Estimation of the Proportion of Treatment Effect Explained by Surrogate Outcome Information

Description

Provides functions to estimate the proportion of treatment effect on a censored primary outcome that is explained by the treatment effect on a censored surrogate outcome/event. All methods are described in detail in Parast, Tian, Cai (2020) "Assessing the Value of a Censored Surrogate Outcome" <doi:10.1007/s10985-019-09473-1>. The main functions are (1) R.q.event() which calculates the proportion of the treatment effect (the difference in restricted mean survival time at time t) explained by surrogate outcome information observed up to a selected landmark time, (2) R.t.estimate() which calculates the proportion of the treatment effect explained by primary outcome information only observed up to a selected landmark time, and (3) IV.event() which calculates the incremental value of the surrogate outcome information.

Details

This package implements all methods proposed in Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265. The main functions are (1) R.q.event() which calculates the proportion of the treatment effect (the difference in restricted mean survival time at time t) explained by surrogate outcome information observed up to a selected landmark time, (2) R.t.estimate() which calculates the proportion of the treatment effect explained by primary outcome information only observed up to a selected landmark time, and (3) IV.event() which calculates the incremental value of the surrogate outcome information.

Author(s)

Layla Parast

Maintainer: Layla Parast <parast@austin.utexas.edu>

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)


R.q.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np")
R.t.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, t = 5, landmark=2)
IV.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np")
R.q.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np", std = TRUE, conf.int = TRUE)
R.t.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, t = 5, landmark=2, std = TRUE, conf.int = TRUE)
IV.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np", std = TRUE, conf.int = TRUE)

Hypothetical data

Description

Hypothetical data to be used in examples; t=5 and the landmark time = 2.

Usage

data(ExampleData)

Format

A list with 6 elements representing 1000 observations from a control group and 1000 observations from a treatment group:

s1

Time of the occurrence of the surrogate outcome for treated observations.

x1

The observed event or censoring time for treated observations; X = min(T, C) where T is the time of the primary outcome and C is the censoring time.

delta1

The indicator identifying whether the treated observation was observed to have the event or was censored; D =1*(T<C) where T is the time of the primary outcome and C is the censoring time.

s0

Time of the occurrence of the surrogate outcome for control observations.

x0

The observed event or censoring time for control observations; X = min(T, C) where T is the time of the primary outcome and C is the censoring time.

delta0

The indicator identifying whether the control observation was observed to have the event or was censored; D =1*(T<C) where T is the time of the primary outcome and C is the censoring time.

Details

Note that the time of the surrogate outcome is used in all functions only if the surrogate outcome occurs before the minimum of the event time and censoring time.

Examples

data(ExampleData)
names(ExampleData)

Calculates the incremental value of the surrogate outcome information

Description

Calculates the incremental value of the surrogate outcome information

Usage

IV.event(xone, xzero, deltaone, deltazero, sone, szero, t, landmark, number = 40, 
transform = FALSE, extrapolate = TRUE, std = FALSE, conf.int = FALSE, 
weight.perturb = NULL, type = "np")

Arguments

Details

The incremental value of the surrogate outcome information only is quantified as IV_S(t,t_0) = R_Q(t,t_0) - R_T(t,t_0) where the definition and estimation procedures for R_Q(t,t_0) and R_T(t,t_0) are described in the documentation for R.q.event and R.t.estimate, respectively. The estimate of the incremental value is \hat{IV}_S(t,t_0) = \hat{R}_Q(t,t_0) - \hat{R}_T(t,t_0).

Value

A list is returned:

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)


IV.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5,
 landmark=2, type = "np")

IV.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5,
 landmark=2, type = "np", std = TRUE, conf.int = TRUE)

Calculates kernel matrix

Description

Helper function; this calculates the kernel matrix

Usage

Kern.FUN(zz, zi, bw, kern0)

Arguments

Value

the kernel matrix

Author(s)

Layla Parast

Calculates the proportion of the treatment effect (the difference in restriced mean survival time at time t) explained by surrogate outcome information observed up to the landmark time

Description

Calculates the proportion of the treatment effect (the difference in restriced mean survival time at time t) explained by surrogate outcome information observed up to the landmark time; also provides standard error estimate and confidence interval.

