R/predictCox.R

In riskRegression: Risk Regression Models and Prediction Scores for Survival Analysis with Competing Risks

## * predictCox (documentation)
#' @title Fast computation of survival probabilities, hazards and cumulative hazards from Cox regression models 
#' @name predictCox
#' 
#' @description Fast routine to get baseline hazards and subject specific hazards
#' as well as survival probabilities from a \code{survival::coxph} or \code{rms::cph} object
#' @param object The fitted Cox regression model object either
#'     obtained with \code{coxph} (survival package) or \code{cph}
#'     (rms package).
#' @param newdata [data.frame or data.table]  Contain the values of the predictor variables
#' defining subject specific predictions.
#' Should have the same structure as the data set used to fit the \code{object}.
#' @param times [numeric vector] Time points at which to return
#' the estimated hazard/cumulative hazard/survival.
#' @param centered [logical] If \code{TRUE} return prediction at the
#'     mean values of the covariates \code{fit$mean}, if \code{FALSE}
#'     return a prediction for all covariates equal to zero.  in the
#'     linear predictor. Will be ignored if argument \code{newdata} is
#'     used. For internal use.
#' @param type [character vector] the type of predicted value. Choices are \itemize{
#'     \item \code{"hazard"} the baseline hazard function when
#'     argument \code{newdata} is not used and the hazard function
#'     when argument \code{newdata} is used.  \item \code{"cumhazard"}
#'     the cumulative baseline hazard function when argument
#'     \code{newdata} is not used and the cumulative hazard function
#'     when argument \code{newdata} is used.  \item \code{"survival"}
#'     the survival baseline hazard function when argument
#'     \code{newdata} is not used and the cumulative hazard function
#'     when argument \code{newdata} is used.  } Several choices can be
#'     combined in a vector of strings that match (no matter the case)
#'     strings \code{"hazard"},\code{"cumhazard"}, \code{"survival"}.
#' @param keep.strata [logical] If \code{TRUE} add the (newdata) strata
#'     to the output. Only if there any.
#' @param keep.times [logical] If \code{TRUE} add the evaluation times
#'     to the output.
#' @param keep.newdata [logical] If \code{TRUE} add the value of the
#'     covariates used to make the prediction in the output list.
#' @param keep.infoVar [logical] For internal use.
#' @param se [logical] If \code{TRUE} compute and add the standard errors to the output.
#' @param band [logical] If \code{TRUE} compute and add the quantiles for the confidence bands to the output.
#' @param iid [logical] If \code{TRUE} compute and add the influence function to the output.
#' @param confint [logical] If \code{TRUE} compute and add the confidence intervals/bands to the output.
#' They are computed applying the \code{confint} function to the output.
#' @param diag [logical] when \code{FALSE} the hazard/cumlative hazard/survival for all observations at all times is computed,
#' otherwise it is only computed for the i-th observation at the i-th time.
#' @param average.iid [logical] If \code{TRUE} add the average of the influence function over \code{newdata} to the output.
#' @param store.iid [character] Implementation used to estimate the influence function and the standard error.
#' Can be \code{"full"} or \code{"minimal"}.
#' 
#' @details
#' When the argument \code{newdata} is not specified, the function computes the baseline hazard estimate.
#' See (Ozenne et al., 2017) section "Handling of tied event times".
#'
#' Otherwise the function computes survival probabilities with confidence intervals/bands.
#' See (Ozenne et al., 2017) section "Confidence intervals and confidence bands for survival probabilities".
#' The survival is computed using the exponential approximation (equation 3).
#'
#' A detailed explanation about the meaning of the argument \code{store.iid} can be found
#' in (Ozenne et al., 2017) Appendix B "Saving the influence functions".
#' 
#' The function is not compatible with time varying predictor variables.
#' 
#' The centered argument enables us to reproduce the results obtained with the \code{basehaz}
#' function from the survival package but should not be modified by the user.
#'
#' The iid decomposition is output using an array containing the value of the influence
#' of each subject used to fit the object (dim 1),
#' for each subject in newdata (dim 3),
#' and each time (dim 2).
#' 
#' @author Brice Ozenne broz@@sund.ku.dk, Thomas A. Gerds tag@@biostat.ku.dk
#'
#' @references
#' Brice Ozenne, Anne Lyngholm Sorensen, Thomas Scheike, Christian Torp-Pedersen and Thomas Alexander Gerds.
#' riskRegression: Predicting the Risk of an Event using Cox Regression Models.
#' The R Journal (2017) 9:2, pages 440-460.
#' 
#' @seealso
#' \code{\link{confint.predictCox}} to compute confidence intervals/bands.
#' \code{\link{autoplot.predictCox}} to display the predictions.

