundamentally can't do without it?

NathanielBlairStahn · 2026-01-10T01:05:28Z

docs/source/models/causes/alzheimers/presymptomatic_and_mci_gbd_2021/index.rst

+with additional evidence on state durations. See :ref:`below for details <cause_alzheimers_rate_calibration>`.
+
+To obtain Alzheimer's-specific estimates (excluding "other dementias"), we
+multiply the GBD 2023 dementia envelope by the proportion due to Alzheimer's


We'll need to explain that we also include 94% of mixed dementias, as specified in #1883

Se references in this comment.

aflaxman and others added 4 commits December 18, 2025 17:26

get the ODE into the docs, plus a little more

ebcde20

Merge branch 'main' into alzheimers/calibration-docs-update

5b4fab1

aflaxman requested review from NathanielBlairStahn, SylLutze and rmudambi December 19, 2025 05:57

NathanielBlairStahn added Vivarium modeling strategy Documentation for Vivarium modeling strategy update Add this tag to any section that is updated Alzheimers_sim Alzheimer's simulation for CSU, starting July 2025 labels Dec 19, 2025

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aflaxman and others added 4 commits December 31, 2025 13:49

Update docs/source/models/causes/alzheimers/presymptomatic_and_mci_gb…

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…d_2021/index.rst Co-authored-by: Nathaniel Blair-Stahn <ndbs@uw.edu>

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NathanielBlairStahn mentioned this pull request Jan 10, 2026

Alzheimers: Add mixed dementias #1883

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	literature values in the data values table above and the assumption that the Weibull distribution is approximated acceptably by a constant for calibration purposes.
	literature values in the data values table above and the assumption that the Weibull distribution is approximated acceptably by a constant hazard for calibration purposes.

		p\_\text{dementia} = \frac{D}{S + \text{BBBM + MCI} + D}


		ODE Consistency Constraints. The calibration produces consistent parameters by

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NathanielBlairStahn Dec 20, 2025 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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