Description Usage Arguments Details Value Author(s) References Examples
View source: R/Functions_SurrogateTest.R
Recover an estimate of the treatment effect at time t in Study B
1 2 |
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 |
Axone |
observed event times in the treatment group in Study A |
Adeltaone |
event/censoring indicators in the treatment group in Study A |
Asone |
surrogate marker values in the treatment 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 |
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 |
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 t_0<t. In both studies, a surrogate marker was measured at time t_0 for individuals still observable at t_0. Let G be the binary treatment indicator with G=1 for treatment and G=0 for control and we assume throughout that subjects are randomly assigned to a treatment group at baseline. Let T_K^{(1)} and T_K^{(0)} denote the time of the primary outcome of interest, death for example, under the treatment and under the control, respectively, in Study K. Let S_K^{(1)} and S_K^{(0)} denote the surrogate marker measured at time t_0 under the treatment and the control, respectively, in Study K.
The treatment effect quantity of interest, Δ_K(t), is the difference in survival rates by time t under treatment versus control,
Δ_K(t)=E\{ I(T_K^{(1)}>t)\} - E\{I(T_K^{(0)}>t)\} = P(T_K^{(1)}>t) - P(T_K^{(0)}>t)
where t>t_0. Here, we recover an estimate of Δ_B(t) using Study B information (which stopped follow-up at time t_0<t) and Study A information (which has follow-up information through time t). The estimate is obtained as
\hat{Δ}_{EB}(t,t_0)/ \hat{R}_{SA}(t,t_0)
where \hat{Δ}_{EB}(t,t_0) is the early treatment effect estimate in Study B, described in the early.delta.test documention, and \hat{R}_{SA}(t,t_0) is the proportion of treatment effect explained by the surrogate marker information at t_0 in Study A. This proportion is calculated as \hat{R}_{SA}(t,t_0) =\hat{Δ}_{EA}(t,t_0)/\hat{Δ}_A(t) where
\hat{Δ}_A(t)=n_{A1}^{-1}∑_{i=1}^{n_{A1}}\frac{I(X_{Ai}^{(1)}>t)}{\hat{W}_{A1}^C(t)}-n_{A0}^{-1}∑_{i=1}^{n_{A0}}\frac{I(X_{Ai}^{(0)}>t)}{\hat{W}_{A0}^C(t)},
and \hat{Δ}_{EA}(t,t_0) is parallel to \hat{Δ}_{EB}(t,t_0) except replacing n_{A0}^{-1} ∑_{i=1}^{n_{A0}} \hat{r}_A^{(0)}(t|S_{Ai}^{(0)}, t_0) \frac{I(X_{Ai}^{(0)} > t_0)}{\hat{W}_{A0}^C(t_0)} by n_{A0}^{-1}∑_{i=1}^{n_{A0}}\hat{W}_{A0}^C(t)^{-1}I(X_{Ai}^{(0)}>t), and \hat{W}^C_{Ag}(\cdot) is the Kaplan-Meier estimator of the survival function for C_{A}^{(g)} for g=0,1.
Perturbation resampling is used to provide a standard error estimate for the estimate of Δ_B(t) and a confidence interval.
recovered.deltaB |
The recovered estimate of Δ_B(t). |
sd.recovered.deltaB |
The standard error estimate of the recovered estimate of Δ_B(t). |
conf.quantile.recovered.deltaB |
A confidence interval for the recovered estimate of Δ_B(t). |
Layla Parast
Parast L, Cai T, Tian L (2019). Using a Surrogate Marker for Early Testing of a Treatment Effect. Biometrics, In press.
Parast L, Cai T and Tian L (2017). Evaluating Surrogate Marker Information using Censored Data. Statistics in Medicine, 36(11): 1767-1782.
1 2 3 4 5 6 7 8 9 10 11 | data(dataA)
data(dataB)
recover.B(Axzero = dataA$x0, Adeltazero = dataA$delta0, Aszero = dataA$s0, Axone
= dataA$x1, Adeltaone = dataA$delta1, Asone = dataA$s1, Bxzero = dataB$x0, Bdeltazero
= dataB$delta0, Bszero = dataB$s0, Bxone = dataB$x1, Bdeltaone = dataB$delta1, Bsone
= dataB$s1, t=1, landmark=0.5, extrapolate = TRUE)
recover.B(Axzero = dataA$x0, Adeltazero = dataA$delta0, Aszero = dataA$s0, Axone
= dataA$x1, Adeltaone = dataA$delta1, Asone = dataA$s1, Bxzero = dataB$x0, Bdeltazero
= dataB$delta0, Bszero = dataB$s0, Bxone = dataB$x1, Bdeltaone = dataB$delta1, Bsone
= dataB$s1, t=0.75, landmark=0.5, extrapolate = TRUE)
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