Usage

R.q.event(xone, xzero, deltaone, deltazero, sone, szero, t, landmark, number = 40, 
transform = FALSE, extrapolate = TRUE, std = FALSE, conf.int = FALSE, 
weight.perturb = NULL, type = "np")

Arguments

Details

Let G \in \{1,0\} be the randomized treatment indicator, T denote the time of the primary outcome of interest, and S denote the time of the surrogate outcome. We use potential outcomes notation such that T^{(G)} and S^{(G)} denote the respective times of the primary and surrogate outcomes under treatment G, for G \in \{1, 0\}. In the absence of censoring, we only observe (T, S)=(T^{(1)}, S^{(1)}) or (T^{(0)}, S^{(0)}) for each individual depending on whether G=1 or 0. Due to censoring, data consist of n = n_1 + n_0 independent observations \{X_{gi}, \delta_{gi}, I(S_{gi}< t_0)I(X_{gi} > t_0), S_{gi}\wedge t_0 I(X_{gi} > t_0), 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, S_{gi} denotes the time of the surrogate outcome, \{(T_{gi}, C_{gi}, S_{gi}), i = 1, ..., n_g\} are identically distributed within treatment group, and t_0 is the landmark time of interest.

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. To define the proportion of treatment effect explained by the surrogate outcome information, let

Q_{t_0} ^{(g)} = (Q_{t_01}, Q_{t_02})'=\{S ^{(g)} \wedge t_0I(T ^{(g)} > t_0), T^{(g)} I(T^{(g)} \le t_0)\}', g=1, 0

and define the residual treatment effect after accounting for the treatment effect on the surrogate outcome information as:

\Delta_Q(t,t_0) = P ^{(0)}_{t_0,2}\int_0^{t_0} \phi_1(t|t_0,s)dF_0(s) + P^{(0)}_{t_0,3}\psi_1(t|t_0) - P(T ^{(0)}> t_0) \nu_0(t|t_0)

where P^{(0)}_{t_0,2} = P(T^{(0)} > {t_0}, S ^{(0)} < t_0) and P^{(0)}_{t_0,3} = P(T^{(0)} > {t_0}, S ^{(0)} > t_0), \psi_1(t \mid t_0) = E(T^{(1)}\wedge t \mid T^{(1)}> t_0, S^{(1)} > t_0), \phi_1(t\mid t_0,s) = E(T^{(1)}\wedge t \mid T ^{(1)}> t_0, S ^{(1)} = s), \quad \nu_0(t|t_0) = E(T ^{(0)} \wedge t | T ^{(0)}> t_0), and F_0(\cdot\mid t_0) is the cumulative distribution function of S^{(0)} conditional on T ^{(0)}> t_0 and S ^{(0)} < t_0. Then, the proportion of treatment effect on the primary outcome that is explained by surrogate information up to t_0, Q_{t_0}, can be expressed as a contrast between \Delta(t) and \Delta_Q(t,t_0):

R_Q(t,t_0) = \{\Delta(t) - \Delta_Q(t,t_0) \} / \Delta(t) = 1- \Delta_Q(t,t_0) / \Delta(t).

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). The residual treatment effect \Delta_Q(t,t_0) can be estimated nonparametrically or semi-parametrically. For nonparametric estimation, \psi_{1}(t|t_0) is estimated by \hat{\psi}_{1}(t|t_0) = \sum_{i=1}^{n_1}\frac{ { \hat{W}^C_1(t_0)} I(S_{1i}>t_0, X_{1i} > t_0) }{ \sum_{i=1}^{n_1}I(S_{1i}>t_0, X_{1i} > t_0)} \hat{M}_{1i}(t), and \phi_1(t \mid t_0,s) = E(T^{(1)}\wedge t\mid X^{(1)}> t_0, S ^{(1)} = s) is estimated using a nonparametric kernel Nelson-Aalen estimator for \Lambda_1(t\mid t_0,s ), the cumulative hazard function of T^{(1)} conditional on S^{(1)}=s and T^{(1)}>t_0, as

