listdtr: Estimation of List-based Optimal Dynamic Treatment Regime

Description

Estimate the optimal dynamic treatment regime / individualized treatment rule, in the form of decision list, namely, a sequence of if-then clauses.

Usage

listdtr(y, a, x, stage.x, 
  seed = NULL, kfolds = 5L, fold = NULL, 
  maxlen = 10L, zeta.choices = NULL, eta.choices = NULL)

Arguments

a matrix of immediate outcomes, of size n.obs by n.stage, where n.obs is the number of observations and n.stage is the number of stages. Assume larger outcomes are more favorable.

a matrix of treatments/interventions actually received at each stage, of size n.obs by n.stage.

a matrix of features (such as demographics, biomarkers, confounders), of size n.obs by n.feature, where n.feature is the number of features measured at any of the stages.

stage.x

a vector of length n.feature, with values in 1, ..., n.stage that gives the stage at which each feature is measured.

seed

seed for random number generator to obtain fold. Omitted if fold is not null.

kfolds

number of folds to perform cross validation.

fold

a vector of length n.obs that specifies fold membership for each observation.

maxlen

maximum length of the decision list in each stage. Should be a scalar.

zeta.choices

Choices for the tuning parameter zeta. Larger value of zeta tends to construct a condition that covers more observations in each if-then clause. Should be null or a numeric vector.

eta.choices

Choices for the tuning parameter eta. Larger value of eta tends to construct a condition that uses less features in each if-then clause. Should be null or a numeric vector.

Value

An object of class listdtr.

Details

The algorithm is quite complicated. See the reference if interested.

References

https://arxiv.org/abs/1606.01472

Examples

Run this code

# NOT RUN {
  
  # an example for one-stage study
  x <- matrix(rnorm(500), 100, 5)
  stage.x <- rep(1, 5)
  a <- rbinom(100, 1, 0.5)
  y <- a * x[, 1] + rnorm(100, 0, 0.1)
  dtr <- listdtr(y, a, x, stage.x)
  
  dtr                # display the regime in words
  plot(dtr)          # display the regime in diagrams
  yrec <- predict(dtr, x, 1)
  yopt <- ifelse(x[, 1] > 0, 1, 0)
  table(yrec, yopt)  # discrepancy between recommended and optimal

  # an example for two-stage study
  x <- matrix(rnorm(500), 100, 5)
  stage.x <- c(1, 1, 1, 2, 2)
  a1 <- rbinom(100, 1, 0.5)
  a2 <- rbinom(100, 1, 0.5)
  y1 <- rep(0, 100)
  y2 <- 9 * a1 * sin(x[, 1] * pi / 8) - 2 * a2 * x[, 4] + rnorm(100)
  dtr <- listdtr(cbind(y1, y2), cbind(a1, a2), x, stage.x)
  
  dtr                # display the regime in words
  plot(dtr)          # display the regime in diagrams
  yrec <- predict(dtr, x, 1)
  yopt <- ifelse(x[, 1] > 0, 1, 0)
  table(yrec, yopt)  # discrepancy between recommended and optimal

# }

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