## * predictCox (examples)
#' @examples
##' 
#' library(survival)
#' library(data.table)
#'
#' #### generate data ####
#' set.seed(10)
#' d <- sampleData(40,outcome="survival") ## training dataset
#' nd <- sampleData(4,outcome="survival") ## validation dataset
#' d$time <- round(d$time,1) ## create tied events
#' # table(duplicated(d$time))
#' 
#' #### stratified Cox model ####
#' fit <- coxph(Surv(time,event)~X1 + strata(X2) + X6,
#'              data=d, ties="breslow", x = TRUE, y = TRUE)
#' 
#' ## compute the baseline cumulative hazard
#' fit.haz <- predictCox(fit)
#' cbind(survival::basehaz(fit), fit.haz$cumhazard)
#'
#' ## compute individual specific cumulative hazard and survival probabilities 
#' fit.pred <- predictCox(fit, newdata=nd, times=c(3,8), se = TRUE, band = TRUE)
#' fit.pred
#'
#' ####  other examples ####
#' # one strata variable
#' fitS <- coxph(Surv(time,event)~strata(X1)+X2,
#'               data=d, ties="breslow", x = TRUE, y = TRUE)
#' 
#' predictCox(fitS)
#' predictCox(fitS, newdata=nd, times = 1)
#'
#' # two strata variables
#' set.seed(1)
#' d$U=sample(letters[1:5],replace=TRUE,size=NROW(d))
#' d$V=sample(letters[4:10],replace=TRUE,size=NROW(d))
#' nd$U=sample(letters[1:5],replace=TRUE,size=NROW(nd))
#' nd$V=sample(letters[4:10],replace=TRUE,size=NROW(nd))
#' fit2S <- coxph(Surv(time,event)~X1+strata(U)+strata(V)+X2,
#'               data=d, ties="breslow", x = TRUE, y = TRUE)
#'
#' cbind(survival::basehaz(fit2S),predictCox(fit2S,type="cumhazard")$cumhazard)
#' predictCox(fit2S)
#' predictCox(fitS, newdata=nd, times = 3)
#'
#' # left truncation
#' test2 <- list(start=c(1,2,5,2,1,7,3,4,8,8), 
#'               stop=c(2,3,6,7,8,9,9,9,14,17), 
#'               event=c(1,1,1,1,1,1,1,0,0,0), 
#'               x=c(1,0,0,1,0,1,1,1,0,0)) 
#' m.cph <- coxph(Surv(start, stop, event) ~ 1, test2, x = TRUE)
#' as.data.table(predictCox(m.cph))
#'
#' basehaz(m.cph)

## * predictCox (code)
#' @rdname predictCox
#' @export
predictCox <- function(object,
                       times,
                       newdata=NULL,
                       centered = TRUE,
                       type=c("cumhazard","survival"),
                       keep.strata = TRUE,
                       keep.times = TRUE,
                       keep.newdata = FALSE,
                       keep.infoVar = FALSE,
                       se = FALSE,
                       band = FALSE,
                       iid = FALSE,
                       confint = (se+band)>0,
                       diag = FALSE,
                       average.iid = FALSE,
                       store.iid = "full"){

    call <- match.call()
    newdata <- data.table::copy(newdata)
    ## centering
    if(!is.null(newdata)){
        if(inherits(centered,"data.frame")){
            df.reference <- centered
            centered2 <- TRUE ## for the linear predictor of the hazard
        }else{
            df.reference <- NULL
            centered2 <- centered ## for the linear predictor of the hazard
        }
        centered <- TRUE ## for the linear predictor of the baseline hazard
    }else{
        centered2 <- FALSE
    }
    
