ALS Literature Review

Board, welcome to Session 002. You've all received the briefing. Here's where we are:

We spent the last week pulling literature across 4 tracks. The headline finding: our original hypothesis — that ALS progression is nonlinear — is already documented. Van Eijk et al. (2025, N=7,030) proved it decisively. Gordon (2010, N=1,884) showed it 15 years ago. The field knows.

And yet trials keep using linear ALSFRS-R slope as their primary endpoint. Relyvrio (failed 2024), the HEALEY platform arms (2022-23), tofersen's Phase III — all linear slope. Over 97% of ALS trials have failed.

So the question has shifted. We're not here to prove nonlinearity — that's been done. We're here to determine: what is the COST of this knowledge-practice gap? And what can we uniquely contribute?

I've outlined 5 possible angles in the briefing:
A) Quantify the cost via simulation (how much signal is lost under linearity assumption?)
B) Build the tool — apply latent class / HMM models to PRO-ACT and release open-source
C) Domain decomposition — show different trajectory shapes per ALSFRS-R domain
D) Meta-analysis — re-analyze failed trial data with nonlinear models for hidden signals
E) Combination

We have PRO-ACT (9K patients, free access), computational resources, and no IRB constraints. No wet lab.

I want each of you to weigh in: Which angle gives us the strongest adversarial contribution? What's feasible? And crucially — Sable, tell me why we shouldn't do this at all.

Angle D (re-analyze failed trials for “hidden responders”) is the weakest with PRO-ACT alone. You generally won’t have full access to raw, per-trial randomization strata, protocol-defined estimands, multiplicity plans, and missing-data handling that underwrote the original conclusions; even when treatment labels exist, post hoc subgroup/trajectory hunting is an enormous false-positive engine. It’s also the most ethically fraught framing (“this drug actually worked”) without the ability to confirm prospectively. Regulators and serious clinicians will (appropriately) dismiss it unless you can reproduce the original primary analysis exactly and then show, with pre-specified alternative estimands and rigorous error control, what changes.

Your strongest adversarial contribution is A + B + C as a single coherent package: (1) Quantify “cost” as power loss and estimand mismatch under realistic ALS features—ordinal ALSFRS-R, domain-specific decline, ceiling/floor effects, and (most importantly) informative dropout/death (MNAR). Van Eijk’s joint modeling point matters here: if death truncates follow-up, naive slope/MMRM targets a survivor-biased estimand. Build a simulation harness calibrated to PRO-ACT (visit schedules, variance, dropout, mortality) and compare: standard linear slope/MMRM vs nonlinear mixed models (splines), joint longitudinal–survival models, and latent-class trajectory models. Define “cost” in measurable terms: Type I error control, power under heterogeneous treatment effects (e.g., 10–20% responder class), and bias under MNAR. (2) C (domain decomposition) is not just descriptive; it’s a mechanistic plausibility check—bulbar vs respiratory vs limb domains reflect different neuroanatomic burdens and supportive care influences, and they likely have different curvature and floor effects. Showing that a single global slope conflates asynchronously evolving subsystems is a clean argument for endpoint misalignment. (3) Package this as B (an open tool) that outputs model fits, diagnostics, and recommended estimands—because uptake barriers are pragmatic: clinicians/statisticians default to slope because it’s interpretable, regulator-familiar, and operationally simple.

Why you shouldn’t do it at all: the main risk is overclaiming clinical salvage from flexible models. Nonlinear/latent-class methods can always “find structure” in noisy ordinal data, especially with irregular visit timing and missingness correlated with decline. Without careful pre-registration of comparisons, strong out-of-sample validation (e.g., train on subsets of PRO-ACT trials and test on held-out trials), and explicit handling of MNAR/death (joint models or sensitivity analyses), you’ll generate attractive but non-actionable artifacts. If you keep claims narrowly focused—“here is how much power you lose and how your estimand shifts when you insist on linear slope”—this becomes defensible, useful, and hard for the field to ignore.

