R/survtmle.R

In survtmle: Compute Targeted Minimum Loss-Based Estimates in Right-Censored Survival Settings

#' Compute Targeted Minimum Loss-Based Estimators in Survival Analysis Settings
#'
#' This function estimates the marginal cumulative incidence for failures of
#' specified types using targeted minimum loss-based estimation.
#'
#' @param ftime An integer-valued vector of failure times. Right-censored observations
#'        should have corresponding \code{ftype} set to 0.
#' @param ftype An integer-valued vector indicating the type of failure. Observations
#'        with \code{ftype=0} are treated as a right-censored observation. Each
#'        unique value besides zero is treated as a separate type of failure.
#' @param trt A numeric vector indicating observed treatment assignment. Each
#'        unique value will be treated as a different type of treatment.
#'        Currently, only two unique values are supported.
#' @param adjustVars A data.frame of adjustment variables that will be used in
#'        estimating the conditional treatment, censoring, and failure (hazard
#'        or conditional mean) probabilities.
#' @param t0 The time at which to return cumulative incidence estimates. By
#'        default this is set to \code{max(ftime[ftype > 0])}.
#' @param SL.ftime A character vector or list specification to be passed to the
#'        \code{SL.library} option in the call to \code{SuperLearner} for the
#'        outcome regression (either cause-specific hazards or iterated mean).
#'        See \code{?SuperLearner} for more information on how to specify valid
#'        \code{SuperLearner} libraries. It is expected that the wrappers used
#'        in the library will play nicely with the input variables, which will
#'        be called \code{"trt"}, \code{names(adjustVars)}, and \code{"t"} (if
#'        \code{method="hazard"}).
#' @param SL.ctime A character vector or list specification to be passed to the
#'        \code{SL.library} argument in the call to \code{SuperLearner} for the
#'        estimate of the conditional hazard for censoring. It is expected that
#'        the wrappers used in the library will play nicely with the input
#'        variables, which will be called \code{"trt"} and
#'        \code{names(adjustVars)}.
#' @param SL.trt A character vector or list specification to be passed to the
#'        \code{SL.library} argument in the call to \code{SuperLearner} for the
#'        estimate of the conditional probability of treatment. It is expected
#'        that the wrappers used in the library will play nicely with the input
#'        variables, which will be \code{names(adjustVars)}.
#' @param glm.ftime A character specification of the right-hand side of the
#'        equation passed to the \code{formula} option of a call to \code{glm}
#'        for the outcome regression. Ignored if \code{SL.ftime} is not equal
#'        to \code{NULL}. Use \code{"trt"} to specify the treatment in this
#'        formula (see examples). The formula can additionally include any
#'        variables found in \code{names(adjustVars)}.
#' @param glm.ctime A character specification of the right-hand side of the
#'        equation passed to the \code{formula} option of a call to \code{glm}
#'        for the estimate of the conditional hazard for censoring. Ignored if
#'        \code{SL.ctime} is not equal to \code{NULL}. Use \code{"trt"} to
#'        specify the treatment in this formula (see examples). The formula can
#'        additionally include any variables found in \code{names(adjustVars)}.
#' @param glm.trt A character specification of the right-hand side of the
#'        equation passed to the \code{formula} option of a call to \code{glm}
#'        for the estimate of the conditional probability of treatment. Ignored
#'        if \code{SL.trt} is not equal to \code{NULL}. The formula can include
#'        any variables found in \code{names(adjustVars)}.
#' @param returnIC A boolean indicating whether to return vectors of influence
#'        curve estimates. These are needed for some post-hoc comparisons, so it
#'        is recommended to leave as \code{TRUE} (the default) unless the user
#'        is sure these estimates will not be needed later.
#' @param returnModels A boolean indicating whether to return the
#'        \code{SuperLearner} or \code{glm} objects used to estimate the
#'        nuisance parameters. Must be set to \code{TRUE} if the user plans to
#'        use \code{timepoints} to obtain estimates of incidence at times other
#'        than \code{t0}. See \code{?timepoints} for more information.
#' @param ftypeOfInterest An input specifying what failure types to compute
#'        estimates of incidence for. The default value computes estimates for
#'        values \code{unique(ftype)}. Can alternatively be set to a vector of
#'        values found in \code{ftype}.
#' @param trtOfInterest An input specifying which levels of \code{trt} are of
#'        interest. The default value computes estimates for values
#'        \code{unique(trt)}. Can alternatively be set to a vector of values
#'        found in \code{trt}.
#' @param method A character specification of how the targeted minimum
#'        loss-based estimators should be computed, either \code{"mean"} or
#'        \code{"hazard"}. The \code{"mean"} specification uses a closed-form
#'        targeted minimum loss-based estimation based on the G-computation
#'        formula of Bang and Robins (2005). The \code{"hazard"} specification
#'        uses an iteratively algorithm based on cause-specific hazard
#'        functions. The latter specification has no guarantee of convergence in
#'        finite samples. The convergence can be influenced by the stopping
#'        criteria specified in the \code{tol}. Future versions may implement a
