ICA.BinCont {Surrogate}R Documentation

Assess surrogacy in the causal-inference single-trial setting in the binary-continuous case

Description

The function ICA.BinCont quantifies surrogacy in the single-trial setting within the causal-inference framework (individual causal association) when the surrogate endpoint is continuous (normally distributed) and the true endpoint is a binary outcome. For details, see Alonso Abad et al. (2023).

Usage

ICA.BinCont(Dataset, Surr, True, Treat, 
  BS=FALSE,
  G_pi_10=c(0,1), 
  G_rho_01_00=c(-1,1), 
  G_rho_01_01=c(-1,1), 
  G_rho_01_10=c(-1,1), 
  G_rho_01_11=c(-1,1), 
  Theta.S_0, 
  Theta.S_1, 
  M=1000, Seed=123, 
  Monotonicity=FALSE,
  Independence=FALSE,
  HAA=FALSE,
  Cond_ind=FALSE,
  Plots=TRUE, Save.Plots="No", Show.Details=FALSE)

Arguments

Dataset

A data.frame that should consist of one line per patient. Each line contains (at least) a surrogate value, a true endpoint value, and a treatment indicator.

Surr

The name of the variable in Dataset that contains the surrogate endpoint values.

True

The name of the variable in Dataset that contains the true endpoint values.

Treat

The name of the variable in Dataset that contains the treatment indicators. The treatment indicator should be coded as 11 for the experimental group and 1-1 for the control group.

BS

Logical. If BS=TRUE, the sampling variability is accounted for in the analysis by using a bootstrap procedure. Default BS=FALSE.

G_pi_10

The lower and upper limits of the uniform distribution from which the probability parameter π10\pi_{10} is sampled. Default c(0,1). When Monotonicity=TRUE the values of these limits are set as c(0,0).

G_rho_01_00

The lower and upper limits of the uniform distribution from which the association parameter ρ0100\rho_{01}^{00} is sampled. Default c(-1,1).

G_rho_01_01

The lower and upper limits of the uniform distribution from which the association parameter ρ0101\rho_{01}^{01} is sampled. Default c(-1,1).

G_rho_01_10

The lower and upper limits of the uniform distribution from which the association parameter ρ0110\rho_{01}^{10} is sampled. Default c(-1,1).

G_rho_01_11

The lower and upper limits of the uniform distribution from which the association parameter ρ0111\rho_{01}^{11} is sampled. Default c(-1,1).

Theta.S_0

The starting values of the means and standard deviations for the mixture distribution of the surrogate endpoint in the control group. The argument should contain eight values, where the first four values represent the starting values for the means and the last four values represent the starting values for the standard deviations. These starting values should be approximated based on the data on hand. Example: Theta.S_0=c(-10,-5,5,10,10,10,10,10).

Theta.S_1

The starting values of the means and standard deviations for the mixture distribution of the surrogate endpoint in the treatment group. The argument should contain eight values, where the first four values represent the starting values for the means and the last four values represent the starting values for the standard deviations. These starting values should be approximated based on the data on hand. Example: Theta.S_1=c(-10,-5,5,10,10,10,10,10).

M

The number of Monte Carlo iterations. Default M=1000.

Seed

The random seed to be used in the analysis (for reproducibility). Default Seed=123.

Monotonicity

Logical. If Monotonicity=TRUE, the analysis is performed assuming monotonicity, i.e. P(T1<T0)=0P(T_1 < T_0) = 0. Default Monotonicity=FALSE.

Independence

Logical. If Independence=TRUE, the analysis is performed assuming independence between the treatment effect in both groups, i.e. πij=πi.×π.j\pi_{ij} = \pi_{i.} \times \pi_{.j}. Default Independence=FALSE.

HAA

Logical. If HAA=TRUE, the analysis is performed assuming homogeneous association, i.e. ρ01ij=ρ01\rho_{01}^{ij} = \rho_{01}. Default HAA=FALSE.

Cond_ind

Logical. If Cond_ind=TRUE, the analysis is performed assuming conditional independence, i.e. ρ01=0\rho_{01} = 0. Default Cond_ind=FALSE.

Plots

Logical. Should histograms of S0S_0 (surrogate endpoint in control group) and S1S_1 (surrogate endpoint in experimental treatment group) be provided together with density of fitted mixtures? Default Plots=TRUE.

Save.Plots

Should the plots (see previous item) be saved? If Save.Plots="No", no plots are saved. If plots have to be saved, replace "No" by the desired location, e.g., Save.Plots="C:/". Default Save.Plots="No".

Show.Details

Should some details regarding the availability of some output from the function be displayed in the console when the analysis is running? Setting Show.Details=TRUE could be useful for debugging procedure (if any). Default Show.Details=FALSE.

Value

An object of class ICA.BinCont with components,

R2_H

The vector of the RH2R_H^2 values.

pi_00

The vector of π00T\pi_{00}^T values.

pi_01

The vector of π01T\pi_{01}^T values.

pi_10

The vector of π10T\pi_{10}^T values.

pi_11

The vector of π11T\pi_{11}^T values.

G_rho_01_00

The vector of the ρ0100\rho_{01}^{00} values.

G_rho_01_01

The vector of the ρ0101\rho_{01}^{01} values.

