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 i_MCI. In the baseline scenario, i_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 (i_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.
Below are tables with details on how to model these states and transitions, and necessary data values. The value of \(i_{MCI}\) 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- and location-specific treatment initiation rate |
Lilly: “The percent of patients with a positive BBBM test who initiate treatment will vary by location and over time – but will not vary by age or sex. In the US: 30% of eligible patients initiate (constant 2030-2100); Japan: 80% of eligible patients initiate (constant 2030-2100); all other countries: 40% of eligible patients initiate in 2030, increasing linearly to 70% by 2035, remaining constant at 70% until 2100.”” |
|
\(R_h\) |
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 i_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. Random draw |
|
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 period is instantaneous. See Assumptions and Limitations for info about treatment/discontinuation timing. |
Zero duration. Random draw |
Full treatment effect LONG |
Treatment takes effect exactly 6 months after recieving 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 |
|
Waning treatment effect LONG |
On every time step where the simulant started the time step in this state (ie, don’t do it on the initial transition), 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 transition to the No treatment effect 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 |
|
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 2030, on simulation initialization no simulants have received treatment.
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
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 (ie, the duration of the 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 Lilly 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 fixed 6 month duration for all simulants. Discontinuation occurs during this instantaneous treatment period.