R/tmle_hazard.R

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

#' TMLE for Cause-Specific Hazard Functions
#'
#' This function estimates the marginal cumulative incidence for failures of
#' specified types using targeted minimum loss-based estimation based on the
#' initial estimates of the cause-specific hazard functions for failures of each
#' type. The function is called by \code{survtmle} whenever
#' \code{method = "hazard"} is specified. However, power users could, in theory,
#' make calls directly to this function.
#'
#' @param ftime A numeric vector of failure times. Right-censored observations
#'        should have corresponding \code{ftype} set to 0.
#' @param ftype A numeric 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
#'        cause-specific hazards. 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 glm.family The type of regression to be performed if fitting GLMs in
#'        the estimation and fluctuation procedures. The default is "binomial"
#'        for logistic regression. Only change this from the default if there
#'        are justifications that are well understood. This is passed directly
#'        to \code{estimateCensoring} and \code{estimateHazards}.
#' @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 bounds A \code{data.frame} of bounds on the conditional hazard
#'        function. 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. 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 maxIter The maximum number of iterations for the algorithm. 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.
#' @param ... Other options. Not currently used.
#'
#' @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
#'
#' ## Single failure type examples
#' # simulate data
#' set.seed(1234)
#' n <- 100
#' 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 hazard_tmle object with GLMs for treatment, censoring, failure
#' fit1 <- hazard_tmle(ftime = ftime, ftype = ftype,
#'                     trt = trt, adjustVars = adjustVars,
#'                     glm.trt = "W1 + W2",
#'                     glm.ftime = "trt + W1 + W2",
#'                     glm.ctime = "trt + W1 + W2",
#'                     returnModels = TRUE)
#'
#' @export
#'

hazard_tmle <- function(ftime,
                        ftype,
                        trt,
                        t0 = max(ftime[ftype > 0]),
                        adjustVars = NULL,
                        SL.ftime = NULL,
                        SL.ctime = NULL,
                        SL.trt = NULL,
                        glm.ftime = NULL,
                        glm.ctime = NULL,
                        glm.trt = "1",
                        glm.family = "binomial",
                        returnIC = TRUE,
                        returnModels = FALSE,
                        ftypeOfInterest = unique(ftype[ftype != 0]),
                        trtOfInterest = unique(trt),
                        bounds = NULL,
                        verbose = FALSE,
                        tol = 1 / (length(ftime)),
                        maxIter = 100,
                        gtol = 1e-3,
                        ...) {

  # assemble data frame of necessary variables
  n <- length(ftime)
  id <- seq_len(n)
  dat <- data.frame(id = id, ftime = ftime, ftype = ftype, trt = trt)
  if (!is.null(adjustVars)) dat <- cbind(dat, adjustVars)

  nJ <- length(ftypeOfInterest)
  allJ <- sort(unique(ftype[ftype != 0]))
  ofInterestJ <- sort(ftypeOfInterest)

  # calculate number of groups
  ntrt <- length(trtOfInterest)
  uniqtrt <- sort(trtOfInterest)

  # estimate trt probabilities
  trtOut <- estimateTreatment(
    dat = dat,
    ntrt = ntrt,
    uniqtrt = uniqtrt,
    adjustVars = adjustVars,
    SL.trt = SL.trt,
    glm.trt = glm.trt,
    returnModels = returnModels,
    gtol = gtol
  )
  dat <- trtOut$dat
  trtMod <- trtOut$trtMod

  # make long version of data sets needed for estimation and prediction
  dataList <- makeDataList(
    dat = dat, J = allJ, ntrt = ntrt, uniqtrt = uniqtrt,
    t0 = t0, bounds = bounds
  )

  # estimate censoring
  censOut <- estimateCensoring(
    dataList = dataList,
    ntrt = ntrt,
    uniqtrt = uniqtrt,
    t0 = t0,
    verbose = verbose,
    adjustVars = adjustVars,
    SL.ctime = SL.ctime,
    glm.ctime = glm.ctime,
    glm.family = glm.family,
    returnModels = returnModels,
    gtol = gtol
  )
  dataList <- censOut$dataList
  ctimeMod <- censOut$ctimeMod

