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Restricted mean time in favor of treatment (first-event competing risks)

Source: R/getRMTIF.R
getRMTIF.Rd

The restricted mean time in favor of treatment (RMT-IF; Mao 2023) is the average amount of time over \([0,\tau]\) that a randomly chosen treated patient spends in a strictly more favorable state than a randomly chosen control. Unlike the (unitless) win ratio, it is reported in time units, which clinicians find easier to interpret. It is the time integral of the instantaneous net benefit, $$\mathrm{RMT\text{-}IF}(\tau) = \int_0^\tau \big[w(t) - l(t)\big]\,dt,$$ where \(w(t)\) (resp. \(l(t)\)) is the probability that the treated patient is in a better (resp. worse) state than the control at time \(t\).

For a single event this reduces exactly to the restricted mean survival time difference, \(\mathrm{RMT\text{-}IF} = \mathrm{RMST}_1 - \mathrm{RMST}_0\): with states alive, with-event, \(w(t)-l(t) = S_1(t) - S_0(t)\). For a prioritized hierarchy of competing events the state at \(t\) is "event-free" or "first event was type \(k\) by \(t\)", ranked by priority (highest priority = least favorable), so \(w(t)\) and \(l(t)\) are bilinear in the two arms' cause-specific cumulative incidences. RMT-IF is therefore a smooth functional of the targeted marginal curves, with the same covariate-adjusted, doubly-robust, censoring-corrected influence-function inference as the other estimands.

This is the first-event version: a higher-priority event that follows a lower-priority one is not credited (it treats the events as competing risks), exactly as in getWinRatio(). For the clinically intended death-priority hierarchy that credits death after a non-fatal event, use the multistate version (see clinicalWinRatio() and ?clinicalRMTIF).

Usage

getRMTIF(
  ConcreteEst,
  Horizon = NULL,
  Intervention = c(1, 2),
  TargetEvent = NULL,
  Signif = 0.05
)

Arguments

ConcreteEst

a "ConcreteEst" object from doConcrete().

Horizon

numeric: the restriction horizon \(\tau\) (default: the largest target time). RMT-IF is reported in the time units of Horizon.

Intervention

length-2 numeric: treatment and control indices; a positive RMT-IF favors Intervention[1].

TargetEvent

numeric: the event code, or an ordered vector of codes giving the priority hierarchy from highest to lowest (default: the first targeted event).

Signif

numeric (default 0.05): alpha for confidence intervals and the two-sided Wald p-value.

Value

a data.table of class "ConcreteOut" with RMT-IF (net), the time in favor (\(\int w\)) and against (\(\int l\)), each with an influence-function CI; the net carries a p-value against the null of no difference. With a Strata fit the SEs are design-corrected.

See also

getRMST() (the single-event special case), getWinRatio(), getSimultaneousFamily().