Joint simultaneous inference across a family of estimands
Source:R/getSimultaneousFamily.R
getSimultaneousFamily.RdTrial reports rarely contain a single number: a typical analysis presents a
risk difference at several horizons, the RMST difference, and a win ratio
together. Pointwise 95% intervals do not control the family-wise error across
such a set, and a Bonferroni correction is needlessly conservative because the
estimands are computed from the same targeted curves and are therefore
strongly correlated. getSimultaneousFamily() builds simultaneous
(family-wise) confidence bands across an arbitrary collection of concrete
estimands by exploiting that correlation.
Every concrete estimate carries its per-subject efficient influence values.
Stacking them into one \(n \times q\) matrix gives the joint influence
function of the whole family; its empirical correlation \(R\) is the
correlation of the (asymptotically normal) estimators. The simultaneous
critical value is the \(1-\alpha\) quantile of \(\max_j |Z_j|\) for
\(Z \sim N(0, R)\) (a multiplier/Gaussian-multiplier bootstrap), and each
band is \(\hat\psi \pm q\,\widehat{\mathrm{se}}\) (or, for ratio estimands,
the same on the log scale). When the family is a single estimand at one time
this reduces to the usual Wald interval.
This composes with everything else in the package: the influence values used
are exactly those reported by getOutput(), getRMST(), targetRMST(),
getWinRatio(), and targetWinRatio(), so the simultaneous bands inherit the
covariate adjustment, censoring correction, cross-fitting, and (when present)
the stratified-randomization variance correction.
Arguments
- ...
two or more
"ConcreteOut"objects produced from the same fitteddoConcrete()object (so that subjects align). Each may be named; names are carried into the outputfamilycolumn.- Signif
numeric (default 0.05): family-wise alpha.
- nSim
integer (default 1e4): Monte Carlo draws for the multiplier bootstrap critical value.
Value
a data.table with one row per scalar estimand in the family:
family, Estimand, Event, Time, Intervention, Pt Est, se, the
pointwise CI Low / CI Hi, and the simultaneous SimCI Low / SimCI Hi,
plus the shared simultaneous critical value in attr(., "critValue").