Estimate a conditional survival function via local survival stacking

Usage

stackL(
  time,
  event = rep(1, length(time)),
  entry = NULL,
  X,
  newX,
  newtimes,
  direction = "prospective",
  bin_size = NULL,
  time_basis = "continuous",
  learner = "SuperLearner",
  SL_control = list(SL.library = c("SL.mean"), V = 10, method = "method.NNLS", stratifyCV
    = FALSE),
  tau = NULL
)

Arguments

time: n x 1 numeric vector of observed follow-up times If there is censoring, these are the minimum of the event and censoring times.
event: n x 1 numeric vector of status indicators of whether an event was observed. Defaults to a vector of 1s, i.e. no censoring.
entry: Study entry variable, if applicable. Defaults to NULL, indicating that there is no truncation.
X: n x p data.frame of observed covariate values on which to train the estimator.
newX: m x p data.frame of new observed covariate values at which to obtain m predictions for the estimated algorithm. Must have the same names and structure as X.
newtimes: k x 1 numeric vector of times at which to obtain k predicted conditional survivals.
direction: Whether the data come from a prospective or retrospective study. This determines whether the data are treated as subject to left truncation and right censoring ("prospective") or right truncation alone ("retrospective").
bin_size: Size of bins for the discretization of time. A value between 0 and 1 indicating the size of observed event time quantiles on which to grid times (e.g. 0.02 creates a grid of 50 times evenly spaced on the quantile scaled). If NULL, defaults to every observed event time.
time_basis: How to treat time for training the binary classifier. Options are "continuous" and "dummy", meaning an indicator variable is included for each time in the time grid.
learner: Which binary regression algorithm to use. Currently, only SuperLearner is supported, but more learners will be added. See below for algorithm-specific arguments.
SL_control: Named list of parameters controlling the Super Learner fitting process. These parameters are passed directly to the SuperLearner function. Parameters include SL.library (library of algorithms to include in the binary classification Super Learner), V (Number of cross validation folds on which to train the Super Learner classifier, defaults to 10), method (Method for estimating coefficients for the Super Learner, defaults to "method.NNLS"), stratifyCV (logical indicating whether to stratify by outcome in SuperLearner's cross-validation scheme), and obsWeights (observation weights, passed directly to prediction algorithms by SuperLearner).
tau: The maximum time of interest in a study, used for retrospective conditional survival estimation. Rather than dealing with right truncation separately than left truncation, it is simpler to estimate the survival function of tau - time. Defaults to NULL, in which case the maximum study entry time is chosen as the reference point.

Value

A named list of class stackL.

S_T_preds: An m x k matrix of estimated event time survival probabilities at the m covariate vector values and k times provided by the user in newX and newtimes, respectively.
fit: The Super Learner fit for binary classification on the stacked dataset.

References

Polley E.C. and van der Laan M.J. (2011). "Super Learning for Right-Censored Data" in Targeted Learning.

Craig E., Zhong C., and Tibshirani R. (2021). "Survival stacking: casting survival analysis as a classification problem."

Examples


# This is a small simulation example
set.seed(123)
n <- 500
X <- data.frame(X1 = rnorm(n), X2 = rbinom(n, size = 1, prob = 0.5))

S0 <- function(t, x){
  pexp(t, rate = exp(-2 + x[,1] - x[,2] + .5 * x[,1] * x[,2]), lower.tail = FALSE)
}
T <- rexp(n, rate = exp(-2 + X[,1] - X[,2] + .5 *  X[,1] * X[,2]))

G0 <- function(t, x) {
  as.numeric(t < 15) *.9*pexp(t,
                              rate = exp(-2 -.5*x[,1]-.25*x[,2]+.5*x[,1]*x[,2]),
                              lower.tail=FALSE)
}
C <- rexp(n, exp(-2 -.5 * X[,1] - .25 * X[,2] + .5 * X[,1] * X[,2]))
C[C > 15] <- 15

entry <- runif(n, 0, 15)

time <- pmin(T, C)
event <- as.numeric(T <= C)

sampled <- which(time >= entry)
X <- X[sampled,]
time <- time[sampled]
event <- event[sampled]
entry <- entry[sampled]

# Note that this a very small Super Learner library, for computational purposes.
SL.library <- c("SL.mean", "SL.glm")

fit <- stackL(time = time,
               event = event,
               entry = entry,
               X = X,
               newX = X,
               newtimes = seq(0, 15, .1),
               direction = "prospective",
               bin_size = 0.1,
               time_basis = "continuous",
               SL_control = list(SL.library = SL.library,
                                 V = 5))

plot(fit$S_T_preds[1,], S0(t =  seq(0, 15, .1), X[1,]))
abline(0,1,col='red')