R.t.surv.estimate {Rsurrogate} | R Documentation |
Calculates the proportion of treatment effect explained by the primary outcome information up to a specified time
Description
This function calculates the proportion of treatment effect on the primary outcome explained by the treatment effect on the primary outcome up to . The user can also request a variance estimate, estimated using perturbating-resampling, and a 95% confidence interval. If a confidence interval is requested three versions are provided: a normal approximation based interval, a quantile based interval and Fieller's confidence interval, all using perturbation-resampling.
Usage
R.t.surv.estimate(xone, xzero, deltaone, deltazero, t, weight.perturb = NULL,
landmark, var = FALSE, conf.int = FALSE, approx = T)
Arguments
xone |
numeric vector, the observed event times in the treatment group, X = min(T,C) where T is the time of the primary outcome and C is the censoring time. |
xzero |
numeric vector, the observed event times in the control group, X = min(T,C) where T is the time of the primary outcome and C is the censoring time. |
deltaone |
numeric vector, the event indicators for the treatment group, D = I(T<C) where T is the time of the primary outcome and C is the censoring time. |
deltazero |
numeric vector, the event indicators for the control group, D = I(T<C) where T is the time of the primary outcome and C is the censoring time. |
t |
the time of interest. |
weight.perturb |
weights used for perturbation resampling. |
landmark |
the landmark time |
var |
TRUE or FALSE; indicates whether a variance estimate for delta is requested, default is FALSE. |
conf.int |
TRUE or FALSE; indicates whether a 95% confidence interval for delta is requested, default is FALSE. |
approx |
TRUE or FALSE indicating whether an approximation should be used when calculating the probability of censoring; most relevant in settings where the survival time of interest for the primary outcome is greater than the last observed event but before the last censored case, default is TRUE. |
Details
Let be the binary treatment indicator with
for treatment and
for control and we assume throughout that subjects are randomly assigned to a treatment group at baseline. Let
denote the time of the primary outcome of interest, death for example. We use potential outcomes notation such that
denotes the time of the primary outcome under treatment
. The proportion of treatment effect explained by T observed up to
only is
where
To estimate , we use the estimator
where
and
for
where
is the Kaplan-Meier estimator of survival for censoring for
Value
A list is returned:
delta |
the estimate, |
delta.t |
the estimate, |
R.t |
the estimate, |
delta.var |
the variance estimate of |
delta.t.var |
the variance estimate of |
R.t.var |
the variance estimate of |
conf.int.normal.delta |
a vector of size 2; the 95% confidence interval for |
conf.int.quantile.delta |
a vector of size 2; the 95% confidence interval for |
conf.int.normal.delta.t |
a vector of size 2; the 95% confidence interval for |
conf.int.quantile.delta.t |
a vector of size 2; the 95% confidence interval for |
conf.int.normal.R.t |
a vector of size 2; the 95% confidence interval for |
conf.int.quantile.R.t |
a vector of size 2; the 95% confidence interval for |
conf.int.fieller.R.t |
a vector of size 2; the 95% confidence interval for |
Note
If the treatment effect is not significant, the user will receive the following message: "Warning: it looks like the treatment effect is not significant; may be difficult to interpret the residual treatment effect in this setting".
Author(s)
Layla Parast
References
Parast, L., Cai, T., & Tian, L. (2017). Evaluating surrogate marker information using censored data. Statistics in Medicine, 36(11), 1767-1782.
Examples
data(d_example_surv)
names(d_example_surv)