This function estimates the potential cumulative incidence function based on
efficient influence functions using hypothetical strategy (competing risks data structure).
Cox models are employed for survival models. The intercurrent event is assumed to be absent
in the hypothetical scenario.
surv.removed.eff(A, Time, cstatus, X = NULL, subset = NULL)
Arguments
- A
Treatment indicator, 1 for treatment and 0 for control.
- Time
Time to event.
- cstatus
Indicator of event, 1 for the primary event, 2 for the intercurrent event, 0 for censoring.
- X
Baseline covariates.
- subset
Subset, either numerical or logical.
Value
A list including
- time1
Time points in the treated group.
- time0
Time points in the control group.
- cif1
Estimated cumulative incidence function in the treated group.
- cif0
Estimated cumulative incidence function in the control group.
- se1
Standard error of the estimated cumulative incidence function in the treated group.
- se0
Standard error of the estimated cumulative incidence function in the control group.
- time
Time points in both groups.
- ate
Estimated treatment effect (difference in cumulative incidence functions).
- se
Standard error of the estimated treatment effect.
- p.val
P value of testing the treatment effect based on the efficient influence function of
the restricted mean survival time lost by the end of study.
Details
The hypothetical strategy envisions a hypothetical clinical trial condition where the occurrence
of intercurrent events is restricted in certain ways. By doing so, the distribution of potential
outcomes under the hypothetical scenario can capture the impact of intercurrent events explicitly
through a pre-specified criterion. We use T'(w), w = 1, 0 to denote the time to the
primary outcome event in the hypothetical scenario. The time-dependent treatment effect specific
to this hypothetical scenario is written as
\tau(t) = P(T'(1) < t) - P(T'(0) < t),
representing the difference in probabilities of experiencing primary outcome events during (0,t)
in the pre-specified hypothetical scenario under active treatment and placebo.
The key question is how to envision T'(w). We manipulate the hazard specific to intercurrent
event \lambda_2(t; w) while assuming the hazard specific to the primary outcome event
\lambda_1(t; w) remains unchanged. Specifically, we envision that intercurrent events are
absent in the hypothetical scenario for all individuals, so \lambda_2'(t;0) = \Lambda_2'(t;1) = 0.
This hypothetical scenario leads to an estimand called the marginal cumulative incidence. The treatment
effect corresponds to the controlled direct effect with the intercurrent events removed.