SAS: Sequential advantage selection for optimal dynamic treatment...

In ITRSelect: Variable Selection for Optimal Individualized Dynamic Treatment Regime

Description

Select variables that are qualitatively interacted with the treatment based on a modified S-score method and a BIC-type criterion. This function can be applied to two-stage studies where treatments are sequentially assigned at two different time points.

Usage

SAS(formula, data, subset, na.action, step,
	model = TRUE, y = TRUE, a1 = TRUE, x1 = TRUE, a2 = TRUE, x2 = TRUE, ...)
	
SAS.fit(y, x1, x2 = NULL, a1, a2 = NULL, step)	

Arguments

formula	A symbolic description of the model to be fitted(of type y ~ x1 | a1 or y ~ x1 | a1 | x2 | a2. Details are given 'Details').
data	An optional list or environment containing variables in formula.
subset, na.action	Arguments controlling formula processing via model.frame.
step	SAS uses a forward selection procedure. The maximum size of the model is specified by step. By default, it is equal to n/\log(n) where n is the sample size.
model	A logical value indicating whether model frame should be included as a component of the return value.
y, a1, x1, a2, x2	For SAS: logical values indicating whether the response, the first and second treatments, the baseline and intermediate covariates should be included as a component of the return value. For SAS.fit: y is the response vector (the larger the better), a1 and a2 are the first and second treatments patients receive, x1 and x2 are the design matrices consisting of patients' baseline covariates and intermediate covariates.
...	Currently not used

.

Details

For single-stage study, the formula should specified as y ~ x1 | a1 where y is the reponse vector (y should be specified in such a way that a larger value of y indicates better clinical outcomes), x1 is patient's baseline covariates and a1 is the treatment that patient receives.

For two-stage study, the formula should be specified as y ~ x1 | a1 | x2 | a2 where y is the response vector, a1 and a2 the vectors of patients' first and second treatments, x1 and x2 are the design matrices consisting of patients' baseline covariates and intermediate covariates.

The function returns linear dynamic treatment regimes. For single-stage study, the estimated treamtent regime for future patients is given by I(\code{x1}^T \code{beta1.est}>0). For two-stage study, the estimated regime is given by \code{a1}=I(x1^T \code{beta1.est}>0) and \code{a2}=I(\code{x}^T \code{beta2.est}>0) where x=c(x1, a1, x2).

Value

beta2.est	Estimated coefficients in the second decision rule.
beta1.est	Estimated coefficients in the first decision rule.
model	The full model frame (if model = TRUE).
y	Response vector (if y = TRUE).
x1	Baseline covariates (if x1 = TRUE).
a1	A vector of first treatment (if a1 = TRUE).
x2	Intermediate covariates (if x2 = TRUE).
a2	A vector of second treatment (if a2 = TRUE).

Author(s)

Ailin Fan and Chengchun Shi

References

Fan, A. and Lu, W. and Song, R. (2016) Sequential Advantage Selection for Optimal Treatment Regime. Annals of Applied Statistics, 10: 32-53.

Examples

## single-stage study
set.seed(12345)
n <- 200
p <- 200
X <- matrix(rnorm(n*p), nrow=n, ncol=p)
A <- rbinom(n, 1, 0.5)
CX <- (X[,1] + X[,2])
h <- 1 + X[,1] * X[,3]
Y <- h + A*CX + 0.5*rnorm(n)
result <- SAS(Y~X|A)

## two-stage study
set.seed(12345*2)
n <- 200
p <- 200
X1 <- matrix(rnorm(n*p), nrow=n, ncol=p)
A1 <- rbinom(n, 1, 0.5)
X2 <- X1[,1] + A1 + 0.5*rnorm(n)
A2 <- rbinom(n, 1, 0.5)
Y <- A2*(A1 + X2) + A1*X1[,1] + 0.5*rnorm(n)
result <- SAS(Y~X1|A1|X2|A2)


## single-stage study
set.seed(12345)
n <- 50
p <- 20
X <- matrix(rnorm(n*p), nrow=n, ncol=p)
A <- rbinom(n, 1, 0.5)
CX <- (X[,1] + X[,2])
h <- 1 + X[,1] * X[,3]
Y <- h + A*CX + 0.5*rnorm(n)
result <- SAS(Y~X|A)

## two-stage study
set.seed(12345*2)
n <- 50
p <- 20
X1 <- matrix(rnorm(n*p), nrow=n, ncol=p)
A1 <- rbinom(n, 1, 0.5)
X2 <- X1[,1] + A1 + 0.5*rnorm(n)
A2 <- rbinom(n, 1, 0.5)
Y <- A2*(A1 + X2) + A1*X1[,1] + 0.5*rnorm(n)
result <- SAS(Y~X1|A1|X2|A2)

ITRSelect documentation built on May 1, 2019, 10:56 p.m.