Fit a competing-risks PAMM to interval-censored data via multiple imputation

Competing-risks extension of pamm_ic. The event time is drawn from the all-cause conditional hazard within \((L, R]\) and a cause is assigned: observed causes are retained (with the time drawn so that it follows the cause-specific conditional density, via rejection), unknown causes are sampled with probability proportional to the cause-specific hazards at the imputed time (see impute_ic_cr). Each completed data set is transformed with as_ped_cr (cause-specific hazards) and re-fit. Cf. Delord & Genin (2016) for MI of interval-censored competing-risks data.

pamm_ic_cr(
  formula,
  data,
  cause,
  model_formula = NULL,
  cut = NULL,
  max_time = NULL,
  m = 10L,
  iter = 1L,
  censor_code = 0L,
  id = "id",
  engine = "gam",
  ...
)

Arguments

formula

A two-sided formula whose left-hand side is an interval-censored response Surv(L, R, type = "interval2") and whose right-hand side lists the covariates to retain (as in as_ped).

data

A data frame in standard (one row per subject) format.

cause

Name of the column in data giving the observed cause for events (any factor/character coding). Rows with the censoring code are treated as right-censored; NA marks an event with unknown cause.

model_formula

Optional model formula passed to pamm (e.g.\ ped_status ~ s(tend) + x). If NULL, a default ped_status ~ s(tend) + <covariates> formula is constructed.

cut

Optional fixed vector of interval cut-points shared across all imputations. If NULL, the finite interval endpoints are used.

max_time

Optional cap on the cut-points.

m

Number of imputations (default 10).

iter

Number of impute-refit iterations per imputation chain (default 1 = classic one-step MI: all m imputations are drawn from the single initialiser fit). For iter = k > 1, each chain alternates imputation and re-fitting on its own completed data set k times, so later imputations are drawn from fits whose dependence on the midpoint initialiser is progressively attenuated – a sequential ("chained") MI scheme that progressively removes initialiser bias under sparse inspection, at roughly iter-fold fitting cost. Simulation evidence (see the package's interval-censoring benchmark): with inspection gaps that are small relative to the time scale, iter = 1 is unbiased; with wide gaps (mean gap of order 1/3 of the follow-up), early-time survival estimates from iter = 1 are biased upward and iter = 3 removes most of that bias (iter = 5 essentially all of it), with bias shrinking roughly geometrically in iter. Caveat: with flexible time-varying effect terms and small samples, iterating can occasionally amplify a weakly identified imputation chain into divergent estimates with very wide intervals (without mgcv warnings) – inspect pooled smooth effects for plausibility when iterating such models.

censor_code

Value of cause that encodes censoring (default 0).

id

Name of the subject identifier column.

engine

Estimation engine passed to pamm ("gam" or "bam").

...

Further arguments passed to pamm / mgcv.

Value

An object of class pamm_ic with type = "cr"; fits are cause-specific (stacked ped_cr) pamm objects and cause_levels records the competing causes.

See also

pamm_ic, add_cif