    ## ** Extract elements from object
    if (missing(times)) {
        nTimes <- 0
        times <- numeric(0)
    }else{
        nTimes <- length(times)
    }
    needOrder <- (nTimes[1]>0 && is.unsorted(times))
    if (all(!is.na(times)) && needOrder) {
        order.times <- order(times)
        oorder.times <- order(order.times)
        times.sorted <- sort(times)
    }else{
        if (nTimes==0){
            times.sorted <- numeric(0)
        } else{
            times.sorted <- times
            order.times <- 1:nTimes
            oorder.times <- 1:nTimes
        }
    }
    object.n <- coxN(object)  
    object.modelFrame <- coxModelFrame(object)
    infoVar <- coxVariableName(object, model.frame = object.modelFrame)
    object.baseEstimator <- coxBaseEstimator(object)

    ## ease access
    is.strata <- infoVar$is.strata
    object.levelStrata <- levels(object.modelFrame$strata) ## levels of the strata variable
    nStrata <- length(object.levelStrata) ## number of strata
    nVar.lp <- length(infoVar$lpvars) ## number of variables in the linear predictor

    ## ** normalize model frame
    ## convert strata to numeric
    object.modelFrame[,c("strata.num") := as.numeric(.SD$strata) - 1]

    ## linear predictor
    ## if we predict the hazard for newdata then there is no need to center the covariates
    object.modelFrame[,c("eXb") := exp(coxLP(object, data = NULL, center = if(is.null(newdata)){centered}else{FALSE}))]
    ## add linear predictor and remove useless columns
    rm.name <- setdiff(names(object.modelFrame),c("start","stop","status","eXb","strata","strata.num"))
    if(length(rm.name)>0){
        object.modelFrame[,c(rm.name) := NULL]
    }
  
    ## sort the data
    object.modelFrame[, c("statusM1") := 1-.SD$status] ## sort by statusM1 such that deaths appear first and then censored events
    object.modelFrame[, c("XXXindexXXX") := 1:.N] ## keep track of the initial positions (useful when calling calcSeCox)
    data.table::setkeyv(object.modelFrame, c("strata.num","stop","start","statusM1"))

    ## last event time in each strata
    if(!is.null(attr(times,"etimes.max"))){ ## specified by the user
        etimes.max <- attr(times,"etimes.max")
        attr(times,"etimes.max") <- NULL
        attr(times.sorted,"etimes.max") <- etimes.max
    }else if(is.strata){ ## based on the data
        if(nVar.lp==0){
            iDTtempo <- object.modelFrame[, .SD[which.max(.SD$stop)], by = "strata.num"]
            etimes.max <- iDTtempo[,if(.SD$status==1){1e12}else{.SD$stop}, by = "strata.num"][[2]]
        }else{
            etimes.max <- object.modelFrame[, max(.SD$stop), by = "strata.num"][[2]]
        }
    }else{
        if(nVar.lp==0 && (utils::tail(object.modelFrame$status,1)==1)){ ## no covariates and ends by a death
            etimes.max <- 1e12
        }else{
            etimes.max <- max(object.modelFrame[["stop"]])
        }
    }