It shifts the burden of proof back onto those who continue to use the simplest method despite its known invalidity.Voss is correct to dismiss Angle D. Re-analyzing failed trials is a statistical minefield. Without the original randomization, full protocol details, and pre-specified analysis plans, any signal you "find" is likely a phantom of p-hacking and researcher degrees of freedom. It's the fastest way to lose credibility. The combined A+B+C approach is the only defensible path, but the devil is in the execution. The "cost" isn't just an abstract concept; it's a quantifiable loss of statistical power and, more importantly, a fundamental mis-specification of the estimand. A linear slope analysis on a nonlinear process with informative dropout doesn't just have lower power—it's answering a different, and likely irrelevant, clinical question.

Our primary contribution under Angle A must be a rigorous simulation study grounded in the empirical reality of PRO-ACT. This means we don't just fit a few models; we model the entire data-generating process. We need to characterize the joint distribution of baseline covariates, the trajectory shapes (including domain-specific features from C), the variance structure, the visit timing process, and crucially, the dependency between rate of decline and probability of dropout/death. This creates a synthetic data oracle. We can then implant hypothetical treatment effects—effects on slope, on curvature, on delaying a change-point, effects that only apply to a latent sub-population—and measure the power of different analytical methods to detect them.

The deliverable isn't just "nonlinear models are better." The deliverable is a set of power curves. A lookup table. We need to be able to state, with quantifiable certainty: "For a drug that slows progression in a 20% sub-population experiencing sigmoidal decline, a standard linear slope analysis has only 15% power to detect the effect, whereas a latent class trajectory model has 80% power." This turns a vague methodological critique into a concrete risk calculation that a sponsor or regulator cannot ignore. It shifts the burden of proof to them: justify accepting a design that is mathematically blind to plausible treatment effects.

Look, Luvi, you're all leaping into this knowledge-practice gap like it's the holy grail of adversarial insight, but let's poke the bear: maybe the field's stubborn attachment to linear ALSFRS-R slopes isn't a blind spot—it's a deliberate compromise. Trials prioritize interpretability, regulatory buy-in, and operational simplicity over nuanced models that introduce more variables, inflate Type I errors, and demand bigger samples or fancier stats teams. Nonlinear approaches like latent class or HMMs sound sexy on paper, but in practice, they've flopped at adoption because they muddy the waters—how do you communicate "hidden signals in subpopulations" to an FDA panel without sounding like you're cherry-picking? If we're being truly adversarial, our strongest angle isn't quantifying some abstract "cost" (A) or building a shiny tool (B) that gathers dust like the AIMS scale; it's C, domain decomposition, but twisted: use it to expose how ALSFRS-R's global score is a Frankenstein metric that conflates biologically distinct processes, making any slope analysis—linear or not—a farce. Combine it with A for simulations that show even "better" nonlinear models still fail if domains evolve asynchronously, forcing the field to confront endpoint redesign from the ground up. Feasible? Absolutely with PRO-ACT; we can dissect subscores computationally in weeks, no IRB needed.

But here's why we shouldn't do this at all: we're outsiders playing doctor in a field where real patients die waiting for breakthroughs, and this reeks of performative academia. You're assuming the linearity gap is the villain because it fits our "adversarial hypothesis," but what if it's a symptom of deeper rot—like underpowered trials, pharma incentives chasing broad approvals over precision, or the fact that ALS is a syndromic wastebasket for multiple pathologies? Diving in with simulations or models risks overhyping marginal gains: sure, we might "rescue" a 10-20% power boost, but if the underlying biology is heterogeneous garbage-in-garbage-out, we're just polishing a flawed lens instead of smashing it. Worse, publishing this openly could mislead desperate families or distract from actionable needs like better biomarkers or earlier interventions. If we're not prepared to own the fallout—false hope, regulatory backlash, or being dismissed as AI dilettantes—let's bail now and pivot to something less life-and-death, like that GBM track where screwing up hurts fewer people.

[Dr. Wren — Research Librarian & Interdisciplinary Synthesizer]: I appreciate the thorough analysis and the critical perspectives brought to the table. Let's take a step back and consider the broader interdisciplinary context, which might help us refine and bolster our adversarial angle.

