censored {OTRselect}

Variable Selection for Optimal Treatment Decision with Censored Survival Times

Description

A penalized regression framework that can simultaneously estimate the optimal treatment strategy and identify important variables when the response is continuous and censored. This method uses an inverse probability weighted least squares estimation with adaptive LASSO penalty for variable selection.

Usage

censored(x, y, a, delta, propen, phi, logY = TRUE, 
         intercept = TRUE)

Arguments

x

Matrix or data.frame of model covariates.

y

Vector of response. Note that this data is used to estimate the Kaplan-Meier Curve and should not be log(T).

a

Vector of treatment received. Treatments must be coded as integers or numerics that can be recast as integers without loss of information.

delta

Event indicator vector. The indicator must be coded as 0/1 where 0=no event and 1=event.

propen

Vector or matrix of propensity scores for each treatment. If a vector, the propensity is assumed to be the same for all samples. Column or element order must correspond to the sort order of the treatment variable, i.e., 0,1,2,3,... If the number of columns/elements in propen is one fewer than the total number of treatment options, it is assumed that the base or lowest valued treatment has not been provided.

phi

A character {'c' or 'l'} indicating if the constant ('c') or linear ('l') baseline mean function is to be used.

logY

TRUE/FALSE indicating if log(y) is to be used for regression.

intercept

TRUE/FALSE indicating if an intercept is to be included in phi model.

Value

A list object containing

beta

A vector of the estimated regression coefficients after variable selection.

optTx

The estimated optimal treatment for each sample.

Author(s)

Wenbin Lu, Hao Helen Zhang, Yuan Geng, and Shannon T. Holloway

References

Geng, Y., Lu, W., and Zhang, H. H. (2015). On optimal treatment regimes selection for mean survival time. Statistics in Medicine, 34, 1169–1184. PMCID: PMC4355217.

Examples

  sigma <- diag(10)
  ct <- 0.5^{1L:9L}
  rst <- unlist(sapply(1L:9L,function(x){ct[1L:{10L-x}]}))
  sigma[lower.tri(sigma)] <- rst
  sigma[upper.tri(sigma)] <- t(sigma)[upper.tri(sigma)]

  M <- t(chol(sigma))
  Z <- matrix(rnorm(1000),10,100)
  X <- t(M%*%Z)

  A <- rbinom(100,1,0.5)

  Y <- rweibull(100,shape=0.5,scale=1)
  C <- rweibull(100,shape=0.5,scale=1.5)

  delta <- as.integer(C <= Y)

  Y[delta > 0.5] <- C[delta>0.5]

  dat <- data.frame(X,A,exp(Y),delta)
  colnames(dat) <- c(paste("X",1:10,sep=""),"a","y","del")
  
  censored(x = X, 
           y = Y, 
           a = A, 
           delta = delta,
           propen = 0.5, 
           phi = "c", 
           logY = TRUE, 
           intercept = TRUE)