Package 'CSTE' reference manual

Title:	Covariate Specific Treatment Effect (CSTE) Curve
Description:	A uniform statistical inferential tool in making individualized treatment decisions, which implements the methods of Ma et al. (2017)<DOI:10.1177/0962280214541724> and Guo et al. (2021)<DOI:10.1080/01621459.2020.1865167>. It uses a flexible semiparametric modeling strategy for heterogeneous treatment effect estimation in high-dimensional settings and can gave valid confidence bands. Based on it, one can find the subgroups of patients that benefit from each treatment, thereby making individualized treatment selection.
Authors:	Peng Wu [aut], Wenjie Hu [aut, cre], Yuhao Deng [aut], Haoxiang Wang [aut], Xiaohua Zhou [aut]
Maintainer:	Wenjie Hu <[email protected]>
License:	GPL (>= 2)
Version:	3.0.0
Built:	2025-02-18 05:26:58 UTC
Source:	https://github.com/cran/CSTE

Estimate the CSTE curve for binary outcome.

Description

Estimate covariate-specific treatment effect (CSTE) curve. Input data contains covariates $X$ , treatment assignment $Z$ and binary outcome $Y$ . The working model is

$logit(\mu(X, Z)) = g_1(X\beta_1)Z + g_2(X\beta_2),$

where $\mu(X, Z) = E(Y|X, Z)$ . The model implies that $CSTE(x) = g_1(x\beta_1)$ .

Usage

cste_bin(
  x,
  y,
  z,
  beta_ini = NULL,
  lam = 0,
  nknots = 1,
  max.iter = 200,
  eps = 0.001
)
cste_bin(
  x,
  y,
  z,
  beta_ini = NULL,
  lam = 0,
  nknots = 1,
  max.iter = 200,
  eps = 0.001
)

Arguments

`x`	samples of covariates which is a $n*p$ matrix.
`y`	samples of binary outcome which is a $n*1$ vector.
`z`	samples of treatment indicator which is a $n*1$ vector.
`beta_ini`	initial values for $(\beta_1', \beta_2')'$ , default value is NULL.
`lam`	value of the lasso penalty parameter $\lambda$ for $\beta_1$ and $\beta_2$ , default value is 0.
`nknots`	number of knots for the B-spline for estimating $g_1$ and $g_2$ .
`max.iter`	maximum iteration for the algorithm.
`eps`	numeric scalar $\geq$ 0, the tolerance for the estimation of $\beta_1$ and $\beta_2$ .

Value

A S3 class of cste, which includes:

beta1: estimate of $\beta_1$ .
beta2: estimate of $\beta_2$ .
B1: the B-spline basis for estimating $g_1$ .
B2: the B-spline basis for estimating $g_2$ .
delta1: the coefficient of B-spline for estimating $g_1$ .
delta2: the coefficient for B-spline for estimating $g_2$ .
iter: number of iteration.
g1: the estimate of $g_1(X\beta_1)$ .
g2: the estimate of $g_2(X\beta_2)$ .

References

Guo W., Zhou X. and Ma S. (2021). Estimation of Optimal Individualized Treatment Rules Using a Covariate-Specific Treatment Effect Curve with High-dimensional Covariates, Journal of the American Statistical Association, 116(533), 309-321

Examples

## Quick example for the cste

library(mvtnorm)
library(sigmoid)

# --------  Example 1: p = 20 ---------  #  
## generate data 
n <- 2000
p <- 20
set.seed(100)

# generate X
sigma <- outer(1:p, 1:p, function(i, j){ 2^(-abs(i-j)) } )
X <- rmvnorm(n, mean = rep(0,p), sigma = sigma)
X <- relu(X + 2) - 2
X <- 2 - relu(2 - X)

# generate Z
Z <- rbinom(n, 1, 0.5)

# generate Y
beta1 <- rep(0, p)
beta1[1:3] <- rep(1/sqrt(3), 3)
beta2 <- rep(0, p)
beta2[1:2] <- c(1, -2)/sqrt(5)
mu1 <- X %*% beta1
mu2 <- X %*% beta2
g1 <- mu1*(1 - mu1)
g2 <- exp(mu2)      
prob <- sigmoid(g1*Z + g2)
Y <- rbinom(n, 1, prob)