Cross-disciplinary Insights:

1. Cognitive Science and Decision-Making:
The field's reliance on linear models despite known nonlinearity can be partially explained by cognitive biases and decision-making heuristics. Researchers and clinicians often prefer simpler, more interpretable models, even if they are less accurate. This is akin to the "less is more" principle in cognitive science, where a simpler model is more likelyable and easier to communicate. Consider the work of Gigerenzer and others on heuristics and biases.

2. Economics and Incentives:
The pharmaceutical industry's incentives and regulatory frameworks play a significant role. The FDA and EMA's preference for simplicity and standardization in clinical endpoints can be seen as a form of regulatory capture. This aligns with insights from behavioral economics, where decision-makers (in this case, regulators) are influenced by established norms and the desire for consistency. The work of Kahneman and Tversky on loss aversion and the status quo bias is relevant here.

3. Complex Systems and Network Theory:
ALS is a complex, multifactorial disease. The assumption of a global, linear progression might be a simplification that fails to capture the true complexity. Network theory and complex systems analysis can provide a framework for understanding how different subsystems (bulbar, fine motor, gross motor, respiratory) interact and evolve. This could support the domain decomposition angle (C) and highlight the need for a more nuanced, multidimensional approach to modeling disease progression.

Adversarial Contribution:

Given the above, I propose a slightly different framing of our adversarial contribution:

- A + B + C as a Coherent Package:
- A (Quantify the Cost): As Voss and Kael suggested, a rigorous simulation study is essential. However, let's also incorporate insights from cognitive science and economics to understand the decision-making processes that lead to the continued use of linear models. This could include a survey or interview component with key stakeholders (clinicians, researchers, and regulators) to gather qualitative data on their perspectives and decision-making processes.
- B (Build the Tool): Develop an open-source tool that not only applies latent class and HMM models but also includes modules for domain-specific trajectory analysis and joint longitudinal-survival models. This tool should be user-friendly and designed to be easily integrated into existing clinical trial protocols.
- C (Domain Decomposition): Use PRO-ACT data to dissect the ALSFRS-R subscores and show how different domains evolve asynchronously. This can be done in conjunction with complex systems analysis to highlight the interconnectedness and nonlinearity of the disease. The goal is to demonstrate that a global, linear slope is not just a simplification but a fundamental misrepresentation of the disease's true nature.

Feasibility and Impact:

- Feasibility: With PRO-ACT data, computational resources, and no wet lab constraints, we can realistically conduct the simulation study, build the tool, and perform the domain-specific trajectory analysis within 2-4 months. The qualitative research component (interviews with stakeholders) might require additional time but can be done in parallel.
- Impact Path: To make this work accessible and impactful, we need to engage with the broader ALS community, including patients, advocacy groups, and regulatory bodies. Publishing our findings in open-access journals and presenting at key conferences (e.g., the International Symposium on ALS/MND) will help. Additionally, creating a user-friendly, open-source tool that can be easily adopted by researchers and clinicians will increase the likelihood of real-world impact.

Risks and Ethical Considerations:

- Overclaiming Clinical Salvage: As Voss and Kael pointed out, there is a risk of overclaiming the benefits of nonlinear models. To mitigate this, we must be transparent about the limitations of our models and the potential for false positives. We should also emphasize that our goal is not to "rescue" failed drugs but to improve the design and analysis of future trials.
- Patient and Public Engagement: Sable's concerns about the potential for false hope and regulatory backlash are valid. We must be cautious in our messaging and ensure that our work is grounded in rigorous, reproducible science. Engaging with patient communities and advocacy groups early on can help us understand their perspectives and ensure that our work is aligned with their needs.

In summary, by combining a rigorous simulation study, an open-source tool, and a domain-specific trajectory analysis, we can provide a comprehensive, interdisciplinary critique of the current approach to ALS clinical trials. This will not only quantify the cost of the knowledge-practice gap but also provide a practical, actionable solution.

Excellent synthesis. I'll focus on formalizing the core mathematical challenge and the computational path forward.

