IPCW sandwich for multinomial-outcome g-computation (23a-2c) + g-formula direct-censoring-term fix

[lorenzoFabbri]

Summary

Completes the analytic sandwich for multinomial-outcome point g-computation by adding the IPCW (missing-Y) path (Phase 23a-2c), and fixes a pre-existing conservatism the new tight oracle exposed in the scalar gcomp IPCW sandwich.

Under IPCW the censoring model's estimation uncertainty enters the per-class influence function through two channels, both carried through the censoring model's own IF:

• Indirect — γ → IPCW-weighted outcome model β → marginal mean (the A_{β,γ}ᵀh cross-term).
• Direct — the IPCW-weighted average carries γ in its own weights: ∂μ/∂γ = (1/Σw) Σ (dwᵢ/dγ)(p_{k,i} − μ), dwᵢ/dγ = −wᵢ(1−p_unc,ᵢ)X_cens,ᵢ, summed over target rows with positive weight.

The direct term recovers the efficiency gain from estimating the censoring model (Robins, Rotnitzky & Zhao 1994) and cancels in contrasts — reported ATE difference/ratio/OR SEs are unchanged; only the per-class marginal-mean SEs move.

What this exposed (and fixed)

Building the first tight IPCW M-estimation oracle (a delicatessen-style stack that carries the censoring γ block) revealed that the scalar gcomp IPCW sandwich captured only the indirect path, so its per-class marginal-mean SEs ran ~1–1.5% above the truth. The direct term is now added there too via the shared ipcw_direct_grad_setup() / ipcw_direct_grad() helpers.

Point IPW and point AIPW were Monte-Carlo-verified to need no such term — their marginal mean is the model parameter, so the γ-dependence is already captured by the indirect cross-term. The gap is specific to the plug-in g-formula's separate covariate-averaging step.

Also fixes a benign non-integer #successes warning from the survey-weighted binomial censoring model by switching to quasibinomial() when weights are present (identical coefficients/SEs/predictions; mirrors fit_bernoulli_density()).

Validation

• New Python M-estimation oracle multinom_gcomp_ipcw_sandwich.py (stacks logistic censoring score + IPCW-weighted multinomial score + marginal-mean equations) — matched to ~1e-7 on per-class means and every diff/ratio/OR contrast.
• Scalar gcomp IPCW oracle (inline stacked-EE) — exact; survey-weighted variant matched too.
• Multinomial IPCW SE-vs-empirical-SD calibration MC: ratio 0.99 over 300 reps.
• Two direct-term-active guards (full < known-γ on means; cancels in contrasts).
• IPW-no-gap MC regression guard.
• Independent adversarial review found no reproducible correctness bugs.
• Full suite: 84/84 files, 0 failures, 0 warnings.

Known follow-up

Longitudinal ICE IPCW likely shares the same plug-in direct-term gap (its coverage test only asserts the conservative [0.85, 2.0] band). Not addressed here — it needs the stacked-cascade derivation and a longitudinal oracle. Tracked separately.