    ## ** checks
    ## check user imputs 
    if(nTimes[1]>0 && any(is.na(times))){
        stop("Missing (NA) values in argument \'times\' are not allowed.\n")
    }
    type <- tolower(type)
    if(any(type %in% c("lp","hazard","cumhazard","survival") == FALSE)){
        stop("type can only be \"lp\", \"hazard\", \"cumhazard\" or/and \"survival\" \n") 
    }
    if(is.null(newdata) && "lp" %in% type){
        stop("Cannot evaluate the linear predictor when argument \'newdata\' is missing. \n")
    }
    if(length(times)>1 && "lp" %in% type){
        stop("Cannot evaluate the linear predictor when there are multiple timepoints. \n")
    }
    ## predictCox is not compatible with all coxph/cph object (i.e. only handle only simple cox models)
    if(!is.null(object$weights) && !all(object$weights==1)){
        stop("predictCox does not know how to handle Cox models fitted with weights \n")
    }
    if(!is.null(object$naive.var)){
        stop("predictCox does not know how to handle frailty.") 
    }
    ## if(any(object.modelFrame[["start"]]!=0)){
    ##     warning("The current version of predictCox was not designed to handle left censoring \n",
    ##             "The function may be used on own risks \n") 
    ## }    
    if(object.baseEstimator == "exact"){
        stop("Prediction with exact handling of ties is not implemented.\n")
    }
    if(!is.null(object$call$tt)){
        stop("predictCox does not know how to handle time varying effects.\n") 
    }
    ## convergence issue
    if(!is.null(coef(object)) && any(is.na(coef(object)))){
        print(coef(object))
        stop("One or several parameters of the regression model have no value, i.e., a value 'NA'.\n")
    }
    ## prediction 
    if (missing(newdata) && (se || iid || average.iid)){
        stop("Argument 'newdata' is missing. Cannot compute standard errors in this case.")
    }
    if(!is.null(newdata)){
        if(nTimes[1]==0 && !identical(as.character(type),"lp")){
            stop("Time points at which to evaluate the predictions are missing \n")
        }
        if(!is.vector(times)){
            stop("Argument \'times\' must be a vector \n")
        }
        name.regressor <- c(infoVar$lpvars.original, infoVar$stratavars.original)
        if(length(name.regressor) > 0 && any(name.regressor %in% names(newdata) == FALSE)){
            stop("Missing variables in argument \'newdata\': \"",
                 paste0(setdiff(name.regressor,names(newdata)), collapse = "\" \""),
                 "\"\n")
        }
        if(se[1] && ("hazard" %in% type)){
            stop("Standard error cannot be computed for the hazard \n")
        }
        if(band[1] && ("hazard" %in% type)){
            stop("confidence bands cannot be computed for the hazard \n")
        }
    }
    ## diag argument
    if(!is.logical(diag)){
        stop("Argument \'diag\' must be of type logical \n")
    }
    if(diag){
        if(NROW(newdata)!=length(times)){
            stop("When argument \'diag\' is TRUE, the number of rows in \'newdata\' must equal the length of \'times\' \n")
        }
    }
    if(average.iid==TRUE && !is.null(attr(average.iid,"factor"))){
        if(is.null(store.iid) && !is.null(object$iid$store.iid)){
            store.iid <- object$iid$store.iid
        }
        if(store.iid == "full"){
            if(iid){
                stop("Attribute \"factor\" of argument \'average.iid\' not available when \'iid\' is TRUE with argument \'store.iid\' set to \"full\" \n",
                     "Consider setting  \'store.iid\' set to \"minimal\" \n")
            }
            if(se){
                stop("Attribute \"factor\" of argument \'average.iid\' not available when \'se\' is TRUE with argument \'store.iid\' set to \"full\" \n",
                     "Consider setting  \'store.iid\' set to \"minimal\" \n")
            }
        }
        test.list <- !is.list(attr(average.iid,"factor"))
        if(test.list){
            stop("Attribute \"factor\" of argument \'average.iid\' must be a list \n")
        }
        test.matrix <- any(unlist(lapply(attr(average.iid,"factor"), is.matrix))==FALSE)
        if(test.matrix){
            stop("Attribute \"factor\" of argument \'average.iid\' must be a list of matrices \n")
        }
        for(iFactor in 1:length(attr(average.iid,"factor"))){ ## iFactor <- 1
            ## when only one column and diag = FALSE, use the same weights at all times
            if((diag == FALSE) && (NCOL(attr(average.iid,"factor")[[iFactor]])==1) && (nTimes > 1)){
                attr(average.iid,"factor")[[iFactor]] <- matrix(attr(average.iid,"factor")[[iFactor]][,1],
                                                                nrow = NROW(attr(average.iid,"factor")[[iFactor]]),
                                                                ncol = nTimes, byrow = FALSE)
            }
            ## check dimensions
            if(any(dim(attr(average.iid,"factor")[[iFactor]])!=c(NROW(newdata), diag + (1-diag)*nTimes))){
                stop("Attribute \"factor\" of argument \'average.iid\' must be a list of matrices of size ",new.n,",",diag + (1-diag)*nTimes," \n")
            }
        }
    }