## estimate the CSTE curve
fit <- cste_bin(X, Y, Z)

## plot 
plot(mu1, g1, cex = 0.5, xlim = c(-2,2), ylim = c(-8, 3), 
     xlab = expression(X*beta), ylab = expression(g1(X*beta)))
     ord <- order(mu1)
     points(mu1[ord], fit$g1[ord], col = 'blue', cex = 0.5)
     
## compute 95% simultaneous confidence band (SCB)
res <- cste_bin_SCB(X, fit, alpha = 0.05)

## plot 
plot(res$or_x, res$fit_x, col = 'red', 
     type="l", lwd=2, lty = 3, ylim = c(-10,8),
     ylab=expression(g1(X*beta)), xlab = expression(X*beta), 
     main="Confidence Band")
lines(res$or_x, res$lower_bound, lwd=2.5, col = 'purple', lty=2)
lines(res$or_x, res$upper_bound, lwd=2.5, col = 'purple', lty=2)
abline(h=0, cex = 0.2, lty = 2)
legend("topleft", legend=c("Estimates", "SCB"), 
        lwd=c(2, 2.5), lty=c(3,2), col=c('red', 'purple'))
        
        
# --------  Example 2: p = 1 ---------  #  

## generate data 
set.seed(15)
p <- 1
n <- 2000
X <- runif(n)
Z <- rbinom(n, 1, 0.5)
g1 <- 2 * sin(5*X) 
g2 <- exp(X-3) * 2
prob <- sigmoid( Z*g1 + g2)
Y <- rbinom(n, 1, prob)

## estimate the CSTE curve
fit <- cste_bin(X, Y, Z)  

## simultaneous confidence band (SCB)
X <- as.matrix(X)
res <- cste_bin_SCB(X, fit)  

## plot 
plot(res$or_x, res$fit_x, col = 'red', type="l", lwd=2, 
     lty = 3, xlim = c(0, 1), ylim = c(-4, 4), 
     ylab=expression(g1(X)), xlab = expression(X), 
     main="Confidence Band")
lines(res$or_x, res$lower_bound, lwd=2.5, col = 'purple', lty=2)
lines(res$or_x, res$upper_bound, lwd=2.5, col = 'purple', lty=2)
abline(h=0, cex = 0.2)
lines(X[order(X)], g1[order(X)], col = 'blue', lwd = 1.5)
legend("topright", legend=c("Estimates", "SCB",'True CSTE Curve'), 
lwd=c(2, 2.5, 1.5), lty=c(3,2,1), col=c('red', 'purple','blue'))

## Quick example for the cste

library(mvtnorm)
library(sigmoid)

# --------  Example 1: p = 20 ---------  #  
## generate data 
n <- 2000
p <- 20
set.seed(100)

# generate X
sigma <- outer(1:p, 1:p, function(i, j){ 2^(-abs(i-j)) } )
X <- rmvnorm(n, mean = rep(0,p), sigma = sigma)
X <- relu(X + 2) - 2
X <- 2 - relu(2 - X)

# generate Z
Z <- rbinom(n, 1, 0.5)

# generate Y
beta1 <- rep(0, p)
beta1[1:3] <- rep(1/sqrt(3), 3)
beta2 <- rep(0, p)
beta2[1:2] <- c(1, -2)/sqrt(5)
mu1 <- X %*% beta1
mu2 <- X %*% beta2
g1 <- mu1*(1 - mu1)
g2 <- exp(mu2)      
prob <- sigmoid(g1*Z + g2)
Y <- rbinom(n, 1, prob)

## estimate the CSTE curve
fit <- cste_bin(X, Y, Z)

## plot 
plot(mu1, g1, cex = 0.5, xlim = c(-2,2), ylim = c(-8, 3), 
     xlab = expression(X*beta), ylab = expression(g1(X*beta)))
     ord <- order(mu1)
     points(mu1[ord], fit$g1[ord], col = 'blue', cex = 0.5)
     