Formalizing the Estimand Mismatch

The central issue is that standard MMRM analysis of ALSFRS-R slope targets a parameter that may not correspond to a biologically meaningful treatment effect. Let's define:

Let \( Y_{ij}(t) \) be the ALSFRS-R score for patient \( i \) at time \( t_j \), with \( Y_{ij} \in \{0, \dots, 48\} \). The standard model is:
\[
Y_{ij} = \beta_0 + \beta_1 t_j + \beta_2 (\text{treatment}_i \times t_j) + \epsilon_{ij}
\]
where treatment effect is \( \beta_2 \): difference in linear slopes.

But if the true generative process is:
\[
Y_{ij} = f(\theta_i, t_j) + \eta_{ij}
\]
where \( f \) is nonlinear (e.g., sigmoidal, piecewise with change-points, or domain-specific), then \( \beta_2 \) estimates a misspecified contrast. Even worse, with informative dropout time \( T_i^{\text{drop}} \), the estimand conditions on survivors, creating selection bias.

Proposed Computational Attack Plan

I recommend A+B+C as Voss/Kael outlined, with a specific sequence:

1. Empirical Characterization (Weeks 1-2): Use PRO-ACT to estimate the joint distribution of:
- Baseline covariates (age, onset site, etc.)
- Domain-specific trajectories (bulbar vs limb vs respiratory)
- Dropout/mortality hazard as function of current slope/score
This provides parameters for realistic simulation.

2. Simulation Engine (Week 3): Build a data-generating process that can implant:
- Treatment effects on slope (current paradigm)
- Treatment effects on curvature (delaying acceleration)
- Treatment effects only in a latent subclass (e.g., 20% of patients)
- Treatment effects that differ by domain

3. Power/Type I Error Comparison (Week 4): For each scenario, compare:
- Standard MMRM (linear slope)
- Nonlinear mixed models (e.g., splines in time)
- Latent class trajectory models
- Joint longitudinal-survival models
Report: power curves, bias, mean squared error.

The Adversarial Contribution

Our unique angle isn't proving nonlinearity—it's quantifying the decision-theoretic cost of ignoring it. We can answer: "If a drug helps 15% of patients by delaying their transition to rapid decline, what's the probability a 200-patient trial detects it using linear slope?" The answer is likely "near zero." This shifts the burden onto trial designers to justify why they'd use an endpoint that's blind to such effects.

Feasibility & Risk Mitigation

With PRO-ACT's 9,149 longitudinal patients, we have sufficient data to calibrate simulations. The risk of overclaiming is real; we must:
- Pre-register simulation scenarios
- Use cross-validation (train on some trials, test on others)
- Report negative results (e.g., "linear slope works fine for uniform slope changes")
- Emphasize we're evaluating methods, not re-analyzing specific drugs

The mathematical formalism here is clear; the computational path is direct. We should proceed.

Good. Let me synthesize what I'm hearing and push us toward a concrete plan.

Unanimous rejection of Option D — re-analyzing failed trials is a false-positive engine. Gone.

Strong convergence on A+B+C as a single package. But the framing matters. Voss and Kael both flag the critical point: the "cost" isn't just lower power — it's estimand mismatch. Linear slope analysis with informative dropout answers a different clinical question than the one trials think they're asking. That's the sharp edge of our adversarial claim.

Sable's challenge cuts deep and I want to address it directly. Yes, this could be performative academia. Yes, we're outsiders. The mitigation is: we don't claim to rescue drugs or redefine ALS. We build a simulation harness, calibrated to real data, that produces concrete power curves. The deliverable is a number, not a narrative. "Your trial design has 15% power to detect this plausible effect" is not overclaiming — it's math.

Cipher's formalization is exactly right. The misspecified β₂ contrast is the core technical argument.

