Add interval-censored survival support via multiple imputation

[fabian-s]

Summary

Adds support for interval-censored time-to-event data via a multiple-imputation (MI) workflow. Surv(L, R, type = "interval2") responses are detected automatically by as_ped(); the new fitters repeatedly draw exact event times from the model-based conditional hazard on (L, R], re-fit the standard right-censored PAMM pipeline on each completed data set (one shared cut grid, so fits are poolable), and pool inference with Rubin's rules.

The workflow was validated in a 39-cell × 500-replication Monte Carlo benchmark (ADEMP design; oracle / midpoint-imputation / icenReg ic_par + ic_sp / Turnbull comparators). The benchmark materials are deliberately not part of this PR; they live in the fork under attic/ic-benchmark/ (design, decision log, and full report) if you want to inspect them.

What's included

Fitters

• pamm_ic() (single event) and pamm_ic_cr() (competing risks; retains observed causes, imputes unknown ones from the fitted cause-specific hazards). Imputation is always proper: coefficients are drawn from the imputation model's asymptotic posterior before each draw.
• iter argument (default 1): chained refit-and-reimpute within each imputation chain. One-step MI is biased for early-time survival when inspection intervals are wide (benchmark: coverage falls with n); iter = 3 removes most of that bias at ~linear fit cost. Documented recommendation: default for densely inspected data, iter = 3 for sparse panels.
• warn_unstable_chains(): flags numerically degenerate imputation chains (a silent mgcv failure mode that can occur when iterating flexible time-varying models on small samples) via a warning and $unstable_chains.

Pooled inference

• print()/summary() report the pooled fit: Rubin-combined coefficients/covariances, median-p term tests, fraction-of-missing-information diagnostics.
• add_hazard(), add_cumu_hazard(), add_surv_prob(), add_cif() gain pamm_ic methods that combine per-imputation posterior draws (each fit evaluated with its own design matrix, since mgcv bases are data-dependent), so intervals carry within- plus between-imputation uncertainty. add_cumu_hazard()/add_surv_prob() are converted to S3 generics with default methods (backward compatible).
• Per-imputation fits are stored slimmed (strip_pamm_fit()), so memory does not scale with m.

Supporting changes

• R/as-ped-ic.R / R/impute-ic.R: IC detection/parsing/transformation and the conditional-hazard imputation sampler (calibration unit-tested: PIT uniformity, draws respect (L, R]).
• add_inspections() (R/sim-ic.R): manufactures IC panel data from exact simulated times for examples/testing. Uses a coherent end-of-study-examination censoring convention (terminal_exam) — mixing exact exit times for survivors with open intervals for undetected events would make right-censoring informative and bias every IC likelihood (regression-tested).
• sim_pexp(): now factor-safe — bare factor arithmetic in the formula errors loudly instead of silently coercing to NA.
• resolve_rhs_vars() helper in R/formula-utils.R (dot-formula resolution, used by the IC pipeline).
• Vignette interval-censored.Rmd: worked single-event and competing-risks examples, guidance on choosing m (via FMI) and iter, comparison against midpoint imputation and the Turnbull NPMLE.
• Tests: test-interval-censored.R (+ a sim_pexp factor-safety test); full package suite passes (688 assertions).

Notes for review

• Exact-only data through the IC entry points reproduces the plain right-censored PAMM exactly (tested).
• Recurrent-event / general multi-state interval censoring is out of scope (imputing one transition time changes the next at-risk window, so draws must be joint along each path) — noted in the vignette as a planned extension.
• This PR is intentionally isolated from my other open work (gg_smooth/get_terms refactor etc.); only IC-related changes are included.

🤖 Generated with Claude Code

[fabian-s]

simulation study for this:
report.html

especially with iterated MI, this seems to work quite well for both point and interval estimates...

[fabian-s]

suggested vignette for this:
interval-censored.html

[fabian-s]

see #292