G_rho_01_10

The vector of the ρ0110\rho_{01}^{10} values.

G_rho_01_11

The vector of the ρ0111\rho_{01}^{11} values.

pi_Delta_T_min1

The vector of the π1ΔT\pi_{-1}^{\Delta T} values.

pi_Delta_T_0

The vector of the π0ΔT\pi_{0}^{\Delta T} values.

pi_Delta_T_1

The vector of the π1ΔT\pi_{1}^{\Delta T} values.

pi_0_00

The vector of π00\pi_{00} values of f(S0)f(S_0).

pi_0_01

The vector of π01\pi_{01} values of f(S0)f(S_0).

pi_0_10

The vector of π10\pi_{10} values of f(S0)f(S_0).

pi_0_11

The vector of π11\pi_{11} values of f(S0)f(S_0).

mu_0_00

The vector of mean μ000\mu_{0}^{00} values of f(S0)f(S_0).

mu_0_01

The vector of mean μ001\mu_{0}^{01} values of f(S0)f(S_0).

mu_0_10

The vector of mean μ010\mu_{0}^{10} values of f(S0)f(S_0).

mu_0_11

The vector of mean μ011\mu_{0}^{11} values of f(S0)f(S_0).

sigma2_00_00

The vector of variance σ0000\sigma_{00}^{00} values of f(S0)f(S_0).

sigma2_00_01

The vector of variance σ0001\sigma_{00}^{01} values of f(S0)f(S_0).

sigma2_00_10

The vector of variance σ0010\sigma_{00}^{10} values of f(S0)f(S_0).

sigma2_00_11

The vector of variance σ0011\sigma_{00}^{11} values of f(S0)f(S_0).

pi_1_00

The vector of π00\pi_{00} values of f(S1)f(S_1).

pi_1_01

The vector of π01\pi_{01} values of f(S1)f(S_1).

pi_1_10

The vector of π10\pi_{10} values of f(S1)f(S_1).

pi_1_11

The vector of π11\pi_{11} values of f(S1)f(S_1).

mu_1_00

The vector of mean μ100\mu_{1}^{00} values of f(S1)f(S_1).

mu_1_01

The vector of mean μ101\mu_{1}^{01} values of f(S1)f(S_1).

mu_1_10

The vector of mean μ110\mu_{1}^{10} values of f(S1)f(S_1).

mu_1_11

The vector of mean μ111\mu_{1}^{11} values of f(S1)f(S_1).

sigma2_11_00

The vector of variance σ1100\sigma_{11}^{00} values of f(S1)f(S_1).

sigma2_11_01

The vector of variance σ1101\sigma_{11}^{01} values of f(S1)f(S_1).

sigma2_11_10

The vector of variance σ1110\sigma_{11}^{10} values of f(S1)f(S_1).

sigma2_11_11

The vector of variance σ1111\sigma_{11}^{11} values of f(S1)f(S_1).

mean_Y_S0

The vector of mean μ0\mu_{0} values of f(S0)f(S_0).

mean_Y_S1

The vector of mean μ1\mu_{1} values of f(S1)f(S_1).

var_Y_S0

The vector of variance σ00\sigma_{00} values of f(S0)f(S_0).

var_Y_S1

The vector of variance σ11\sigma_{11} values of f(S1)f(S_1).

dev_S0

The vector of deviance values of the normal mixture for f(S0)f(S_0).

dev_S1

The vector of deviance values of the normal mixture for f(S1)f(S_1).

code_nlm_0

An integer indicating why the optimization process to estimate the mixture normal parameters of f(S0)f(S_0) terminated: 1) relative gradient is close to zero, current iterate is probably solution; 2) successive iterates within tolerance, current iterate is probably solution; 3) last global step failed to locate a point lower than the estimate, the estimate might be an approximate local minimum of the function.

code_nlm_1

An integer indicating why the optimization process to estimate the mixture normal parameters of f(S1)f(S_1) terminated: 1) relative gradient is close to zero, current iterate is probably solution; 2) successive iterates within tolerance, current iterate is probably solution; 3) last global step failed to locate a point lower than the estimate, the estimate might be an approximate local minimum of the function.

mean.S0

The mean of S0S_0.

var.S0

The variance of S0S_0.

mean.S1

The mean of S1S_1.

var.S1

The variance of S1S_1.

Author(s)

Wim Van der Elst, Fenny Ong, Ariel Alonso, and Geert Molenberghs

References

Alonso Abad, A., Ong, F., Stijven, F., Van der Elst, W., Molenberghs, G., Van Keilegom, I., Verbeke, G., & Callegaro, A. (2023). An information-theoretic approach for the assessment of a continuous outcome as a surrogate for a binary true endpoint based on causal inference: Application to vaccine evaluation.

See Also

ICA.ContCont, MICA.ContCont, ICA.BinBin

Examples

## Not run: # Time consuming code part
data(Schizo)
Fit <- ICA.BinCont(Dataset = Schizo, Surr = BPRS, True = PANSS_Bin, 
Theta.S_0=c(-10,-5,5,10,10,10,10,10), Theta.S_1=c(-10,-5,5,10,10,10,10,10), 
Treat=Treat, M=50, Seed=1)

summary(Fit)
plot(Fit)

## End(Not run)

[Package Surrogate version 3.3.0 Index]