Hypothetical Alzheimer’s Treatment
Abbreviation |
Definition |
Note |
|---|---|---|
BBBM |
Blood-based biomarker |
BBBM tests measure blood plasma protein levels and are less invasive than CSF (Cerebrospinal Fluid) or PET (Positron Emission Topography) tests |
MCI |
Mild cognitive impairment |
Intervention Overview
The hypothetical treatment intervention is triggered by a positive BBBM test, and has the effect of slowing the progression from pre-clinical to MCI state via the BBBM to MCI transition hazard rate h_BBBM→MCI. In the baseline scenario, h_BBBM→MCI equals the time-dependent hazard function \(h_{MCI}\), which in the treatment scenario is multiplied by a hazard ratio \(R_h\) < 1 when a simulant has an active treatment effect in order to slow the progression. This effect can wane over time (udpated each time step) and when the effect fully expires, \(R_h\) returns to 1.
This treatment is hypothetical and we don’t have confirmed information about the mechanism.
Outcome |
Effect |
Modeled? |
Note |
|---|---|---|---|
BBBM to MCI transition hazard rate (h_BBBM→MCI) |
Adjust multiplicatively using hazard ratio R_h |
Yes |
Vivarium Modeling Strategy
The diagram above illustrates how a simulant should progress through the various testing and treatment related states defined by the client. Each simulant may transition to a new state on each time step.
Most states have a fixed duration (a multiple of the time step length) where simulants will transition after \(\text{duration} / \text{time step}\) time steps. The duration is marked in the state node in brackets eg [6 mo]. As desribed in the testing intervention, some simulants in the BBBM test eligible state may transition to tested immediately (low propensity value), some may always self-transition (ie, never get tested, high propensity value), and some may self-transition for some number of time steps but eventually transition to tested as a result of the time-specific testing rate increasing.
Some states have zero duration, illustrated with a dashed box (rather than the solid ovals for states with nonzero durations). Transitions from a state with zero duration are illustrated with a dashed line. If a simulant transitions to a zero-duration state on a time step, they should also immediately continue to the next state during that same time step, as a part of the same transition.
For example, a simulant in BBBM test eligible who is tested and moves to BBBM test received would then immediately move to one of that state’s two sinks, and would even move directly to another state during the same transition/ time step on a positive test.
The “Months to discontinuation” state randomly assigns a number of months the simulant will be on treatment before discontinuing. The number of months then determines the duration of time with full and waning treatment effect. For example, if a simulant discontinues after 4 months, they would have (4/9) * 6 years of full effect, or 2.67 which we round to the nearest 6 month interval, which is 2.5 years.
Below are tables with details on how to model these states and transitions, and necessary data values. The value of h_BBBM→MCI in the cause model is now updated to be equal to \(h_{adj} = h_{MCI} \cdot R_h\), where \(h_{adj}\) is the intervention-adjusted hazard rate used for progression to MCI, \(h_{MCI}\) is the time-dependent hazard function and \(R_h\) is defined below.
Variable |
Definition |
Source or value |
Notes |
|---|---|---|---|
\(\text{prop}_I\) |
Simulant lifetime treatment “initiation propensity” |
Drawn uniformly from \([0,1)\) |
Lower value means more likely to initiate testing. Independent from testing propensities. |
\(I\) |
Time-varying treatment initiation rate |
The percent of patients with a positive BBBM test who initiate treatment will vary over time – but will not vary by age, sex, or location. We will use a piecewise linear ramp-up with knots at the following (year, level) values: (2022.0, 0), (2027.0, 0), (2035.5, 30), (2100.0, 80), (2101.0, 80). This captures the CSU client’s specification that “30% of eligible patients initiate by 2035, with a steady increase to 80% by 2100, for all countries,” and that treatment should first be available in 2027, slowly ramping up to 30% in 2035. |
|
\(D_t\) |
Months to discontinuation |
A full course of treatment is 9 months. We assume simulants discontinue evenly for each monthly injection. The months to discontinuation will be assigned a uniformly distributed whole number between 1 and 8 inclusive. |
|
\(R_h\) |
Effect hazard ratio |
1 if simulant has never recieved treatment or has transitioned to the No treatment effect state after completing or discontinuing treatment. Set to R_d on transition to a Full treatment effect state, and adjusted linearly during Waning treatment effect states. See below table for waning value details. |
\(R_h \cdot h_{MCI} = h_{adj}\), adjusting h_BBBM→MCI. |
\(R_d\) |
Draw-specific effect size value |
Drawn uniformly from [.4, .6] |
The effect size value will be the same for all simulants in a single draw. |
