R/tmle_mean.R

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

#' TMLE for G-Computation of Cumulative Incidence
#'
#' @description This function estimates the marginal cumulative incidence for
#'  failures of specified types using targeted minimum loss-based estimation
#'  based on the G-computation representation of cumulative incidence. The
#'  function is called by \code{\link{survtmle}} whenever \code{method="mean"}
#'  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 having been right-censored. 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 \code{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 of \code{\link[SuperLearner]{SuperLearner}} for
#'  the outcome regression (either cause-specific hazards or iterated mean).
#'  See the documentation of \code{\link[SuperLearner]{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} option of \code{\link[SuperLearner]{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} option of \code{\link[SuperLearner]{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{\link[stats]{formula}} option of a call to
#'  \code{\link[stats]{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{\link[stats]{formula}} option of a call to
#'  \code{\link[stats]{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{\link[stats]{formula}} option of a call to
#'  \code{\link[stats]{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{\link{estimateCensoring}}.
#' @param returnIC A \code{logical} 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 \code{logical} indicating whether to return the
#'  \code{glm} or \code{SuperLearner} objects used to estimate the nuisance
#'  parameters. Must be set to \code{TRUE} if the user plans to use
#'  \code{\link{timepoints}} to obtain estimates of incidence at times other
#'  than \code{t0}. See the documentation of \code{\link{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 all values in
#'  \code{unique(trt)}. Can alternatively be set to a vector of values found in
#'  \code{trt}.
#' @param cvControl A \code{list} providing control options to be fed directly
#'  into calls to \code{\link[SuperLearner]{SuperLearner}}. This should match
#'  the contents of \code{SuperLearner.CV.control} exactly. For details,
#'  consult the documentation of the \pkg{SuperLearner} package. This is
#'  usually passed in through the \code{\link{survtmle}} wrapper function.
#' @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{1: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 \code{logical} indicating whether the function should print
#'  messages to indicate progress. If \code{SuperLearner} is called internally,
#'  this option will be passed to \code{\link[SuperLearner]{SuperLearner}}.
#' @param Gcomp A \code{logical} indicating whether to compute the
#'  G-computation estimator (i.e., a substitution estimator with no targeting
#'  step). Theory does not support inference for the G-computation estimator if
#'  Super Learner is used to estimate failure and censoring distributions. The
#'  G-computation is only implemented if \code{method = "mean"}.
#' @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{\link[SuperLearner]{SuperLearner}} or \code{\link[stats]{glm}}
#'     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{\link[SuperLearner]{SuperLearner}} or \code{\link[stats]{glm}}
#'     or for the pooled hazard regression model for the censoring mechanism.
#'     If \code{returnModels = FALSE}, this entry will be \code{NULL}.}
#'   \item{trtMod}{If \code{returnModels = TRUE} the fit object for the call to
#'     \code{\link[SuperLearner]{SuperLearner}} or \code{\link[stats]{glm}} for
#'     the conditional probability of the \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 \code{numeric} vector of failure times used in the fit.}
#'   \item{ftype}{The \code{numeric} vector of failure types used in the fit.}
#'   \item{trt}{The \code{numeric} vector of treatment assignments used in the
#'     fit.}
#'   \item{adjustVars}{The \code{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 mean_tmle object with GLMs for treatment, censoring, failure
#' fit1 <- mean_tmle(
#'   ftime = ftime, ftype = ftype,
#'   trt = trt, adjustVars = adjustVars,
#'   glm.trt = "W1 + W2",
#'   glm.ftime = "trt + W1 + W2",
#'   glm.ctime = "trt + W1 + W2"
#' )
#' @export
mean_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),
                      cvControl,
                      bounds = NULL,
                      verbose = FALSE,
                      Gcomp = FALSE,
                      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)
  }

  # calculate number of failure types
  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,
    cvControl = cvControl,
    returnModels = returnModels,
    gtol = gtol,
    trtOfInterest = trtOfInterest
  )
  dat <- trtOut$dat
  trtMod <- trtOut$trtMod

  # make long version of data sets needed for estimation of censoring
  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,
    cvControl = cvControl,
    returnModels = returnModels,
    gtol = gtol
  )
  dataList <- censOut$dataList
  ctimeMod <- censOut$ctimeMod

  wideDataList <- makeWideDataList(
    dat = dat, dataList = dataList,
    adjustVars = adjustVars, t0 = t0,
    allJ = allJ, ntrt = ntrt, uniqtrt = uniqtrt
  )

