Directly target the restricted mean survival time

targetRMST() runs an additional one-step TMLE update that targets the restricted mean survival time (RMST) and cause-specific life-years-lost (LYL) estimands directly, rather than integrating pointwise-targeted absolute risks (the approach used by getRMST()).

The estimand $\mathrm{LYL}_j(\tau)=\int_0^\tau F_j(t)\,dt$ is a smooth time-average of the cumulative incidence, so its efficient influence function is the time-integral of the pointwise risk influence functions and its clever covariate is the time-integral of the pointwise clever covariates: $$H_{l,j,\tau}(s) = \frac{\pi^*(A\mid W)}{\pi(A\mid W) S_c(s^-)} \left[\mathbf 1(l=j)(\tau-s) - \frac{\int_s^\tau F_j(t)\,dt - (\tau-s)F_j(s)}{S(s)}\right].$$ Targeting this single, well-conditioned functional avoids the dependence on a dense TargetTime grid and tends to converge and cover better than the pointwise approach in rare-event, competing-risk, and long-horizon settings.

Starting from the hazards in ConcreteEst (already fit by doConcrete()), targetRMST() fluctuates them along $H$ until the empirical mean of the RMST/LYL influence function is small, then reports the directly-targeted estimates with influence-function standard errors, p-values, and (optionally) a non-inferiority assessment.

Usage

targetRMST(
  ConcreteEst,
  Horizon = NULL,
  Intervention = seq_along(ConcreteEst),
  TargetEvent = NULL,
  MaxUpdateIter = 50L,
  OneStepEps = 0.1,
  Signif = 0.05,
  NIMargin = NULL,
  NIDirection = c("lower", "upper"),
  EICStopRule = c("hybrid", "relative", "absolute"),
  EICStopAbsTol = NULL,
  Verbose = FALSE
)

Arguments

ConcreteEst: a "ConcreteEst" object from doConcrete().
Horizon: numeric: the restriction horizon $\tau$. Defaults to the largest target time; snapped to the nearest target time at or below it.
Intervention: numeric (default seq_along(ConcreteEst)): interventions to summarize; the first two are treated as treatment and control.
TargetEvent: numeric: event types to target. Defaults to the events the model was fit on.
MaxUpdateIter: integer: maximum fluctuation steps.
OneStepEps: numeric: initial step size for the fluctuation.
Signif: numeric (default 0.05): alpha for confidence intervals and two-sided Wald p-values.
NIMargin, NIDirection: optional non-inferiority margin and direction, passed to the contrast estimands (see getOutput()).
EICStopRule: one of "hybrid" (default), "relative", or "absolute": the stopping rule for the RMST/LYL estimating equation, evaluated on the rescaled fraction-of-horizon scale.
EICStopAbsTol: numeric absolute tolerance for the "absolute" and "hybrid" rules on the fraction scale. Defaults to 0.02 / sqrt(n).
Verbose: logical: print per-step convergence diagnostics.

Value

a data.table of class "ConcreteOut" with the directly-targeted RMST / life-years-lost estimates. The per-arm convergence status is stored in attr(., "RMSTConverged"). If the fit was built with Strata (see formatArguments()), the standard errors are corrected for the stratified / covariate-adaptive randomization design.

Directly target the restricted mean survival time

Usage

Arguments

Value

See also