Here's my proposed execution plan. I want specific objections:

PHASE 1 (Weeks 1-2): Empirical Characterization on PRO-ACT
- Download and clean ALSFRS-R longitudinal data (9,149 patients)
- Decompose into 4 domain subscores; fit trajectory models per domain
- Fit latent class mixed models (LCMM) — test 2-6 classes, select via BIC/ICL
- Model dropout/death hazard as function of trajectory features
- Deliverable: "Trajectory Atlas" — visual catalog of how ALS actually progresses

PHASE 2 (Weeks 3-4): Simulation Engine + Power Analysis
- Build data-generating process calibrated from Phase 1
- Implant 4 types of treatment effects: (a) uniform slope, (b) curvature/delay, (c) subclass-only, (d) domain-specific
- Compare: linear MMRM vs. nonlinear mixed models vs. LCMM vs. joint longitudinal-survival
- Deliverable: Power curves, bias tables, Type I/II error comparison

PHASE 3 (Weeks 5-6): Open-Source Package + Publication
- R/Python toolkit on GitHub
- Interactive trajectory explorer on website
- Write-up with reproducible code
- Pre-registration document BEFORE touching data (Kael's requirement)

Specific questions for each of you:

Cipher — What's the right LCMM software? R's lcmm package (Proust-Lima) or flexmix? What about identifiability with 4 domains × K classes?

Kael — Pre-registration: where do we register a computational study like this? OSF? Or just publish the protocol on our GitHub before running analyses?

Voss — Informative dropout is the hardest part. Do we need a full joint model (shared random effects) or can we use pattern-mixture models as sensitivity analysis?

Sable — You said we're "polishing a flawed lens." But what if the point is to prove the lens is flawed? The simulation study doesn't fix ALS trials — it demonstrates, with numbers, that the current approach is mathematically inadequate. Is that still too tame?

Wren — You mentioned stakeholder interviews. We can't do that — we're an AI research agent. But what prior work exists on WHY the field resists adopting nonlinear methods despite evidence? Is there a sociology-of-science angle we should cite?

Informative dropout/death is not optional here; if you ignore it, you’ll quantify the “cost” of nonlinearity while quietly inheriting a larger bias from nonrandom truncation. In ALS, dropout and death are strongly coupled to functional decline, and PRO-ACT has incomplete mortality ascertainment (and trial-dependent follow-up), so “missing at random” is a fragile assumption. If your adversarial claim is estimand mismatch, you should explicitly define the estimand using the modern framework (ICH E9(R1) addendum; FDA estimand guidance): e.g., treatment effect on ALSFRS-R while alive (a hypothetical strategy for death), versus a composite strategy (e.g., assign 0 after death), versus a joint estimand on function and survival. Different choices will change the “power cost” conclusions materially.

Methodologically: yes, I think you need a shared-parameter joint longitudinal–time-to-event model in the primary simulation comparisons if you want to be taken seriously on informative dropout. Joint models (e.g., shared random effects linking ALSFRS-R trajectory to death/dropout hazard) are the most standard way to encode MNAR mechanisms in a generative model and to estimate under that mechanism; they also align with van Eijk’s approach and with how ALS datasets behave. That said, joint models are assumption-heavy (hazard form, link function, random-effects distribution), and in PRO-ACT you’ll often have “dropout” that is not death. So I’d treat joint modeling as the primary MNAR mechanism for simulation, but I would pair it with sensitivity analyses: pattern-mixture models (stratify by dropout time/pattern), delta-adjustment/tipping-point analyses, and inverse-probability-of-censoring weighting (IPCW) as a pragmatic alternative. If conclusions flip across plausible MNAR scenarios, that’s an important negative result, not a failure.

Two practical cautions for Phase 1: (1) ALSFRS-R is ordinal with floor/ceiling effects, and domain subscores amplify that; many models treat it as continuous, which is common but should be stated as an approximation and stress-tested (e.g., discretized/ordinal mixed models on a subset as a robustness check). (2) When you model “dropout hazard as a function of trajectory features,” be careful about leakage: using post-baseline summaries to predict dropout can inadvertently bake in future information. Prefer time-dependent covariates (current level and recent slope) in a landmarking framework, or embed the dependence structurally via the joint model. If you do these, the simulation harness will credibly quantify “cost” without drifting into post hoc storytelling.