    ## ** baseline hazard

    ## compute the baseline hazard
    Lambda0 <- baseHaz_cpp(starttimes = object.modelFrame$start,
                           stoptimes = object.modelFrame$stop,
                           status = object.modelFrame$status,
                           eXb = object.modelFrame$eXb,
                           strata = object.modelFrame$strata.num,
                           nPatients = object.n,
                           nStrata = nStrata,
                           emaxtimes = etimes.max,
                           predtimes = times.sorted,
                           cause = 1,
                           Efron = (object.baseEstimator == "efron"))
    ## restaure strata levels
    Lambda0$strata <- factor(Lambda0$strata, levels = 0:(nStrata-1), labels = object.levelStrata)
  
    ## ** compute cumlative hazard and survival
    if (is.null(newdata)){  
        if (!("hazard" %in% type)){
            Lambda0$hazard <- NULL
        } 
        if ("survival" %in% type){  ## must be before cumhazard
            Lambda0$survival = exp(-Lambda0$cumhazard)
        }
        if (!("cumhazard" %in% type)){
            Lambda0$cumhazard <- NULL
        } 
        if (keep.times==FALSE){
            Lambda0$times <- NULL
        }
        if (keep.strata[[1]]==FALSE ||(is.null(call$keep.strata) && !is.strata)){
            Lambda0$strata <- NULL
        }
        if( keep.newdata[1]==TRUE){
            Lambda0$newdata <- object.modelFrame
        }
        add.list <- list(lastEventTime = etimes.max,
                         se = FALSE,
                         band = FALSE,                         
                         type = type,
                         nTimes = nTimes,
                         baseline = TRUE,
                         var.lp = infoVar$lpvars.original,
                         var.strata = infoVar$stratavars.original)
        if(keep.infoVar){
            add.list$infoVar <- infoVar
        }
        
        Lambda0[names(add.list)] <- add.list
        class(Lambda0) <- "predictCox"
        return(Lambda0)
    } else {
    
        out <- list()
        ## *** reformat newdata (compute linear predictor and strata)
        new.n <- NROW(newdata)
        newdata <- data.table::as.data.table(newdata)

        Xb <- coxLP(object, data = newdata, center = FALSE)
        if ("lp" %in% type){
            out$lp <- cbind(Xb)
            lp.iid <- centered2 ## when ask for centered then we need the iid for exporting the correct se
        }else{
            lp.iid <- FALSE
        }
        new.eXb <- exp(Xb)
        new.strata <- coxStrata(object, data = newdata, 
                                sterms = infoVar$strata.sterms, 
                                strata.vars = infoVar$stratavars, 
                                strata.levels = infoVar$strata.levels)

      new.levelStrata <- levels(droplevels(new.strata))