  # estimate cause specific hazards
  estOut <- estimateHazards(
    dataList = dataList,
    J = allJ,
    verbose = verbose,
    bounds = bounds,
    adjustVars = adjustVars,
    SL.ftime = SL.ftime,
    glm.ftime = glm.ftime,
    glm.family = glm.family,
    returnModels = returnModels
  )
  dataList <- estOut$dataList
  ftimeMod <- estOut$ftimeMod
  # check for convergence
  suppressWarnings(
    if (all(dataList[[1]] == "convergence failure")) {
      return("estimation convergence failure")
    }
  )

  # calculate cum inc and clever covariates needed for fluctuations
  dataList <- updateVariables(
    dataList = dataList, allJ = allJ,
    ofInterestJ = ofInterestJ,
    nJ = nJ, uniqtrt = uniqtrt, ntrt = ntrt,
    t0 = t0, verbose = verbose
  )

  # calculate influence function
  dat <- getHazardInfluenceCurve(
    dataList = dataList, dat = dat,
    ofInterestJ = ofInterestJ, allJ = allJ,
    nJ = nJ, uniqtrt = uniqtrt, ntrt = ntrt,
    verbose = verbose, t0 = t0
  )
  infCurves <- dat[, grep("D.j", names(dat))]
  if(!is.numeric(infCurves)){
    meanIC <- colMeans(infCurves)    
  }else{
    meanIC <- mean(infCurves)
  }

  attr(dataList, "fluc") <- rep(Inf, ntrt * nJ^2)
  ct <- 0
  while (any(abs(meanIC) > tol) & ct <= maxIter) {
    ct <- ct + 1
    dataList <- fluctuateHazards(
      dataList = dataList, ofInterestJ = ofInterestJ,
      tol = tol, allJ = allJ, nJ = nJ,
      uniqtrt = uniqtrt, ntrt = ntrt,
      verbose = verbose, t0 = t0
    )
    suppressWarnings(
      if (all(dataList[[1]] == "convergence failure")) {
        return("fluctuation convergence failure")
      }
    )

    # calculate influence function
    dat <- getHazardInfluenceCurve(
      dataList = dataList, dat = dat,
      ofInterestJ = ofInterestJ, allJ = allJ,
      nJ = nJ, uniqtrt = uniqtrt, ntrt = ntrt,
      verbose = verbose, t0 = t0
    )
    infCurves <- dat[, grep("D.j", names(dat))]
    meanIC <- colMeans(infCurves)

    if (verbose) {
      # print(attr(dataList,"fluc"))
      cat("TMLE Iteration ", ct, "  : ", round(meanIC, 4), "\n")
    }
  }
  if (ct == maxIter + 1) {
    warning("TMLE fluctuations did not converge. Check that meanIC is adequately
            small and proceed with caution.")
  }

  # calculate point estimate
  est <- rowNames <- NULL
  for (j in ofInterestJ) {
    for (z in uniqtrt) {
      eval(parse(text = paste(
        "est <- rbind(est, dat$margF", j, ".z", z,
        ".t0[1])",
        sep = ""
      )))
      rowNames <- c(rowNames, paste(c(z, j), collapse = " "))
    }
  }
  row.names(est) <- rowNames

  # calculate standard error
  var <- t(as.matrix(infCurves)) %*% as.matrix(infCurves) / n^2
  row.names(var) <- colnames(var) <- rowNames

  out <- list(
    est = est, var = var, meanIC = meanIC, ic = infCurves,
    trtMod = trtMod, ftimeMod = ftimeMod, ctimeMod = ctimeMod,
    ftime = ftime, ftype = ftype, trt = trt, adjustVars = adjustVars
  )
  class(out) <- "survtmle"
  return(out)
}