Help for package CSTE

Version:

3.0.0

Date:

2024-11-16

Type:

Package

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.

License:

GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]

Encoding:

UTF-8

Imports:

Rcpp (≥ 1.0.4), fda, splines, survival, locpol, dfoptim

LinkingTo:

Rcpp

RoxygenNote:

7.1.1

Suggests:

mvtnorm, sigmoid

NeedsCompilation:

yes

Packaged:

2024-11-18 16:47:21 UTC; wenjiehu

Author:

Peng Wu [aut], Wenjie Hu [aut, cre], Yuhao Deng [aut], Haoxiang Wang [aut], Xiaohua Zhou [aut]

Maintainer:

Wenjie Hu <huwenjie@pku.edu.cn>

Repository:

CRAN

Date/Publication:

2024-11-19 12:00:15 UTC

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
)

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'))

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)

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)

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)

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)

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)

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
)

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.

References

tool functions

Description

tool functions

Usage

ztrans(z, x, x0, h)

lpl(input, x, x0, R, z, s, h)

g(x0, sep, sloped)

cntcov(l, beta0, beta0dot, g0dot, x, x0, R, Z, s, h, sep, sloped)

sampleQ(i, l, stdel, stgam, std, x, R, Z, s, h, sep, sloped, m)

getthres(alpha, l, stdel, stgam, std, x, R, Z, s, h, sep, sloped, m)

get.bound(thres, l, stdel, stgam, std, x, R, Z, s, h, sep, sloped)

pu(x, beta)

pu_inv(x, beta, u)

normalize(x)

logitinv(x)

my_logit(x, y, off = NULL, beta = NULL, lam = 0, pen = 2)

my_surv(x, y, atrisk, off = NULL, beta = NULL, lam = 0)

prev_fit_cste(u1, u2, fit)

Arguments

z

treatment indicators which is n*K matrix.

x

numeric vector or matrix.

x0

biomarkers at a fixed point.

h

kernel bandwidth.

input

parameters with dimension (2*K+1).

R

indicator matrix of individuals at risk prior to y_i.

s

censoring indicator which is a n*1 vector.

sloped

the first derivative of g.

l

contraction vector with dimension K.

beta0, beta0dot

the value of beta and its first derivative at x0.

g0dot

the first derivative of g0 at x0.

i

the i-th observation.

stdel, stgam, std

store the values of beta0, beta0dot, and godot at each x_i.

m

number of turns of resampling.

alpha

the (1-alpha)-confidence level of SCB.

thres

the output of getthres function.

y, u, u1, u2, beta, atrisk

numeric vector.

off

numeric value, offset.

lam

numeric value, penalty parameter.

pen

hyper-parameter that used in MCP and SCAD penalty functions.

fit

a S3 class of cste.

sep

parameter for trapezoid rule.

Value

Intermediate results.

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

tool functions

Description

Usage

Arguments

Value