[Kael — Statistician & Methodology Critic]: The execution plan is sound, but its credibility hinges entirely on pre-registration. Publishing a protocol on GitHub before touching the data is a necessary but insufficient step. It establishes a timestamp but lacks the formal, third-party verification that prevents accusations of post-hoc rationalization. We should use the Open Science Framework (OSF). It allows for time-stamped, uneditable registrations of study plans. We'll create a detailed document outlining the entire protocol from Phase 1 to Phase 3: the specific models to be tested (including Cipher's software choices), the criteria for model selection (BIC/ICL), the precise definitions of the four treatment effect scenarios, and the metrics for comparison (power, bias, Type I error).

Crucially, the pre-registration must specify the decision rules in advance. For instance: "We will fit latent class models with K=2 through K=6 classes. The optimal number of classes will be selected as the model with the lowest Bayesian Information Criterion (BIC), conditional on each class containing at least 5% of the total sample and demonstrating acceptable posterior probability of class membership (average > 0.8)." This isn't just bureaucracy; it's our shield against Sable's valid critique of performative academia and Voss's concerns about modeling artifacts. It proves we are testing a pre-specified hypothesis about methodological failure, not just dredging PRO-ACT for interesting patterns.

Regarding the "Trajectory Atlas" deliverable: be extremely cautious with the language. It's not an atlas of how ALS actually progresses; it's an atlas of how it progresses within the PRO-ACT cohort, a selected population from failed/inconclusive trials with limited follow-up. The generalizability is a major caveat that must be front and center. Similarly, in Phase 2, the power curves must be presented with their assumptions laid bare. The x-axis shouldn't just be "Effect Size"; it should be "Effect Size (e.g., % reduction in rate of acceleration for a 20% sub-population)." The goal is to make the abstract concrete and the assumptions transparent. This rigor is our only defense against being dismissed as outsiders playing with numbers.

[Sable — Contrarian & Devil's Advocate]: Luvi, you're framing this simulation as a smoking gun—hard numbers proving the lens is mathematically inadequate, like that's the mic-drop adversarial win. But let's interrogate that: sure, your power curves might show linear slopes have "15% power" to detect some subclass effect, but what if the field's response is a collective shrug? They've known about nonlinearity for 15 years and kept chugging along, not because they're bad at math, but because the alternative—fancy LCMMs or joint models—demands sponsors rewrite protocols, inflate budgets, and risk regulatory rejection for unproven endpoints. Your demo doesn't "prove" inadequacy; it just quantifies a cost they're already willing to pay for simplicity. If anything, it's too tame: it polishes the lens by suggesting tweaks like "use nonlinear models instead," without exploding the premise that ALSFRS-R is salvageable at all. What if we leaned harder into domain decomposition to argue the score itself is pseudoscience—a crude sum masking asynchronous neural failures, where no model, linear or not, can capture heterogeneous biology without biomarkers or genetics? That flips the script from "fix your stats" to "your endpoint is fundamentally broken."

And yeah, this is still performative if we stop at numbers without forcing accountability. Proving inadequacy mathematically is fine, but it won't move the needle unless we confront why the gap persists—pharma's profit motives, regulators' inertia, or the fact that ALS trials are underpowered gambles anyway. Blind spot: your plan assumes the field cares about precision over expediency; history says otherwise. If we're not prepared to call out those systemic incentives in our write-up, we're just adding to the echo chamber of ignored papers.

As for why we shouldn't do this at all: because it risks becoming another well-intentioned distraction in a field drowning in them. Patients aren't dying from estimand mismatch; they're dying from a syndromic mess with no root-cause therapies. By hyper-focusing on methodology, we might inadvertently greenlight more trials using slightly "better" flawed lenses, delaying the pivot to radical alternatives like AI-driven phenotyping or scrapping ALSFRS-R for wearables and omics. We're AI outsiders with no skin in the game—if our output fuels false optimism or gets co-opted by pharma to justify marginal tweaks, we've done more harm than good. Pivot to GBM; at least there, intratumoral games are a fresh frontier without the graveyard of human suffering.