## compute 95% simultaneous confidence band (SCB)
res <- cste_bin_SCB(X, fit, alpha = 0.05)

## plot 
plot(res$or_x, res$fit_x, col = 'red', 
     type="l", lwd=2, lty = 3, ylim = c(-10,8),
     ylab=expression(g1(X*beta)), xlab = expression(X*beta), 
     main="Confidence Band")
lines(res$or_x, res$lower_bound, lwd=2.5, col = 'purple', lty=2)
lines(res$or_x, res$upper_bound, lwd=2.5, col = 'purple', lty=2)
abline(h=0, cex = 0.2, lty = 2)
legend("topleft", legend=c("Estimates", "SCB"), 
        lwd=c(2, 2.5), lty=c(3,2), col=c('red', 'purple'))
        
        
# --------  Example 2: p = 1 ---------  #  

## generate data 
set.seed(15)
p <- 1
n <- 2000
X <- runif(n)
Z <- rbinom(n, 1, 0.5)
g1 <- 2 * sin(5*X) 
g2 <- exp(X-3) * 2
prob <- sigmoid( Z*g1 + g2)
Y <- rbinom(n, 1, prob)

## estimate the CSTE curve
fit <- cste_bin(X, Y, Z)  

## simultaneous confidence band (SCB)
X <- as.matrix(X)
res <- cste_bin_SCB(X, fit)  

## plot 
plot(res$or_x, res$fit_x, col = 'red', type="l", lwd=2, 
     lty = 3, xlim = c(0, 1), ylim = c(-4, 4), 
     ylab=expression(g1(X)), xlab = expression(X), 
     main="Confidence Band")
lines(res$or_x, res$lower_bound, lwd=2.5, col = 'purple', lty=2)
lines(res$or_x, res$upper_bound, lwd=2.5, col = 'purple', lty=2)
abline(h=0, cex = 0.2)
lines(X[order(X)], g1[order(X)], col = 'blue', lwd = 1.5)
legend("topright", legend=c("Estimates", "SCB",'True CSTE Curve'), 
lwd=c(2, 2.5, 1.5), lty=c(3,2,1), col=c('red', 'purple','blue'))

Calculate simultaneous confidence bands of CSTE curve for binary outcome.

Description

This function calculates simultaneous confidence bands of CSTE curve for binary outcome.

Usage

cste_bin_SCB(x, fit, h = NULL, alpha = 0.05)
cste_bin_SCB(x, fit, h = NULL, alpha = 0.05)

Arguments

`x`	samples of predictor, which is a $m*p$ matrix.
`fit`	a S3 class of cste.
`h`	kernel bandwidth.
`alpha`	the simultaneous confidence bands are of $1-\alpha$ confidence level.

Value

A list which includes:

or_x: the ordered value of $X\beta_1$ .
fit_x: the fitted value of CSTE curve corresponding to or_x.
lower_bound: the lower bound of CSTE's simultaneous confidence band.
upper_bound: the upper bound of CSTE's simultaneous confidence band.

References

Estimate the CSTE curve for time to event outcome with right censoring.

Description

Estimate the CSTE curve for time to event outcome with right censoring. The working model is

$\lambda(t| X, Z) = \lambda_0(t) \exp(\beta^T(X)Z + g(X)),$

which implies that $CSTE(x) = \beta(x)$ .

Usage

cste_surv(x, y, z, s, h)
cste_surv(x, y, z, s, h)

Arguments

`x`	samples of biomarker (or covariate) which is a $n*1$ vector and should be scaled between 0 and 1.
`y`	samples of time to event which is a $n*1$ vector.
`z`	samples of treatment indicator which is a $n*K$ matrix.
`s`	samples of censoring indicator which is a $n*1$ vector.
`h`	kernel bandwidth.

Value

A $n*K$ matrix, estimation of $\beta(x)$ .

References

Ma Y. and Zhou X. (2017). Treatment selection in a randomized clinical trial via covariate-specific treatment effect curves, Statistical Methods in Medical Research, 26(1), 124-141.

Calculate simultaneous confidence bands (SCB) of CSTE curve for time to event outcome with right censoring.

Description

This function calculates simultaneous confidence bands of CSTE curve for time to event outcome with right censoring.