\hat \phi_1(t \mid t_0,s) = t_0+\int_ {t_0}^t \exp\{-\hat{\Lambda}_1(t\mid t_0,s) \}dt,

where

\hat{\Lambda}_1(t\mid t_0,s) = \int_{t_0}^t \frac{\sum_{i=1}^{n_1} I(X_{1i}>t_0, {S_{1i} < t_0}) K_h\{\gamma(S_{1i}) - \gamma(s)\}dN_{1i}(z)}{\sum_{i=1}^{n_1} I(X_{1i}>t_0, {S_{1i} < t_0}) K_h\{\gamma(S_{1i}) - \gamma(s)\} Y_{1i}(z)},

is a consistent estimate of \Lambda_1(t\mid t_0,s ), Y_{1i}(t) = I(X_{1i} \geq t), N_{1i}(t) = I(X_{1i} \leq t) \delta_i, K(\cdot) is a smooth symmetric density function, K_h(x) = K(x/h)/h, \gamma(\cdot) is a given monotone transformation function, and h=O(n_1^{-\eta}) is a specified bandwidth with \eta \in (1/2,1/4). Finally, we let

\hat{\nu}_{0}(t|t_0) = \sum_{i=1}^{n_0}\frac{ {\hat{W}^C_0(t_0)}I(X_{0i} > t_0) }{ \sum_{i=1}^{n_0}I(X_{0i} > t_0)} \hat{M}_{0i}(t).

We then estimate \Delta_{Q}(t,t_0) as \hat{\Delta}_{Q}(t,t_0) defined as

n_0^{-1} \sum_{i=1}^{n_0} \left \{ \frac{I_{t_0,2}(X_{0i}, S_{0i})\hat{\phi}_1(t\mid t_0, S_{0i}) + I_{t_0,3}(X_{0i}, S_{0i})\hat{\psi}_1(t\mid t_0) - I_{t_0}(X_{0i})\hat{\nu}(t|t_0) }{\hat{W}^C_0(t_0)} \right \}

where I_{t_0,2}(x, s) = I(x > {t_0}, s < t_0) and I_{t_0,3}(x, s) = I(x > {t_0}, s > t_0) and I_{t_0}(x)=I(x > {t_0}) and thus, \hat{R}_Q(t,t_0) =1- \hat{\Delta}_Q(t,t_0)/\hat{\Delta}(t).

For the semi-parametric estimate, \hat \phi_1(t| t_0,s) is replaced with an estimate obtained using a landmark Cox proportional hazards model

P(T^{(1)}> t\mid T^{(1)}> t_0, S^{(1)} < t_0, S ^{(1)}) = \exp \{ -\Lambda_0(t|t_0)\exp(\beta_0S ^{(1)})\}

where \Lambda_0(t|t_0) is the unspecified baseline cumulative hazard among \Omega_{t_0} = \{T^{(1)}> t_0, S^{(1)} < t_0\} and \beta_0 is unknown. That is, let \tilde \phi_1(t| t_0,s) = t_0+\int_{t_0}^{t}\exp \{ -\hat{\Lambda}_0(t|t_0)\exp(\hat{\beta}s)\} dt, where \hat{\beta} is estimated by fitting a Cox model to the subpopulation \Omega_{t_0} with a single predictor S and \hat{\Lambda}_0(\cdot|t_0) is the corresponding Breslow estimator. Then the semiparametric estimator for \Delta_{Q}(t,t_0) is \tilde{\Delta}_{Q}(t,t_0) defined as

n_0^{-1} \sum_{i=1}^{n_0} \left \{ \frac{I_{t_0,2}(X_{0i}, S_{0i})\tilde{\phi}_1(t\mid t_0, S_{0i}) + I_{t_0,3}(X_{0i}, S_{0i})\hat{\psi}_1(t\mid t_0) - I_{t_0}(X_{0i})\hat{\nu}(t|t_0) }{\hat{W}^C_0(t_0)} \right \}

and \tilde{R}_Q(t,t_0) =1- \tilde{\Delta}_Q(t,t_0)/\hat{\Delta}(t).