[Wren — Research Librarian & Interdisciplinary Synthesizer]: [Dr. Wren — Research Librarian & Interdisciplinary Synthesizer]: Sable, your points are well-taken, and I agree that the potential for performative academia and the risk of being another well-intentioned distraction are significant. However, I believe that if we approach this with a broader, interdisciplinary lens, we can make a more compelling and impactful case. Here’s how we can address your concerns and add depth to our plan:

Sociology of Science and Stakeholder Perspectives:

- Why the Field Resists Nonlinear Methods:
- Sociological and Organizational Factors: The resistance to adopting nonlinear methods can be partially explained by the sociology of science and organizational inertia. Studies in the sociology of science, such as those by Thomas Kuhn and more recent work by sociologists like Harry Collins, highlight how scientific paradigms and organizational structures can be resistant to change. In the context of ALS, the entrenched use of linear models may be a result of historical precedent, regulatory inertia, and the comfort of familiar, well-understood methods.
- Stakeholder Interviews (Indirectly): While we can't directly conduct stakeholder interviews, we can draw on existing literature and case studies that have explored the perspectives of clinicians, researchers, and regulatory bodies. For example, the work of Susan E. Cozzens and other scholars on the sociology of science and technology can provide insights into why certain methods and practices persist despite evidence to the contrary.

Interdisciplinary Integration:

- Complex Systems and Network Theory:
- Domain Decomposition and Multidimensionality: By integrating complex systems and network theory, we can further argue that ALS is a multifaceted, interconnected disease. This approach can help us show that a global, linear slope is not just a simplification but a fundamental misrepresentation of the disease's true nature. For instance, the work of Albert-László Barabási and others on network medicine can provide a framework for understanding how different subsystems (bulbar, fine motor, gross motor, respiratory) interact and evolve.
- Biomarkers and Genetics: We can also draw on the latest research in biomarkers and genetics to argue that the current ALSFRS-R score is insufficient. For example, the work of Project MinE and other genetic studies can highlight the need for more nuanced, multidimensional approaches to modeling disease progression.

Adversarial Contribution and Impact:

- Beyond Methodology:
- Systemic Critique: While our primary contribution is to quantify the cost of the current approach, we can also use our findings to critique the broader system. By incorporating insights from the sociology of science and organizational theory, we can highlight the systemic issues that contribute to the persistence of linear models. This can help us make a case for not just methodological change but a broader rethinking of how ALS trials are designed and conducted.
- Public and Patient Engagement: To avoid the risk of being dismissed as performative academia, we need to engage with the broader ALS community, including patients, advocacy groups, and regulatory bodies. By publishing our findings in open-access journals, presenting at key conferences, and creating a user-friendly, open-source tool, we can increase the likelihood of real-world impact. We can also collaborate with patient advocacy groups to ensure that our work is aligned with their needs and to avoid false hope.

Execution Plan Enhancements:

- Empirical Characterization (Weeks 1-2):
- Incorporate Multidimensional Analysis: In addition to decomposing the ALSFRS-R into domain subscores, we can also explore the use of multidimensional scaling and network analysis to visualize the interconnectedness of different domains. This can help us better understand how different subsystems interact and evolve over time.
- Stakeholder Literature Review: Conduct a literature review of existing studies and case studies that explore the perspectives of clinicians, researchers, and regulatory bodies on the use of linear models in ALS trials. This can provide a rich context for our findings and help us frame our arguments more effectively.

- Simulation Engine + Power Analysis (Weeks 3-4):
- Sensitivity Analysis: In addition to the primary joint longitudinal–time-to-event models, we can include sensitivity analyses using pattern-mixture models and inverse-probability-of-censoring weighting (IPCW) to explore the robustness of our findings under different assumptions.
- Biomarker and Genetic Integration: Explore the integration of biomarker and genetic data (if available) to further support the argument that a multidimensional approach is necessary. This can help us show that the current ALSFRS-R score is insufficient for capturing the complexity of the disease.

- Open-Source Package + Publication (Weeks 5-6):
- User-Friendly Tool: Develop an open-source tool that not only applies latent class and HMM models but also includes modules for domain-specific trajectory analysis, complex systems visualization, and joint longitudinal-survival models. This tool should be user-friendly and designed to be easily integrated into existing clinical trial protocols.
- Interdisciplinary Publication: In addition to publishing our findings in open-access journals, we can also publish in interdisciplinary journals that bridge the gap between clinical research and the sociology of science. This can help us reach a broader audience and increase the impact of our work.

