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Covariate-adjusted restricted win ratio, win odds, and net benefit

Source: R/getWinRatio.R
getWinRatio.Rd

getWinRatio() estimates the restricted win ratio and its relatives (win odds, net benefit) from the covariate-adjusted, censoring-corrected counterfactual cumulative-incidence curves that concrete targets. It supports a single time-to-event outcome or a prioritized hierarchy of competing events (e.g.\ death \(>\) hospitalization \(>\) stroke).

Single event. Comparing a random treated patient to a random control patient over \([0,\tau]\): the treated patient wins if the control has the event first (and within the horizon), loses if the treated has it first, and ties if both are event-free at \(\tau\). By independence of the two patients these are functionals of the marginal survival \(\bar S_a\) and cumulative incidence \(\bar F_a = 1 - \bar S_a\): $$P(\text{win}) = \int_0^\tau \bar S_1(t)\, d\bar F_0(t), \qquad P(\text{loss}) = \int_0^\tau \bar S_0(t)\, d\bar F_1(t).$$

Hierarchy. When TargetEvent lists several event codes in priority order (highest priority first), the comparison is the prioritized (Pocock / Finkelstein–Schoenfeld) rule applied to the patients' first events: a patient who is event-free beats one who had any event; between two patients with events of different priority, the one whose event is lower priority (less severe) wins; between two with the same event, the one whose event is later wins. Writing the per-arm cause-specific cumulative incidences \(F_a^{(k)}\) for priority \(k\) (\(k=1\) highest), the win probability is again a smooth functional of those marginal curves, $$P(\text{win}) = S_1(\tau)\bigl(1 - S_0(\tau)\bigr) + \sum_{a>b} F_1^{(a)}(\tau)F_0^{(b)}(\tau) + \sum_k \int_0^\tau \bigl[F_1^{(k)}(\tau) - F_1^{(k)}(t)\bigr]\, dF_0^{(k)}(t),$$ with \(S_a(\tau) = 1 - \sum_k F_a^{(k)}(\tau)\), and \(P(\text{loss})\) the mirror image. This reduces exactly to the single-event formula when one event is given.

In all cases the win/loss probabilities are smooth functionals of the targeted curves, so their influence functions are weighted combinations of the per-subject curve influence functions and the win ratio, win odds, and net benefit follow by the delta method — giving doubly-robust, covariate-adjusted, censoring-corrected inference, unlike the standard unadjusted, censoring- sensitive win ratio. The integral is taken over the fitted target times, so use a reasonably dense TargetTime grid.

First-event limitation — use clinicalWinRatio() for most trials. The prioritized comparison here uses each patient's first observed event, treating the listed events as competing risks. A higher-priority event that follows a lower-priority one is therefore not counted — death after a non-fatal hospitalization, or a stroke after a hospitalization. For the clinically intended hierarchy (compare on the most serious event first, whenever it occurs), which is what most trials mean, use clinicalWinRatio(): it estimates the death-priority win ratio over an ordered hierarchy of fatal and non-fatal time-to-event tiers via a multistate model. getWinRatio() is the right choice only when events are genuinely mutually exclusive (a higher-priority event can never follow a lower-priority one).

Usage

getWinRatio(
  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).

Intervention

length-2 numeric: treatment and control indices.

TargetEvent

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

Signif

numeric (default 0.05): alpha for confidence intervals and p-values. Win ratio and win odds are inferred on the log scale.

Value

a data.table of class "ConcreteOut" with the win ratio, win odds, net benefit, and the win/loss/tie probabilities, each with a CI and (for the comparative statistics) a p-value against the null of no difference. If the fit was built with Strata (see formatArguments()), the standard errors are corrected for the stratified / covariate-adaptive randomization design.

See also

getRMST(), getOutput()