Value

A list is returned:

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Parast, L and Cai, T (2013). Landmark risk prediction of residual life for breast cancer survival. Statistics in Medicine, 32(20), 3459-3471.

Examples

data(ExampleData)
names(ExampleData)


R.q.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np")
R.q.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "semi")
R.q.event(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, 
landmark=2, type = "np", std = TRUE, conf.int = TRUE)

Calculates the proportion of the treatment effect (the difference in restricted mean survival time at time t) explained by primary outcome information observed up to the landmark time

Description

Calculates the proportion of the treatment effect (the difference in restricted mean survival time at time t) explained by primary outcome information observed up to the landmark time; also provides standard error estimate and confidence interval.

Usage

R.t.estimate(xone, xzero, deltaone, deltazero, t, landmark, std = FALSE, conf.int
 = FALSE, weight.perturb = NULL)

Arguments

Details

Let G \in \{1,0\} be the randomized treatment indicator, T denote the time of the primary outcome of interest, and S denote the time of the surrogate outcome. We use potential outcomes notation such that T^{(G)} and S^{(G)} denote the respective times of the primary and surrogate outcomes under treatment G, for G \in \{1, 0\}. In the absence of censoring, we only observe (T, S)=(T^{(1)}, S^{(1)}) or (T^{(0)}, S^{(0)}) for each individual depending on whether G=1 or 0. Due to censoring, data consist of n = n_1 + n_0 independent observations \{X_{gi}, \delta_{gi}, I(S_{gi}< t_0)I(X_{gi} > t_0), S_{gi}\wedge t_0 I(X_{gi} > t_0), 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, S_{gi} denotes the time of the surrogate outcome, \{(T_{gi}, C_{gi}, S_{gi}), i = 1, ..., n_g\} are identically distributed within treatment group, and t_0 is the landmark time of interest.

The proportion of treatment effect explained by primary outcome information observed up to the landmark time, t_0, is defined as R_T(t, t_0) = 1-\Delta_T(t,t_0) / \Delta(t) where

\Delta_T(t,t_0) = P(T^{(0)} > t_0) E\{T^{(1)} \wedge t - T^{(0)} \wedge t \mid T > t_0 \}

and \Delta(t) is the treatment effect on the primary outcome, defined in the documentation for delta.estimate. The quantity \Delta_T(t,t_0) is estimated using

\hat{\Delta}_T(t,t_0) = n_0^{-1} \sum_{i=1}^{n_0} I(X_{0i} > t_0) /\hat{W}_0^C(t_0) \{\hat{\nu}_{1}(t|t_0) - \hat{\nu}_{0}(t|t_0) \}

where \hat{W}^C_0(t) is the Kaplan-Meier estimator of P(C_{gi} \ge t), \hat{\nu}_{0}(t|t_0) is defined in the documentation for R.q.event and \hat{\nu}_{1}(t|t_0) is obtained by replacing 0 with 1.

Value

A list is returned:

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)


R.t.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone =ExampleData$delta1, 
deltazero = ExampleData$delta0, t = 5, landmark=2)

R.t.estimate(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, t = 5, landmark=2, std = TRUE, conf.int = TRUE)

Repeats a row

Description

Helper function; this function creates a matrix that repeats vc, dm times where each row is equal to the vc vector.

Usage

VTM(vc, dm)

Arguments

Value

a matrix that repeats vc, dm times where each row is equal to the vc vector

Calculates censoring probability for weighting

Description

Helper function; calculates censoring probability needed for inverse probability of censoring weighting

Usage

censor.weight(data.x, data.delta, t, weight = NULL)

Arguments

Details

Computes the Kaplan Meier estimate of survival for the censoring random variable at the specified time

Value

Kaplan Meier estimate of survival for censoring at time t

Author(s)

Layla Parast

Examples

data(ExampleData)
censor.weight(data.x = ExampleData$x1, data.delta = ExampleData$delta1, t=5)

Helper function

Description

Helper function; should not be called directly by user.