      ## *** subject specific hazard
      if (is.strata==FALSE && !identical(as.character(type),"lp")){
          if(diag){
              if(needOrder){
                  iTimes <- prodlim::sindex(jump.times = Lambda0$times, eval.times = times.sorted[oorder.times])
              }else{
                  iTimes <- prodlim::sindex(jump.times = Lambda0$times, eval.times = times.sorted)
              }                  
          }
          
          if ("hazard" %in% type){
              if(diag){
                  out$hazard <- cbind(new.eXb * Lambda0$hazard[iTimes])
              }else{
                  out$hazard <- (new.eXb %o% Lambda0$hazard)
                  if (needOrder) out$hazard <- out$hazard[,oorder.times,drop=0L]
              }
          }
          if ("cumhazard" %in% type || "survival" %in% type){
              if(diag){
                  cumhazard <- cbind(new.eXb * Lambda0$cumhazard[iTimes])
              }else{
                  cumhazard <- new.eXb %o% Lambda0$cumhazard
                  if (needOrder){cumhazard <- cumhazard[,oorder.times,drop=0L]}
              }
              if ("cumhazard" %in% type){
                  out$cumhazard <- cumhazard
              }
              if ("survival" %in% type){
                  out$survival <- exp(-cumhazard)
              }
          }              
           
      }else if(!identical(as.character(type),"lp")){ 
          ## initialization
          if ("hazard" %in% type){
              out$hazard <- matrix(0, nrow = new.n, ncol = nTimes*(1-diag)+diag)
          }
          if ("cumhazard" %in% type){
              out$cumhazard <- matrix(NA, nrow = new.n, ncol = nTimes*(1-diag)+diag)                
          }
          if ("survival" %in% type){
              out$survival <- matrix(NA, nrow = new.n, ncol = nTimes*(1-diag)+diag)
          }

          ## loop across strata
          for(S in new.levelStrata){ ## S <- 1
              id.S <- which(Lambda0$strata==S)
              newid.S <- which(new.strata==S)

              if(diag){
                  if(needOrder){
                      iSTimes <- prodlim::sindex(jump.times = Lambda0$times[id.S], eval.times = times.sorted[oorder.times[newid.S]])
                  }else{
                      iSTimes <- prodlim::sindex(jump.times = Lambda0$times[id.S], eval.times = times.sorted[newid.S])
                  }                  
              }
        
              if ("hazard" %in% type){
                  if(diag){
                      out$hazard[newid.S] <- new.eXb[newid.S] * Lambda0$hazard[id.S][iSTimes]
                  }else{
                      out$hazard[newid.S,] <- new.eXb[newid.S] %o% Lambda0$hazard[id.S]
                      if (needOrder){
                          out$hazard[newid.S,] <- out$hazard[newid.S,oorder.times,drop=0L]
                      }
                  }
              }
              if ("cumhazard" %in% type || "survival" %in% type){
                  if(diag){
                      cumhazard.S <-  cbind(new.eXb[newid.S] * Lambda0$cumhazard[id.S][iSTimes])
                  }else{
                      cumhazard.S <-  new.eXb[newid.S] %o% Lambda0$cumhazard[id.S]
                      if (needOrder){
                          cumhazard.S <- cumhazard.S[,oorder.times,drop=0L]
                      }
                  }

                  if ("cumhazard" %in% type){
                      out$cumhazard[newid.S,] <- cumhazard.S
                  }
                  if ("survival" %in% type){
                      out$survival[newid.S,] <- exp(-cumhazard.S)
                  }
              }
          }
      }
    
    if(se[[1]] || band[[1]] || iid[[1]] || average.iid[[1]]){
        if(nVar.lp > 0){
            ## get the (new) design matrix
            new.LPdata <- model.matrix(object, data = newdata)
            if(NROW(new.LPdata)!=NROW(newdata)){
                stop("NROW of the design matrix and newdata differ. \n",
                     "Maybe because newdata contains NA values \n")
            }
            if(any(sort(colnames(new.LPdata))!=sort(names(coef(object))))){
                stop("Names of the design matrix and model parameters differ. \n",
                     "Possible error in model.matrix due to special operator in the formula. \n")
            }
        }else{
            new.LPdata <- matrix(0, ncol = 1, nrow = new.n)
        }

        ## restaure original ordering
        data.table::setkeyv(object.modelFrame,"XXXindexXXX")
        if(diag){
            Lambda0$oorder.times <- oorder.times
        }else{
            Lambda0$oorder.times <- 1:nTimes
        }

