delta.estimate {SurrogateOutcome} | R Documentation |
Estimates the treatment effect at time t, defined as the difference in the restricted mean survival time.
delta.estimate(xone, xzero, deltaone, deltazero, t, std = FALSE, conf.int = FALSE,
weight.perturb = NULL)
xone |
numeric vector, observed event times for the primary outcome in the treatment group. |
xzero |
numeric vector, observed event times for the primary outcome in the control group. |
deltaone |
numeric vector, event/censoring indicators for the primary outcome in the treatment group. |
deltazero |
numeric vector, event/censoring indicators for the primary outcome in the control group. |
t |
time of interest for treatment effect. |
std |
TRUE or FALSE; indicates whether standard error estimates should be provided, default is FALSE. Estimates are calculated using perturbation-resampling. Two versions are provided: one that takes the standard deviation of the perturbed estimates (denoted as "sd") and one that takes the median absolute deviation (denoted as "mad"). |
conf.int |
TRUE or FALSE; indicates whether 95% confidence intervals should be provided. Confidence intervals are calculated using the percentiles of perturbed estimates, default is FALSE. If this is TRUE, standard error estimates are automatically provided. |
weight.perturb |
weights used for perturbation resampling. |
Let G \in \{1,0\}
be the randomized treatment indicator and T
denote the time of the primary outcome of interest. We use potential outcomes notation such that T^{(G)}
denotes the time of the primary outcome under treatment G, for G \in \{1, 0\}
. We define the treatment effect as the difference in restricted mean survival time up to a fixed time t
under treatment 1 versus under treatment 0,
\Delta(t)=E\{T^{(1)}\wedge t\} - E\{T^{(0)}\wedge t \}
where \wedge
indicates the minimum. Due to censoring, data consist of n = n_1 + n_0
independent observations \{X_{gi}, \delta_{gi}, i=1,...,n_g, g = 1,0\}
, where X_{gi} = T_{gi}\wedge C_{ gi}
, \delta_{gi} = I(T_{gi} < C_{gi})
, C_{gi}
denotes the censoring time, T_{gi}
denotes the time of the primary outcome, and \{(T_{gi}, C_{gi}), i = 1, ..., n_g\}
are identically distributed within treatment group. The quantity \Delta(t)
is estimated using inverse probability of censoring weights:
\hat{\Delta}(t) = n_1^{-1} \sum_{i=1}^{n_1} \hat{M}_{1i}(t)- n_0^{-1} \sum_{i=1}^{n_0} \hat{M}_{0i}(t)
where \hat{M}_{gi}(t) = I(X_{gi} > t)t/\hat{W}^C_g(t) + I(X_{gi} < t)X_{gi}\delta_{gi}/\hat{W}^C_g(X_{gi})
and \hat{W}^C_g(t)
is the Kaplan-Meier estimator of P(C_{gi} \ge t).
A list is returned:
delta |
the estimate, |
rmst.1 |
the estimated restricted mean survival time in group 1, described above. |
rmst.0 |
the estimated restricted mean survival time in group 0, described above. |
delta.sd |
the standard error estimate of |
delta.mad |
the standard error estimate of |
conf.int.delta |
a vector of size 2; the 95% confidence interval for |
Layla Parast
Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.
Tian, L, Zhao, L, & Wei, LJ (2013). Predicting the restricted mean event time with the subject's baseline covariates in survival analysis. Biostatistics, 15(2), 222-233.
Royston, P, & Parmar, MK (2011). The use of restricted mean survival time to estimate the treatment effect in randomized clinical trials when the proportional hazards assumption is in doubt. Statistics in Medicine, 30(19), 2409-2421.
data(ExampleData)
names(ExampleData)
delta.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1,
deltazero = ExampleData$delta0, t = 5)
delta.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1,
deltazero = ExampleData$delta0, t = 5, std = TRUE, conf.int = TRUE)