This function nonparametrically estimates the potential cumulative incidence function
using treatment policy strategy (competing risks data structure). This strategy ignores the intercurrent
event and uses the time to the primary event as it was recorded.
surv.treatment(A, Time, cstatus, weights = rep(1, length(A)), 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.
- weights
Weight for each subject.
- 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 logrank test.
Details
The treatment policy strategy addresses the problem of intercurrent events by expanding
the initial treatment conditions to a treatment policy. This strategy is applicable
only if intercurrent events do not hinder primary outcome events. The treatments under
comparison are now two treatment policies: (w, R(w)), where w = 1, 0. One policy
(1,R(1)) involves administering the test drug, along with any naturally occurring
intercurrents, whereas the other policy (0,R(0)) involves administering a placebo,
along with any naturally occurring intercurrents. Thus, the potential outcomes are
T(1,R(1)) and T(0,R(0)). Instead of comparing the test drug and placebo themselves,
the contrast of interest is made between the two treatment policies. The difference in
cumulative incidences under the two treatment policies is then
\tau(t) = P(T(1, R(1)) < t) - P(T(0, R(0)) < t),ATE_tp
representing the difference in probabilities of experiencing primary outcome events during
(0,t) under active treatment and placebo.
The average treatment effect \tau^{\text{tp}}(t) has a meaningful causal interpretation
only when T(1, R(1)) and T(0, R(0)) are well defined. Because the treatment policy
includes the occurrence of the intercurrent event as natural, the entire treatment policy is
determined by manipulating the initial treatment condition $w$ only. Therefore, we can simplify
the notations T(w, R(w)) = T(w) in defining estimands. As such,
\tau(t) = P(T(1)) < t) - P(T(0) < t) as the intention-to-treat analysis.