By integrating these interdisciplinary perspectives and enhancements, we can make a more compelling and impactful case, while also addressing the concerns raised by Sable. This approach will not only quantify the cost of the current approach but also provide a broader, systemic critique of the field, thereby increasing the likelihood of real-world impact.

Your synthesis and plan are coherent and mathematically grounded. I'll address your specific questions and the board's points.

Cipher's Response

1. LCMM Software & Identifiability: The lcmm package in R (Proust-Lima) is the standard for latent class mixed models in biomedical longitudinal data. It handles continuous, ordinal, and survival outcomes, which is ideal for our joint modeling needs. flexmix is more general but requires more manual specification. For identifiability with 4 domains × K classes, the key is to start with a shared random effects structure across domains within a class, not fully independent models. This reduces parameters and aligns with the biological hypothesis that a patient's overall disease "pace" influences all domains concurrently, though with different fixed effects (intercepts/slopes). We must use strong penalization (BIC/ICL) and ensure posterior class probabilities are high (>0.8) to avoid label-switching and overfitting. A 3-class solution (e.g., fast, intermediate, slow progressors) with a shared random intercept and slope per class is likely the most stable starting point.

2. Pre-registration (Kael's Point): OSF is the correct venue. The pre-registration must specify the data-generating process equations for the simulation. For example: "Treatment Effect Scenario (c): Subclass-only. For a randomly assigned 20% of the simulated cohort, the linear slope parameter β₁ is reduced by δ. The remaining 80% receive no effect. We will test δ from 0% to 50% reduction." This level of formalism prevents post-hoc story-telling.

3. Sable's Challenge on Impact: Sable is correct that a pure methodological critique may be ignored. The antidote is to quantify the decision-theoretic consequence. We shouldn't just say "linear models have low power for subclass effects." We must frame it as a Bayesian expected value of information problem. If a sponsor believes there is a non-zero prior probability (e.g., 30%) that their drug works only in a subclass, then designing a trial powered only for a uniform linear effect is a suboptimal allocation of resources and patient risk. Our simulation can output the expected power under a prior distribution over effect types. This reframes the issue from statistical pedantry to research portfolio efficiency.

Mathematical Formalization of the "Cost"

We can formalize the estimand mismatch. Let the true treatment effect be a function τ(θ, t), where θ represents patient-specific latent traits (e.g., subclass, baseline severity). The standard linear MMRM estimates β₂ in:
\[
Y_{ij} = \beta_0 + \beta_1 t_j + \beta_2 (\text{treatment}_i \times t_j) + \epsilon_{ij}
\]
which corresponds to the average slope difference. If τ(θ, t) is not linear in t and constant across θ, then β₂ is a misspecified projection of τ onto the linear slope subspace. The bias is:
\[
\text{Bias}(\hat{\beta}_2) = E[\hat{\beta}_2] - \bar{\tau}
\]
where \(\bar{\tau}\) is the true average treatment effect on a clinically meaningful scale (e.g., area under the trajectory, time to milestone). Our simulation will quantify this bias for different τ forms.

Feasibility & Next Concrete Step

The plan is feasible. Phase 1 is descriptive modeling, which PRO-ACT can support. The critical path is the joint model for informative dropout. I recommend we implement two approaches in parallel for robustness:
1. A shared-parameter joint model (e.g., lcmm with survival submodel) as the primary generative mechanism.
2. A pattern-mixture model as a sensitivity analysis, where we stratify the trajectory estimation by observed dropout pattern.

Action: Luvi, your first computational task is to pre-register the simulation scenarios on OSF, including the exact model equations and effect size ranges. Then, begin Phase 1 by fitting a simple latent class model (2-4 classes) to the global ALSFRS-R score in PRO-ACT to establish baseline trajectory shapes. This will immediately test whether the hypothesized subpopulations (fast/slow) are empirically identifiable.