early.delta.test {SurrogateTest} | R Documentation |
Estimate and test the early treatment effect
Description
Estimates the early treatment effect estimate and provides two versions of the standard error; tests the null hypothesis that this treatment effect is equal to 0
Usage
early.delta.test(Axzero, Adeltazero, Aszero, Bxzero, Bdeltazero, Bszero, Bxone,
Bdeltaone, Bsone, t, landmark, perturb = T, extrapolate = T, transform = F)
Arguments
Axzero |
observed event times in the control group in Study A |
Adeltazero |
event/censoring indicators in the control group in Study A |
Aszero |
surrogate marker values in the control group in Study A, NA for individuals not observable at the time the surrogate marker was measured |
Bxzero |
observed event times in the control group in Study B |
Bdeltazero |
event/censoring indicators in the control group in Study B |
Bszero |
surrogate marker values in the control group in Study B, NA for individuals not observable at the time the surrogate marker was measured |
Bxone |
observed event times in the treatment group in Study B |
Bdeltaone |
event/censoring indicators in the treatment group in Study B |
Bsone |
surrogate marker values in the treatment group in Study B, NA for individuals not observable at the time the surrogate marker was measured |
t |
time of interest |
landmark |
landmark time of interest, t0 |
perturb |
TRUE or FALSE; indicates whether the standard error estimate obtained using perturbation resampling should be calculated |
extrapolate |
TRUE or FALSE; indicates whether local constant extrapolation should be used, default is TRUE |
transform |
TRUE or FALSE; indicates whether a transformation should be used, default is FALSE. |
Details
Assume there are two randomized studies of a treatment effect, a prior study (Study A) and a current study (Study B). Study A was completed up to some time t, while Study B was stopped at time . In both studies, a surrogate marker was measured at time
for individuals still observable at
. 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
and
denote the time of the primary outcome of interest, death for example, under the treatment and under the control, respectively, in Study K. Let
and
denote the surrogate marker measured at time
under the treatment and the control, respectively, in Study K.
The treatment effect quantity of interest, , is the difference in survival rates by time
under treatment versus control,
where . Here, we estimate an early treatment effect quantity using surrogate marker information defined as,
where and
.
To test the null hypothesis that , we test the null hypothesis
using the test statistic
where is a consistent estimate of
and
is the estimated standard error of
We reject the null hypothesis when
where
is the Type 1 error rate.
To obtain , we use
where is the Kaplan-Meier estimator of
and
, where
is a consistent estimate of
,
is a smooth symmetric density function,
and
is a given monotone transformation function. For the bandwidth
, we require the standard undersmoothing assumption of
with
in order to eliminate the impact of the bias of the conditional survival function on the resulting estimator.
The quantity is obtained using either a closed form expression under the null or a perturbation resampling approach. If a confidence interval is desired, perturbation resampling is required.
Value
delta.eb |
The estimate early treatment effect, |
se.closed |
The standard error estimate of the early treatment effect using the closed form expression under the null. |
Z.closed |
The test statistic using the closed form standard error expression. |
p.value.closed |
The p-value using the closed form standard error expression. |
conf.closed.norm |
The confidence interval for the early treatment effect, using a normal approximation and using the closed form standard error expression. |
se.perturb |
The standard error estimate of the early treatment effect using perturbation resampling, if perturb = T. |
Z.perturb |
The test statistic using the perturbed standard error estimate, if perturb = T. |
p.value.perturb |
The p-value using the perturbed standard error estimate, if perturb = T. |
conf.perturb.norm |
The confidence interval for the early treatment effect, using a normal approximation and using the perturbed standard error expression, if perturb = T. |
delta.eb.CI |
The confidence interval for the early treatment effect, using the quantiles of the perturbed estimates, if perturb = T. |
Author(s)
Layla Parast
References
Parast L, Cai T, Tian L (2019). Using a Surrogate Marker for Early Testing of a Treatment Effect. Biometrics, 75(4):1253-1263.
Examples
data(dataA)
data(dataB)
early.delta.test(Axzero = dataA$x0, Adeltazero = dataA$delta0, Aszero = dataA$s0,
Bxzero = dataB$x0, Bdeltazero = dataB$delta0, Bszero = dataB$s0, Bxone = dataB$x1,
Bdeltaone = dataB$delta1, Bsone = dataB$s1, t=1, landmark=0.5, perturb = FALSE,
extrapolate = TRUE)
early.delta.test(Axzero = dataA$x0, Adeltazero = dataA$delta0, Aszero = dataA$s0,
Bxzero = dataB$x0, Bdeltazero = dataB$delta0, Bszero = dataB$s0, Bxone = dataB$x1,
Bdeltaone = dataB$delta1, Bsone = dataB$s1, t=0.75, landmark=0.5, perturb = FALSE,
extrapolate = TRUE)
early.delta.test(Axzero = dataA$x0, Adeltazero = dataA$delta0, Aszero = dataA$s0,
Bxzero = dataB$x0, Bdeltazero = dataB$delta0, Bszero = dataB$s0, Bxone = dataB$x1,
Bdeltaone = dataB$delta1, Bsone = dataB$s1, t=1, landmark=0.5, perturb = TRUE,
extrapolate = TRUE)