        ## Computation of the influence function and/or the standard error
        export <- c("iid"[(iid+band+lp.iid)>0],"se"[(se+band)>0],"average.iid"[average.iid==TRUE])
        if(!is.null(attr(average.iid,"factor"))){
            if(diag){
                attr(export,"factor") <- attr(average.iid,"factor")
            }else{
                ## re-order columns according to times
                attr(export,"factor") <- lapply(attr(average.iid,"factor"), function(iF){
                    iF[,order.times,drop=FALSE]
                })
            }
        }
        if(diag){
            times2 <- times
        }else{
            times2 <- times.sorted
        }
        attr(times2,"etimes.max") <- attr(times.sorted,"etimes.max")
        
        outSE <- calcSeCox(object,
                           times = times2,
                           nTimes = nTimes,
                           type = type,
                           diag = diag,
                           Lambda0 = Lambda0,
                           object.n = object.n,
                           object.time = object.modelFrame$stop,
                           object.eXb = object.modelFrame$eXb,
                           object.strata =  object.modelFrame$strata, 
                           nStrata = nStrata,
                           new.n = new.n,
                           new.eXb = new.eXb,
                           new.LPdata = new.LPdata,
                           new.strata = new.strata,
                           new.survival = if(diag){out$survival}else{out$survival[,order.times,drop=FALSE]},
                           nVar.lp = nVar.lp, 
                           export = export,
                           store.iid = store.iid)

        ## restaure orginal time ordering
        if((iid+band)>0){
            if ("lp" %in% type){
                out$lp.iid <- outSE$lp.iid
            }
            if ("hazard" %in% type){
                if (needOrder[1] && (diag[1] == FALSE))
                    out$hazard.iid <- outSE$hazard.iid[,oorder.times,,drop=0L]
                else
                    out$hazard.iid <- outSE$hazard.iid
            }
            if ("cumhazard" %in% type){
                if (needOrder[1] && (diag[1] == FALSE))
                    out$cumhazard.iid <- outSE$cumhazard.iid[,oorder.times,,drop=0L]
                else
                    out$cumhazard.iid <- outSE$cumhazard.iid
            }
            if ("survival" %in% type){
                if (needOrder[1] && (diag[1] == FALSE))
                    out$survival.iid <- outSE$survival.iid[,oorder.times,,drop=0L]
                else
                    out$survival.iid <- outSE$survival.iid
            }
        }
        if(average.iid == TRUE){
            if("lp" %in% type){
                out$lp.average.iid <- outSE$lp.average.iid
            }
            if ("hazard" %in% type){
                if (needOrder && (diag[1] == FALSE)){
                    if(is.list(outSE$hazard.average.iid)){
                        out$hazard.average.iid <- lapply(outSE$hazard.average.iid, function(iIID){iIID[,oorder.times,drop=0L]})
                    }else{
                        out$hazard.average.iid <- outSE$hazard.average.iid[,oorder.times,drop=0L]
                    }
                }else{
                    out$hazard.average.iid <- outSE$hazard.average.iid
                }
            }
            if ("cumhazard" %in% type){
                if (needOrder && (diag[1] == FALSE)){
                    if(is.list(outSE$cumhazard.average.iid)){
                        out$cumhazard.average.iid <- lapply(outSE$cumhazard.average.iid, function(iIID){iIID[,oorder.times,drop=0L]})
                    }else{
                        out$cumhazard.average.iid <- outSE$cumhazard.average.iid[,oorder.times,drop=0L]
                    }
                }else{
                    out$cumhazard.average.iid <- outSE$cumhazard.average.iid
                }
            }
            if ("survival" %in% type){
                if (needOrder && (diag[1] == FALSE)){
                    if(is.list(outSE$survival.average.iid)){
                        out$survival.average.iid <- lapply(outSE$survival.average.iid, function(iIID){iIID[,oorder.times,drop=0L]})
                    }else{
                        out$survival.average.iid <- outSE$survival.average.iid[,oorder.times,drop=0L]
                    }
                }else {
                    out$survival.average.iid <- outSE$survival.average.iid
                }
            }

