Inference for interval-censored PAMMs (pamm_ic) pools the
m re-fits by drawing from each fit's empirical-Bayes posterior
\(N(\hat\beta^{(m)}, V_\beta^{(m)})\) and propagating every draw through the
quantity of interest using that fit's own design matrix, then taking
empirical quantiles of the combined draws. Because mgcv's identifiability
constraints make the (centered) spline basis depend on each imputed data set,
the design matrix is not shared across fits, so each fit must be
evaluated with its own lpmatrix. Before empirical quantiles are taken,
the per-fit prediction draws are shifted on the quantity-of-interest scale so
their between-imputation component has Rubin's finite-m variance
\((1 + 1/M)B\) rather than the raw mixture variance
\((M - 1)B/M\). Point estimates are the average of the per-fit point
estimates (the MI estimate).
These methods are dispatched automatically by add_hazard,
add_cumu_hazard, add_surv_prob and
add_cif when given a pamm_ic object.