#'        closed form version of this hazard-based estimator.
#' @param bounds A \code{data.frame} of bounds on the conditional hazard
#'        function (if \code{method = "hazard"}) or on the iterated conditional
#'        means (if \code{method = "mean"}). The \code{data.frame} should have a
#'        column named \code{"t"} that includes values \code{seq_len(t0)}. The
#'        other columns should be names \code{paste0("l",j)} and
#'        \code{paste0("u",j)} for each unique failure type label j, denoting
#'        lower and upper bounds, respectively. See examples.
#' @param verbose A boolean indicating whether the function should print
#'        messages to indicate progress. If \code{SuperLearner} is called
#'        internally, this option will additionally be passed to
#'        \code{SuperLearner}.
#' @param tol The stopping criteria when \code{method="hazard"}. The TMLE
#'        algorithm performs updates to the initial estimators until the
#'        empirical mean of the efficient influence function is smaller than
#'        \code{tol} or until \code{maxIter} iterations have been completed. The
#'        default (\code{1/length(ftime)}) is a sensible value. Larger values
#'        can be used in situations where convergence of the algorithm is an
#'        issue; however, this may result in large finite-sample bias.
#' @param Gcomp A boolean indicating whether to compute the G-computation
#'        estimator (i.e., a substitution estimator with no targeting step).
#'        Theory does not support inference for the Gcomp estimator if Super
#'        Learner is used to estimate failure and censoring distributions. The
#'        G-computation is only implemented for \code{method = "mean"}.
#' @param maxIter A maximum number of iterations for the algorithm when
#'        \code{method = "hazard"}. The algorithm will iterate until either the
#'        empirical mean of the efficient influence function is smaller than
#'        \code{tol} or until \code{maxIter} iterations have been completed.
#' @param gtol The truncation level of predicted censoring survival. Setting to
#'        larger values can help performance in data sets with practical
#'        positivity violations.
#'
#' @return An object of class \code{survtmle}.
#' \describe{
#' \item{call}{The call to \code{survtmle}.}
#' \item{est}{A numeric vector of point estimates -- one for each combination of
#'            \code{ftypeOfInterest} and \code{trtOfInterest}.}
#' \item{var}{A covariance matrix for the point estimates.}
#' \item{meanIC}{The empirical mean of the efficient influence function at the
#'               estimated, targeted nuisance parameters. Each value should be
#'               small or the user will be warned that excessive finite-sample
#'               bias may exist in the point estimates.}
#' \item{ic}{The efficient influence function at the estimated, fluctuated
#'           nuisance parameters, evaluated on each of the observations. These
#'           are used to construct confidence intervals for post-hoc
#'           comparisons.}
#' \item{ftimeMod}{If \code{returnModels=TRUE} the fit object(s) for the call to
#'                 \code{glm} or \code{SuperLearner} for the outcome regression
#'                 models. If \code{method="mean"} this will be a list of length
#'                 \code{length(ftypeOfInterest)} each of length \code{t0} (one
#'                 regression for each failure type and for each timepoint). If
#'                 \code{method="hazard"} this will be a list of length
#'                 \code{length(ftypeOfInterest)} with one fit corresponding to
#'                 the hazard for each cause of failure. If
#'                 \code{returnModels = FALSE}, this entry will be \code{NULL}.}
#' \item{ctimeMod}{If \code{returnModels=TRUE} the fit object for the call to
#'                 \code{glm} or \code{SuperLearner} for the pooled hazard
#'                 regression model for the censoring distribution. If
#'                 \code{returnModels=FALSE}, this entry will be \code{NULL}.}
#' \item{trtMod}{If \code{returnModels = TRUE} the fit object for the call to
#'               \code{glm} or \code{SuperLearner} for the conditional
#'               probability of \code{trt} regression model. If
#'               \code{returnModels = FALSE}, this entry will be \code{NULL}.}
#' \item{t0}{The timepoint at which the function was evaluated.}
#' \item{ftime}{The numeric vector of failure times used in the fit.}
#' \item{ftype}{The numeric vector of failure types used in the fit.}
#' \item{trt}{The numeric vector of treatment assignments used in the fit.}
#' \item{adjustVars}{The data.frame of failure times used in the fit.}
#' }
#'
#' @examples
#'
#' # simulate data
#' set.seed(1234)
#' n <- 200
#' trt <- rbinom(n, 1, 0.5)
#' adjustVars <- data.frame(W1 = round(runif(n)), W2 = round(runif(n, 0, 2)))
#'
#' ftime <- round(1 + runif(n, 1, 4) - trt + adjustVars$W1 + adjustVars$W2)
#' ftype <- round(runif(n, 0, 1))
#'
#' # Fit 1
#' # fit a survtmle object with glm estimators for treatment, censoring, and
#' # failure using the "mean" method
#' fit1 <- survtmle(ftime = ftime, ftype = ftype,
#'                  trt = trt, adjustVars = adjustVars,
#'                  glm.trt = "W1 + W2",
#'                  glm.ftime = "trt + W1 + W2",
#'                  glm.ctime = "trt + W1 + W2",
#'                  method = "mean", t0 = 6)
#' fit1
#'
#' # Fit 2
#' # fit an survtmle object with SuperLearner estimators for failure and
#' # censoring and empirical estimators for treatment using the "mean" method
#' fit2 <- survtmle(ftime = ftime, ftype = ftype,
#'                  trt = trt, adjustVars = adjustVars,
#'                  SL.ftime = c("SL.mean"),
#'                  SL.ctime = c("SL.mean"),
#'                  method = "mean", t0 = 6)
#' fit2
#'
#' @export
#'

