Directly targeted win ratio, win odds, and net benefit

A targeted-maximum-likelihood update that fluctuates both arms' cause-specific hazards to solve the efficient-influence-function estimating equations of the win probability and loss probability directly, rather than plugging pointwise-targeted risk curves into the win functional (which is what getWinRatio() does).

For prioritized events $k = 1, \ldots, K$ (first = highest priority) with treated-arm cumulative incidences $G_k$ and control-arm $H_k$, the win probability over horizon $\tau$ is $$P(win) = S_G(\tau)\sum_k H_k(\tau) + \sum_{a \ge 2} G_a(\tau) \sum_{k<a} H_k(\tau) + \sum_k \int_0^\tau [G_k(\tau) - G_k(t)] \, dH_k(t),$$ and $P(loss)$ swaps the arms. The clever covariate for each functional is the gradient-weighted combination of the pointwise clever covariates over the full event-time grid (the chain rule analogue of targetRMST()'s time-integrated clever covariate), so the win integral is evaluated on every event time rather than the getWinRatio() target-time grid. Because the gradient coefficients depend on both arms' current curves, they are recomputed at every fluctuation step and the two arms are updated jointly until $P_n D_{win} \approx P_n D_{loss} \approx 0$.

Compared to the plug-in this removes the target-grid discretization of the win integral and solves the functional's own estimating equation, which matters most for sparse target grids and for the win odds / net benefit. Derivation: notes/target-win-ratio.md in the source repository.

Usage

targetWinRatio(
  ConcreteEst,
  Horizon = NULL,
  Intervention = c(1, 2),
  TargetEvent = NULL,
  MaxUpdateIter = 50L,
  OneStepEps = 0.1,
  Signif = 0.05,
  EICStopRule = c("hybrid", "relative", "absolute"),
  EICStopAbsTol = NULL,
  Verbose = FALSE
)

Arguments

ConcreteEst: a "ConcreteEst" object from doConcrete().
Horizon: numeric: the comparison horizon $\tau$. Defaults to the largest target time; snapped down to the nearest evaluation time.
Intervention: length-2 numeric: ConcreteEst list indices of the treated and control interventions, in that order.
TargetEvent: numeric: event types in priority order (first = highest, e.g. death). Defaults to the fitted target events in their given order.
MaxUpdateIter: integer: maximum fluctuation steps.
OneStepEps: numeric: initial step size for the fluctuation.
Signif: numeric (default 0.05): alpha for CIs and two-sided p-values.
EICStopRule: one of "hybrid" (default), "relative", "absolute": stopping rule for the (win, loss) estimating equations.
EICStopAbsTol: numeric absolute tolerance for the "absolute" and "hybrid" rules. Defaults to 0.02 / sqrt(n) (the functionals are probabilities, so the risk-scale default applies).
Verbose: logical: print per-step convergence diagnostics.

Value

a data.table of class "ConcreteOut" with the win ratio, win odds, net benefit, and win/loss/tie probabilities, each with influence-function CIs and (for the comparative statistics) p-values. Convergence status is in attr(., "WRConverged") and the step count in attr(., "WRSteps"). If the fit was built with Strata (see formatArguments()), the standard errors are corrected for the stratified / covariate-adaptive randomization design.

Directly targeted win ratio, win odds, and net benefit

Usage

Arguments

Value

See also