Usage

cste_surv_SCB(l, x, y, z, s, h, m, alpha = 0.05)
cste_surv_SCB(l, x, y, z, s, h, m, alpha = 0.05)

Arguments

`l`	contraction vector with dimension $K$ .
`x`	samples of biomarker (or covariate) which is a $n*1$ vector and should be scaled between 0 and 1.
`y`	samples of time to event which is a $n*1$ vector.
`z`	samples of treatment indicator which is a $n*K$ matrix.
`s`	samples of censoring indicator which is a $n*1$ vector.
`h`	kernel bandwidth.
`m`	number of turns of resampling.
`alpha`	the $(1-\alpha)$ -confidence level of SCB.

Value

A $n*3$ matrix, estimation of $l^T \beta(x)$ and its simultaneous confidence bands.

References

Ma Y. and Zhou X. (2017). Treatment selection in a randomized clinical trial via covariate-specific treatment effect curves, Statistical Methods in Medical Research, 26(1), 124-141.

Solve the penalized logistic regression.

Description

Solve the penalized logistic regression.

Usage

penC(x, y, off, beta, lam, pen)
penC(x, y, off, beta, lam, pen)

Arguments

`x`	samples of covariates which is a $n*p$ matrix.
`y`	samples of binary outcome which is a $n*1$ vector.
`off`	offset in logistic regression.
`beta`	initial estimates.
`lam`	value of the lasso penalty parameter $\lambda$ for $\beta_1$ and $\beta_2$ .
`pen`	1: MCP estimator; 2: SCAD estimator.

Value

A numeric vector, estimate of beta

Predict the CSTE curve of new data for binary outcome.

Description

Predict the CSTE curve of new data for binary outcome.

Usage

predict_cste_bin(obj, newx)
predict_cste_bin(obj, newx)

Arguments

`obj`	a S3 class of cste.
`newx`	samples of covariates which is a $m*p$ matrix.

Value

A S3 class of cste which includes

g1: predicted $g_1(X\beta_1)$ .
g2: predicted $g_2(X\beta_2)$ .
B1: the B-spline basis for estimating $g_1$ .
B2: the B-spline basis for estimating $g_2$ .

References

Select the optimal tuning parameters in CSTE estimation for binary outcome.

Description

select lasso penalty parameter $\lambda$ for $\beta_1$ and $\beta_2$ in CSTE estimation.

Usage

select_cste_bin(
  x,
  y,
  z,
  lam_seq,
  beta_ini = NULL,
  nknots = 1,
  max.iter = 2000,
  eps = 0.001
)
select_cste_bin(
  x,
  y,
  z,
  lam_seq,
  beta_ini = NULL,
  nknots = 1,
  max.iter = 2000,
  eps = 0.001
)

Arguments

`x`	samples of covariates which is a $n*p$ matrix.
`y`	samples of binary outcome which is a $n*1$ vector.
`z`	samples of treatment indicator which is a $n*1$ vector.
`lam_seq`	a sequence for the choice of $\lambda$ .
`beta_ini`	initial values for $(\beta_1', \beta_2')'$ , default value is NULL.
`nknots`	number of knots for the B-spline for estimating $g_1$ and $g_2$ .
`max.iter`	maximum iteration for the algorithm.
`eps`	numeric scalar $\geq$ 0, the tolerance for the estimation of $\beta_1$ and $\beta_2$ .

Value

A list which includes

optimal: optimal cste within the given the sequence of $\lambda$ .
bic: BIC for the sequence of $\lambda$ .
lam_seq: the sequence of $\lambda$ that is used.

Package 'CSTE'

Help Index

Estimate the CSTE curve for binary outcome.

Description

Usage

Arguments

Value

References

See Also

Examples

Calculate simultaneous confidence bands of CSTE curve for binary outcome.

Description

Usage

Arguments

Value

References

See Also

Estimate the CSTE curve for time to event outcome with right censoring.

Description

Usage

Arguments

Value

References

See Also

Calculate simultaneous confidence bands (SCB) of CSTE curve for time to event outcome with right censoring.

Description

Usage

Arguments

Value

References

See Also

Solve the penalized logistic regression.

Description

Usage

Arguments

Value

Predict the CSTE curve of new data for binary outcome.

Description

Usage

Arguments

Value

References

See Also

Select the optimal tuning parameters in CSTE estimation for binary outcome.

Description

Usage

Arguments

Value

References

See Also