survtmle <- function(ftime, ftype, trt, adjustVars, t0 = max(ftime[ftype > 0]),
                     SL.ftime = NULL, SL.ctime = NULL, SL.trt = NULL,
                     glm.ftime = NULL, glm.ctime = NULL, glm.trt = NULL,
                     returnIC = TRUE, returnModels = TRUE,
                     ftypeOfInterest = unique(ftype[ftype != 0]),
                     trtOfInterest = unique(trt),
                     method = "hazard", bounds = NULL, verbose = FALSE,
                     tol = 1 / (sqrt(length(ftime))),
                     maxIter = 10, Gcomp = FALSE, gtol = 1e-3) {
  call <- match.call(expand.dots = TRUE)

  # check and clean inputs
  clean <- checkInputs(
    ftime = ftime, ftype = ftype, trt = trt,
    t0 = t0, adjustVars = adjustVars,
    SL.ftime = SL.ftime,
    SL.ctime = SL.ctime,
    SL.trt = SL.trt,
    glm.ftime = glm.ftime,
    glm.ctime = glm.ctime,
    glm.trt = glm.trt,
    returnIC = returnIC,
    returnModels = returnModels,
    ftypeOfInterest = ftypeOfInterest,
    trtOfInterest = trtOfInterest,
    bounds = bounds, verbose = verbose, tol = tol,
    Gcomp = Gcomp, method = method
  )

  # hazard-based TMLE
  if (method == "hazard") {
    tmle.fit <- hazard_tmle(
      ftime = clean$ftime,
      ftype = clean$ftype,
      trt = clean$trt,
      t0 = t0,
      adjustVars = clean$adjustVars,
      SL.ftime = clean$SL.ftime,
      SL.ctime = clean$SL.ctime,
      SL.trt = clean$SL.trt,
      glm.ftime = clean$glm.ftime,
      glm.ctime = clean$glm.ctime,
      glm.trt = clean$glm.trt,
      returnIC = returnIC,
      returnModels = returnModels,
      ftypeOfInterest = ftypeOfInterest,
      trtOfInterest = trtOfInterest,
      bounds = bounds,
      verbose = verbose,
      tol = tol,
      maxIter = maxIter,
      gtol = gtol
    )
  } else if (method == "mean") {
    tmle.fit <- mean_tmle(
      ftime = clean$ftime,
      ftype = clean$ftype,
      trt = clean$trt,
      t0 = t0,
      adjustVars = clean$adjustVars,
      SL.ftime = clean$SL.ftime,
      SL.ctime = clean$SL.ctime,
      SL.trt = clean$SL.trt,
      glm.ftime = clean$glm.ftime,
      glm.ctime = clean$glm.ctime,
      glm.trt = clean$glm.trt,
      returnIC = returnIC,
      returnModels = returnModels,
      ftypeOfInterest = ftypeOfInterest,
      trtOfInterest = trtOfInterest,
      bounds = bounds,
      verbose = verbose,
      tol = tol,
      Gcomp = Gcomp,
      gtol = gtol
    )
  }

  out <- list(
    call = call, est = tmle.fit$est, var = tmle.fit$var,
    meanIC = tmle.fit$meanIC, ic = tmle.fit$ic,
    ftimeMod = tmle.fit$ftimeMod, ctimeMod = tmle.fit$ctimeMod,
    trtMod = tmle.fit$trtMod, t0 = t0, ftime = tmle.fit$ftime,
    ftype = tmle.fit$ftype, trt = tmle.fit$trt,
    adjustVars = tmle.fit$adjustVars
  )
  class(out) <- "survtmle"
  return(out)
}