Usage

cumsum2(mydat)

Arguments

Value

Author(s)

Layla Parast

Estimates the treatment effect at time t, defined as the difference in the restricted mean survival time

Description

Estimates the treatment effect at time t, defined as the difference in the restricted mean survival time.

Usage

delta.estimate(xone, xzero, deltaone, deltazero, t, std = FALSE, conf.int = FALSE, 
weight.perturb = NULL)

Arguments

Details

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).

Value

A list is returned:

Author(s)

Layla Parast

References

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.

Examples

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)

Helper function

Description

Helper function; used by delta.estimate function

Usage

delta.estimate.RMST(xone, xzero, deltaone, deltazero, t, weight = NULL, delta.only = F)

Arguments

Value

A list is returned:

Author(s)

Layla Parast

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the surrogate outcome information up to the landmark time

Description

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the surrogate outcome information up to the landmark time; uses nonparametric estimation.

Usage

delta.q.event.RMST(xone, xzero, deltaone, deltazero, sone, szero, t, weight = NULL,
 landmark = landmark, deltaslist = TRUE, transform = FALSE, extrapolate=TRUE, 
 number, warn.extrapolate=TRUE)

Arguments

Details

See documentation for R.q.event for details.

Value

A list is returned:

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)

delta.q.event.RMST(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 5, landmark=2, 
number = 40)
delta.q.event.RMST(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, sone = ExampleData$s1, szero = ExampleData$s0, t = 4, landmark=2, 
number = 40)

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the surrogate outcome information up to the landmark time

Description

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the surrogate outcome information up to the landmark time; uses semi-parametric estimation.

Usage

delta.q.event.semi.RMST(xone, xzero, deltaone, deltazero, sone, szero, t, 
weight = NULL, landmark = landmark, deltaslist = TRUE, number)

Arguments

Details

See documentation for R.q.event for details.

Value

A list is returned:

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)

delta.q.event.semi.RMST(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = 
ExampleData$delta1, deltazero = ExampleData$delta0, sone = ExampleData$s1, 
szero = ExampleData$s0, t = 5, landmark=2, number = 40)
delta.q.event.semi.RMST(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = 
ExampleData$delta1, deltazero = ExampleData$delta0, sone = ExampleData$s1, 
szero = ExampleData$s0, t = 3, landmark=2, number = 40)

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the primary outcome up to the landmark time

Description

Calculates the residual treatment effect (the difference in restricted mean survival time at time t) after accounting for the treatment effect on the primary outcome up to the landmark time

Usage

delta.t.RMST(xone, xzero, deltaone, deltazero, t, weight = NULL, landmark = landmark)

Arguments

Details

See documentation for R.t.estimate for details.

Value

Author(s)

Layla Parast

References

Parast L, Tian L, and Cai T (2020). Assessing the Value of a Censored Surrogate Outcome. Lifetime Data Analysis, 26(2):245-265.

Examples

data(ExampleData)
names(ExampleData)
delta.t.RMST(xone = ExampleData$x1, xzero = ExampleData$x0, deltaone = ExampleData$delta1, 
deltazero = ExampleData$delta0, t = 5, landmark=2)

Helper function

Description

Helper function; should not be called directly by user.

Usage

helper.si(yy,FUN,Yi,Vi=NULL)

Arguments

Value

Author(s)

Layla Parast

Helper function

Description

Helper function; should not be called directly by user. This function differs from the quantile function in that it returns an NA when there are NAs in the supplied vector, rather than causing an error.

Usage

new.q(x, p)

Arguments

Value

returns either NA or the desired sample quantile

Author(s)

Layla Parast

Calculates the conditional probability of survival for control group values

Description

Helper function; calculates the estimated probability of survival for control control group surrogate values using treatment group surrogate and outcome information.

Usage

pred.smooth.surv(xone.f, deltaone.f, sone.f, szero.one, myt, bw = NULL, 
weight, transform, extrapolate = T)

Arguments

Value

A list is returned:

Author(s)

Layla Parast