Predictive confidence interval for survival data

The main function to generate a predictive conformal confidence interval for a unit's survival time.

cfsurv(
  x,
  c_list = NULL,
  pr_list = NULL,
  pr_new_list = NULL,
  Xtrain,
  C,
  event,
  time,
  alpha = 0.05,
  seed = 24601,
  model = "aft",
  dist = "weibull",
  I_fit = NULL,
  ftol = 0.1,
  tol = 0.1,
  n.tree = 500
)

Arguments

x	a vector of the covariate for test point.
c_list	the cutoff for the censoring time (a positive number or a vector).
pr_list	the censoring probability at the cutoff for the fitting and calibration datasets.
pr_new_list	the censoring probability at the cutoff for the test points.
Xtrain	a n-by-p matrix of the covariate of the training data.
C	a length n vector of the censoring time of the training data.
event	a length n vector of indicators if the time observed is censored. TRUE corresponds to NOT censored, and FALSE censored.
time	a vevtor of length n, containing the observed survival time.
alpha	a number between 0 and 1, speciifying the miscoverage rate.
seed	an integer random seed (default: 24601).
model	Options include "aft", "np", "randomforest", "Powell", "Portnoy", "PengHuang", "distBoost", "quantBoost", "gpr". This determines the model used to fit the conformal score (default: "cox").
dist	either "weibull", "exponential" or "gaussian" (default: "weibull"). The distribution of T used in the AFT model.
I_fit	The set of indices corresponding to the fitting data set. (Default: NULL)

Examples

# Generate data
set.seed(24601)
n <- 2000
X <- runif(n, 0, 2)
T <- exp(X + rnorm(n, 0, 1))
C <- rexp(n, rate = 0.05)
event <- (T <= C)
censored_T <- pmin(T, C)
data <- data.frame(X = X, C = C, event = event, censored_T = censored_T)

# Prediction point
n_test <- 1000
X_test <- runif(n_test, 0, 2)
T_test <- exp(X_test + rnorm(n,0,1))

# Running cfsurvival with c0 = 30
c0 <- 30
pr_list <- rep(0.5, n)
pr_new_list <- rep(0.5, n_test)
res <- cfsurv(x = X_test, c_list = c0, pr_list = pr_list, pr_new_list = pr_new_list,
             Xtrain = X, C = C, event = event, time = censored_T, 
             alpha = 0.1, model = "aft")

# Examine the result
cat(sprintf("The coverage is %.3f.\n", mean(res <= T_test)))
#> The coverage is 0.932.