Our central finding across EXP-001 through EXP-006 is that ALS trial methodology loses power when it ignores trajectory heterogeneity. The standard approach (linear mixed model) treats all patients identically; our LCMM pipeline identifies latent subgroups and tests within them.

But there's a well-established alternative we hadn't tested: joint longitudinal-survival models. These simultaneously model the disease trajectory and the survival process, accounting for the fact that sicker patients drop out faster — the collider bias we identified in EXP-003.

If the joint model already solves the dropout problem and detects heterogeneous effects, our pipeline adds nothing. If it solves dropout but not heterogeneity, the two approaches are complementary.

Same data-generating process as EXP-005 and EXP-006: three latent trajectory classes (slow, fast, crash) with class-dependent survival. N = 200 per arm. Four methods fitted to each simulated trial:

• LMM — standard linear mixed model, treatment × time interaction, random intercepts and slopes
• ANCOVA — change from baseline to last observation (survivors only)
• LCMM-Soft — our pipeline: EM clustering → pseudo-class draws → within-class LMMs → Rubin's rules
• Joint Model — shared-parameter model via R's JM package (Rizopoulos, 2010). Longitudinal sub-model (LME with random slopes) linked to a Weibull survival sub-model via shared random effects. Adaptive Gauss-Hermite quadrature.

Three scenarios, 200 simulations each:

• Null: No treatment effect in any class → Type I error calibration
• Uniform: All classes benefit equally (+0.3/month slowing) → standard trial assumption
• Class-specific: Only slow progressors benefit (+0.5/month slowing) → heterogeneous treatment effect

The joint model is well-calibrated at 4.5% — essentially indistinguishable from the LMM's 5.0%. ANCOVA is slightly conservative at 2.5%, which is expected when conditioning on survival biases toward null. The LCMM-Soft shows the same parametric inflation (12%) documented in EXP-006, which is why we recommend permutation inference for the full pipeline.

The joint model's distinguishing feature is the association parameter (α), which captures the relationship between the longitudinal trajectory and the risk of death. Across all 600 simulations, the mean α was −0.067 — a negative association indicating that patients with lower ALSFRS-R scores (worse function) face higher mortality risk. This is biologically correct and confirms the model is learning the right structure.

But learning the right structure for dropout is not the same as learning the right structure for treatment effects. The joint model knows that sicker patients die faster. It doesn't know that some patients' decline follows a fundamentally different trajectory — and that treatment might work for one trajectory but not another.

A future direction — joint latent class mixed models (Proust-Lima et al., 2014) — would combine both: latent trajectory classes with class-dependent survival modeling. We note this as an important extension but consider it beyond the scope of this simulation study.

With EXP-007, the simulation battery now includes seven experiments and over 15,000 simulated ALS clinical trials:

• EXP-001: 4× sample size penalty from ignoring trajectory heterogeneity
• EXP-002: LCMM pipeline recovers half the oracle's advantage
• EXP-003: ANCOVA targets a different estimand (~36% collider bias inflation under MNAR)
• EXP-004: Treatment-induced class splitting explains K over-selection
• EXP-005: Pipeline robust across 11 stress conditions
• EXP-006: Permutation inference confirms nominal calibration under clean data
• EXP-007: Joint model handles dropout but not heterogeneity — complementary, not competing