.. Section title decorators for this document: ============== Document Title ============== Section Level 1 (#.0) +++++++++++++++++++++ Section Level 2 (#.#) --------------------- Section Level 3 (#.#.#) ~~~~~~~~~~~~~~~~~~~~~~~ Section Level 4 ^^^^^^^^^^^^^^^ Section Level 5 ''''''''''''''' The depth of each section level is determined by the order in which each decorator is encountered below. If you need an even deeper section level, just choose a new decorator symbol from the list here: https://docutils.sourceforge.io/docs/ref/rst/restructuredtext.html#sections And then add it to the list of decorators above. .. _intervention_hypothetical_alzheimers_treatment: ======================================== Hypothetical Alzheimer's Treatment ======================================== .. contents:: :local: :depth: 1 .. list-table:: Abbreviations :widths: 15 15 15 :header-rows: 1 * - 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 :ref:`BBBM to MCI transition hazard rate i_MCI <2021_cause_alzheimers_presymptomatic_mci_transition_data_table>`. In the baseline scenario, i_MCI equals the time-dependent hazard function :math:`h_{MCI}`, which in the treatment scenario is multiplied by a hazard ratio :math:`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, :math:`R_h` returns to 1. This treatment is hypothetical and we don't have confirmed information about the mechanism. .. list-table:: Affected Outcomes :widths: 15 15 15 15 :header-rows: 1 * - Outcome - Effect - Modeled? - Note * - BBBM to MCI transition hazard rate (:ref:`i_MCI <2021_cause_alzheimers_presymptomatic_mci_transition_data_table>`) - Adjust multiplicatively using hazard ratio :ref:`R_h ` - Yes - Vivarium Modeling Strategy -------------------------- .. graphviz:: digraph treatment_states { rankdir = TB; el [label="BBBM test eligible [variable]"] test [label="BBBM test received", style=dashed, shape=box] pos [label="BBBM test positive", style=dashed, shape=box] neg [label="BBBM test negative [3 y]"] wait [label="Waiting for treatment [6 mo]"] in_treat [label="Receiving treatment", style=dashed, shape=box] no_treat [label="No treatment effect [permanent]"] treat [label="Full treatment effect LONG [5 y]"] wane [label="Waning treatment effect LONG (update each step) [9 y]"] treat_short [label = "Full treatment effect SHORT [6 mo]"] wane_short [label = "Waning treatment effect SHORT (update each step) [2.5 y]"] el -> test [label = "tested"] el -> el [label = "not tested"] test -> pos [label = "(90%)", style=dashed] test -> neg [label = "(10%)", style=dashed] neg -> el [label = "test re-eligible"] pos -> wait [label = "decides to initiate treatment (I)", style=dashed] pos -> no_treat [label = "decides not to initiate treatment (1 - I)", style=dashed] wait -> in_treat [label = "begins treatment"] in_treat -> treat [label = "completes (90%)", style=dashed] in_treat -> treat_short [label = "discontinues (10%)", style=dashed] treat_short -> wane_short wane_short -> no_treat treat -> wane wane -> no_treat } 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 :math:`\text{duration} / \text{time step}` time steps. The duration is marked in the state node in brackets eg [6 mo]. As desribed in the :ref:`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 :math:`i_{MCI}` in the :ref:`cause model <2021_cause_alzheimers_presymptomatic_mci_transition_data_table>` is now updated to be equal to :math:`h_{adj} = h_{MCI} \cdot R_h`, where :math:`h_{adj}` is the intervention-adjusted hazard rate used for progression to MCI, :math:`h_{MCI}` is the :ref:`time-dependent hazard function <2021_cause_alzheimers_presymptomatic_mci_transition_data_table>` and :math:`R_h` is defined below. .. _alzheimers_intervention_treatment_data_table: .. list-table:: Data values and sources :widths: 15 15 30 15 :header-rows: 1 * - Variable - Definition - Source or value - Notes * - :math:`\text{prop}_I` - Simulant lifetime treatment "initiation propensity" - Drawn uniformly from :math:`[0,1)` - Lower value means more likely to initiate testing. Independent from testing propensities. * - :math:`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."" - * - :math:`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. - :math:`R_h \cdot h_{MCI} = h_{adj}`, adjusting :ref:`i_MCI <2021_cause_alzheimers_presymptomatic_mci_transition_data_table>`. * - :math:`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. .. list-table:: Testing and Treatment State and Transition Modeling :widths: 15 15 30 :header-rows: 1 * - State - Notes - Modeling * - BBBM test eligible - - See :ref:`testing intervention ` * - BBBM test received - - Zero duration. Random draw * - BBBM test positive - - Zero duration. :math:`\text{prop}_I < I`\: initiate. :math:`\text{prop}_I >= I`\: don't initiate. * - BBBM test negative - - Fixed duration * - Waiting for treatment - - Fixed duration * - Receiving treatment - Treatment period is instantaneous. See :ref:`alzheimers_intervention_treatment_assumptions` 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 :math:`\text{prop}_I < I`) - On transition to this state, :math:`R_h = R_d`. Set :math:`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 :math:`R_h` by :math:`\frac{(1 - R_d)}{s}`, where :math:`s` is the number of time steps in this state's duration. This will decrease the effect size linearly until reaching :math:`R_h = 1` on transition to the `No treatment effect` state. Set :math:`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 - - :math:`R_h` should equal 1 on the first time step the simulant spends in this state. So :math:`h_{adj} = h_{MCI}` Initialization ~~~~~~~~~~~~~~ Since :math:`I` is 0 until 2030, on simulation initialization no simulants have received treatment. Outcomes ~~~~~~~~ .. list-table:: Modeled Outcomes :widths: 15 15 15 15 :header-rows: 1 * - 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 .. _alzheimers_intervention_treatment_assumptions: 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.