depCensoring (version 0.1.7)

pi.surv: Estimate the model of Willems et al. (2024+).

Description

This function estimates bounds on the coefficients the single- index model \(\Lambda(x^\top \beta(t))\) for the conditional cumulative distribution function of the event time.

Usage

pi.surv(
  data,
  idx.param.of.interest,
  idxs.c,
  t,
  par.space,
  search.method = "GS",
  add.options = list(),
  verbose = 0,
  picturose = FALSE,
  parallel = FALSE
)

Value

Matrix containing the identified intervals of the specified coefficients, as well as corresponding convergence information of the estimation algorithm.

Arguments

data

Data frame containing the data on which to fit the model. The columns should be named as follows: 'Y' = observed timed, 'Delta' = censoring indicators, 'X0' = intercept column, 'X1' - 'Xp' = covariates.

idx.param.of.interest

Index of element in the covariate vector for which the identified interval should be estimated. It can also be specified as idx.param.of.interest = "all", in which case identified intervals will be computed for all elements in the parameter vector. Note that idx.param.of.interest = 1 corresponds to the intercept parameter.

idxs.c

Vector of indices of the continuous covariates. Suppose the given data contains 5 covariates, of which 'X2' and 'X5' are continuous, this argument should be specified as idxs.c = c(2, 5).

t

Time point for which to estimate the identified set of \(\beta(t)\).

par.space

Matrix containing bounds on the space of the parameters. The first column corresponds to lower bounds, the second to upper bounds. The i'th row corresponds to the bounds on the i'th element in the parameter vector.

search.method

The search method to be used to find the identified interval. Default is search.method = "GS".

add.options

List of additional options to be specified to the method. Notably, it can be used to select the link function \(\Lambda(t))\) that should be considered. Currently, the link function leading to an accelerated failure time model ("AFT_ll", default) and the link function leading to a Cox proportional hazards model ("Cox_wb") are implemented. Other options can range from 'standard' hyperparameters such as the confidence level of the test and number of instrumental functions to be used, to technical hyperparameters regarding the search method and test implementation. For the latter, we refer to the documentations of set.hyperparameters, set.EAM.hyperparameters and set.GS.hyperparameters. We recommend to use the default parameters, unless you really know what you are doing.

verbose

Verbosity level. The higher the value, the more verbose the method will be. Default is verbose = 0.

picturose

Picturosity flag. If TRUE, a plot illustrating the workings of the algorithm will updated during runtime. Default is picturose = FALSE.

parallel

Flag for whether or not parallel computing should be used. Default is parallel = FALSE. When parallel = TRUE, this implementation will use min(detectCores() - 1, 10) cores to construct the parallel back-end.

References

Willems, I., Beyhum, J. and Van Keilegom, I. (2024+). Partial identification for a class of survival models under dependent censoring. (In preparation).

Examples

# \donttest{

  # Clear workspace
  rm(list = ls())
  
  # Load the survival package
  library(survival)
  
  # Set random seed
  set.seed(123)
  
  # Load and preprocess data
  data <- survival::lung
  data[, "intercept"] <- rep(1, nrow(data))
  data[, "status"] <- data[, "status"] - 1
  data <- data[, c("time", "status", "intercept", "age", "sex")]
  colnames(data) <- c("Y", "Delta", "X0", "X1", "X2")
  
  # Standardize age variable
  data[, "X1"] <- scale(data[, "X1"])
  
  ## Example:
  ## - Link function: AFT link function (default setting)
  ## - Number of IF: 5 IF per continuous covariate (default setting)
  ## - Search method: Binary search
  ## - Type of IF: Cubic spline functions for continuous covariate, indicator
  ##   function for discrete covariate (default setting).
  
  # Settings for main estimation function
  idx.param.of.interest <- 2 # Interest in effect of age
  idxs.c <- 1                # X1 (age) is continuous
  t <- 200                   # Model imposed at t = 200
  search.method <- "GS"      # Use binary search
  par.space <- matrix(rep(c(-10, 10), 3), nrow = 3, byrow = TRUE)
  add.options <- list()
  picturose <- TRUE
  parallel <- FALSE
  
  # Estimate the identified intervals
  pi.surv(data, idx.param.of.interest, idxs.c, t, par.space,
          search.method = search.method, add.options = add.options,
          picturose = picturose, parallel = parallel)
# }