State |
Notes |
Modeling |
|---|---|---|
BBBM test eligible |
||
BBBM test received |
Zero duration. Independent random draw to determine whether test is positive or negative |
|
BBBM test positive |
Zero duration. \(\text{prop}_I < I\): initiate. \(\text{prop}_I >= I\): don’t initiate. |
|
BBBM test negative |
Fixed duration |
|
Waiting for treatment |
Fixed duration |
|
Receiving treatment |
Treatment effect is instantaneous. See Assumptions and Limitations for info about treatment/discontinuation timing. |
Zero duration. Independent random draw to determine whether simulant completes or discontinues treatment. |
Months to discontinuation |
See \(D_t\) in the Data values and sources table above for instructions on assigning the number of months to discontinuation |
Zero duration. Independent random draw to determine how many months of treatment simulant receives before discontinuation. |
Full treatment effect LONG |
Treatment takes effect exactly 6 months after receiving a positive BBBM test (if \(\text{prop}_I < I\)) |
On transition to this state, \(R_h = R_d\). Set \(h_{adj} = R_h \cdot h_{MCI}\), slowing progression to MCI. Transition from this state after the fixed duration. |
Full treatment effect SHORT |
Same effect size as in Full treatment effect LONG but with a shorter fixed duration. The duration is dependent on the time of discontinuation, as outlined above. |
|
Waning treatment effect LONG |
On every time step where the simulant ends the time step in this state (i.e., don’t do it on the final transition to the No treatment effect state), increase \(R_h\) by \(\frac{(1 - R_d)}{s}\), where \(s\) is the number of time steps in this state’s duration. This will decrease the effect size linearly until reaching \(R_h = 1\) on the last time step in this state. Set \(h_{adj} = R_h \cdot h_{MCI}\). Transition from this state after the fixed duration. |
|
Waning treatment effect SHORT |
Same effect size as in Waning treatment effect LONG but with a shorter fixed duration. The duration is dependent on the time of discontinuation, as outlined above. |
|
No treatment effect |
\(R_h\) should equal 1 on the first time step the simulant spends in this state. So \(h_{adj} = h_{MCI}\) |
Initialization
Since \(I\) is 0 until 2027, on simulation initialization no simulants have received treatment. We also assume that when simulants are initialized into the simulation (even after 2027), they have not previously initiated treatment, despite this being theoretically possible due to false positive BBBM tests (see assumptions and limitations below).
Outcomes
Outcome |
Effect size measure |
Effect size |
Note |
|---|---|---|---|
Full treatment effect |
Hazard ratio |
Uniform distribution in [.4, .6] |
Duration depends on if simulant completes or discontinues treatment |
Waning treatment effect |
Hazard ratio |
Linear increase during duration from full treatment effect hazard ratio to 1 |
Duration depends on if simulant completes or discontinues treatment |
Assumptions and Limitations
Note
People in the susceptible state (who are not modeled in Vivarium) may also initiate treatment due to false positive BBBM tests. We count these “incorrectly initiated” treatments outside the Vivarium simulation using a multistate life table (MSLT) model.
Those who do not initiate treatment following their first positive BBBM test result, or those who discontinue, will never take the intervention, so propensity can be assigned for simulant lifetime
Treatment occurs instantaneously (i.e., the duration of the “receiving treatment” period is zero), following a six-month waiting period from time of BBBM test. So, treatment takes effect exactly six months after BBBM testing. This interprets the following two client specifications: “The treatment takes immediate full effect in the first 6-month time step” and “There is an average of 6 months between a positive BBBM test result and initiating treatment”. We simplify “average of 6 months” to a fixed 6 month duration for all simulants. Treatment discontinuation only affects the duration of time the treatment will last, not the immediate effect size, so it is consistent with the client’s assumptions to model discontinuation occurring instantaneously during the transient “receiving treatment” and “months to discontinuation” states as above.
A simulant in the susceptible state who incorrectly initiates treatment may actually receive some benefit from this treatment. Namely, they may transition to the BBBM-AD state during the period of 1.89–17 years (depending on months to discontinuation) when the treatment still has an effect. However, our MSLT model does not track simulants’ treatment effect duration, and the Vivarium simulation assumes that no simulants have been treated when they are initialized, so our simulation does not capture this additional benefit. Since the BBBM test is currently assumed to have a very high specificity, there are very few false positive tests, so the effects of modeling this additional benefit would be small.