FROM NOISE TO SIGNAL: UNVEILING TREATMENT EFFECTS FROM DIGITAL HEALTH DATA THROUGH PHARMACOLOGY-INFORMED NEURAL-SDE

Samira Pakravan, Nikolaos Evangelou, Maxime Usdin, Logan Brooks, James Lu

correctmedium confidence

Category: math.DS
Journal tier: Specialist/Solid
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper explicitly discretizes the PD SDE with (symplectic) Euler–Maruyama, assumes the conditional Normal law with mean x_i0 + ν_θ Δt and variance σ_θ^2 Δt, and derives the per-snapshot negative log-likelihood used as the training loss (its Eqns. 3–6). The candidate solution reproduces exactly these steps (including using c_{i1} in ν_θ and σ_θ), and it formalizes the no-dosing counterfactual by setting the PK input to zero, which matches the paper’s counterfactual simulations described as “PK = 0.” Hence both are correct and proceed by the same reasoning. See the paper’s model and loss statements and counterfactual description in the Methods/Results sections .

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} specialist/solid

\textbf{Justification:}

The derivations and claims under review—the Euler–Maruyama snapshot, conditional Normal law, and per-snapshot NLL—are standard and correctly executed. The counterfactual simulation (PK set to zero) is consistent with the model structure and the paper’s stated what-if analysis. Minor clarifications would strengthen the presentation, notably about independence of the Brownian increment, positivity of the diffusion, and the rationale for using c\_{i1} in the PD update under the chosen semi-implicit/symplectic discretization.