  # estimate/fluctuate iterated means
  timeAndType <- expand.grid(rev(seq_len(t0)), ofInterestJ)

  # empty list for Qmod if returnModels
  ftimeMod <- vector(mode = "list", length = length(ofInterestJ))
  names(ftimeMod) <- paste0("J", ofInterestJ)
  for (j in seq_along(ofInterestJ)) {
    ftimeMod[[j]] <- vector(mode = "list", length = t0)
    names(ftimeMod[[j]]) <- paste0("t", seq_len(t0))
  }

  for (i in seq_len(nrow(timeAndType))) {
    estOut <- estimateIteratedMean(
      wideDataList = wideDataList,
      t = timeAndType[i, 1],
      whichJ = timeAndType[i, 2],
      ntrt = ntrt,
      uniqtrt = uniqtrt,
      allJ = allJ,
      t0 = t0,
      SL.ftime = SL.ftime,
      adjustVars = adjustVars,
      glm.ftime = glm.ftime,
      verbose = verbose,
      cvControl = cvControl,
      returnModels = returnModels,
      bounds = bounds
    )

    wideDataList <- estOut$wideDataList
    eval(parse(text = paste0(
      "ftimeMod$J", timeAndType[i, 2], "$t",
      timeAndType[i, 1], "<-estOut$ftimeMod"
    )))
    wideDataList <- fluctuateIteratedMean(
      wideDataList = wideDataList,
      t = timeAndType[i, 1],
      whichJ = timeAndType[i, 2],
      ntrt = ntrt, uniqtrt = uniqtrt,
      allJ = allJ, t0 = t0,
      SL.ftime = SL.ftime,
      glm.ftime = glm.ftime,
      returnModels = returnModels,
      bounds = bounds,
      Gcomp = Gcomp
    )
  }

  # get point estimate
  est <- rowNames <- NULL
  for (j in ofInterestJ) {
    for (z in seq_along(uniqtrt)) {
      thisEst <- eval(parse(text = paste(
        "mean(wideDataList[[", z + 1, "]]$Q",
        j, "star.1)",
        sep = ""
      )))
      est <- rbind(est, thisEst)
      rowNames <- c(rowNames, paste(c(uniqtrt[z], j), collapse = " "))
      eval(parse(text = paste(
        "wideDataList[[1]]$Q", j, "star.0.Z", uniqtrt[z],
        " <- rep(thisEst,n)",
        sep = ""
      )))
      eval(parse(text = paste(
        "wideDataList[[1]]$Q", j, "star.1.Z", uniqtrt[z],
        " <- wideDataList[[(z+1)]]$Q", j, "star.1",
        sep = ""
      )))
    }
  }
  row.names(est) <- rowNames

  # calculate influence function
  for (j in ofInterestJ) {
    for (z in seq_along(uniqtrt)) {
      for (t in rev(seq_len(t0))) {
        outcomeName <- ifelse(t == t0, paste("N", j, ".", t0, sep = ""),
          paste("Q", j, "star.", t + 1, sep = "")
        )
        eval(parse(text = paste(
          "wideDataList[[1]]$D.Z", uniqtrt[z], ".", j,
          "star.", t, " <- wideDataList[[1]]$H",
          uniqtrt[z], ".", t,
          "*(wideDataList[[1]][,outcomeName] - wideDataList[[1]]$Q",
          j, "star.", t, ")",
          sep = ""
        )))
      }
      eval(parse(text = paste(
        "wideDataList[[1]]$D.Z", uniqtrt[z], ".", j,
        "star.0 <- wideDataList[[1]]$Q", j, "star.1.Z",
        uniqtrt[z], " - wideDataList[[1]]$Q", j,
        "star.0.Z", uniqtrt[z],
        sep = ""
      )))
      ind <- eval(parse(text = paste(
        "grep('D.Z", uniqtrt[z], ".", j,
        "star', names(wideDataList[[1]]))",
        sep = ""
      )))
      eval(parse(text = paste(
        "wideDataList[[1]]$IC", j, "star.Z", uniqtrt[z],
        " <- rowSums(cbind(rep(0, nrow(wideDataList[[1]])),wideDataList[[1]][,ind]))",
        sep = ""
      )))
    }
  }

  # calculate standard error
  infCurves <- wideDataList[[1]][
    , grep("IC", names(wideDataList[[1]])),
    drop = FALSE
  ]
  meanIC <- apply(infCurves, MARGIN = 2, FUN = mean)
  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)
}