            if(is.list(attr(average.iid,"factor"))){
                if("hazard" %in% type){
                    names(out$hazard.average.iid) <- names(attr(average.iid,"factor"))
                }
                if("cumhazard" %in% type){
                    names(out$cumhazard.average.iid) <- names(attr(average.iid,"factor"))
                }
                if("survival" %in% type){
                    names(out$survival.average.iid) <- names(attr(average.iid,"factor"))
                }
            }

        }
        if((se+band)>0){
            if("lp" %in% type){
                out$lp.se <- outSE$lp.se
            }
            if ("cumhazard" %in% type){
                if (needOrder && (diag[1] == FALSE)){
                    out$cumhazard.se <- outSE$cumhazard.se[,oorder.times,drop=0L]
                }else{
                    out$cumhazard.se <- outSE$cumhazard.se
                }          
            }
            if ("survival" %in% type){
                if (needOrder && (diag[1] == FALSE)){
                    out$survival.se <- outSE$survival.se[,oorder.times,drop=0L]
                } else{
                    out$survival.se <- outSE$survival.se
                }          
            }
        }      
    }

        ## ** substract reference
        if("lp" %in% type && centered2){
            if(is.null(df.reference)){
                data <- try(eval(object$call$data), silent = TRUE)
                if(inherits(x=data,what="try-error")){
                    stop("Could not evaluate the dataset used to fit the model to define a reference level. \n",
                         "Set argument \'centered\' to FALSE or to a data.frame definining the reference level. \n")
                }
                var.original <- infoVar$lpvars.original
                
                ls.ref <- lapply(var.original, function(iVar){
                    if(is.numeric(data[[iVar]])){
                        return(unname(mean(data[[iVar]])))
                    }else if(is.factor(data[[iVar]])){
                        return(unname(factor(levels(data[[iVar]])[1],levels(data[[iVar]]))))
                    }else if(is.character(data[[iVar]])){
                        return(unname(sort(unique(data[[iVar]])[1])))
                    }
                })
                df.reference <- as.data.frame(setNames(ls.ref,var.original))
            }

            ls.args <- as.list(call)[-1]
            ls.args$newdata <- df.reference
            ls.args$centered <- FALSE
            ls.args$type <- "lp"
            ls.args$se <- (se+band>0)
            ls.args$iid <- (iid+se+band>0)
            ls.args$band <- FALSE
            ls.args$confint <- FALSE
            outRef <- do.call(predictCox, args = ls.args)

            out$lp <- out$lp - as.double(outRef$lp)
            if(band[1] || se[1]){
                out$lp.se <- cbind(sqrt(colSums(colCenter_cpp(outSE$lp.iid, outRef$lp.iid)^2))) ## use outSe$lp.iid instead of out$lp.iid for when not exporting the iid
            }
            if(band[1] || iid[1]){
                out$lp.iid <- colCenter_cpp(out$lp.iid, outRef$lp.iid)
            }
            
        }
        
        ## ** add information to the predictions
        add.list <- list(lastEventTime = etimes.max,
                         se = se,
                         band = band,
                         type = type,
                         diag = diag,
                         nTimes = nTimes,
                         baseline = FALSE,
                         var.lp = infoVar$lpvars.original,
                         var.strata = infoVar$stratavars.original)
        if (keep.times==TRUE){
            add.list$times <- times
        }
        if (is.strata[1] && keep.strata[1]==TRUE){
            add.list$strata <- new.strata
        }
      
      if( keep.infoVar){
          add.list$infoVar <- infoVar
      }
      all.covars <- c(infoVar$stratavars.original,infoVar$lpvars.original)
        if( keep.newdata[1]==TRUE && length(all.covars)>0){
            if (data.table::is.data.table(newdata))
                add.list$newdata <- newdata[, all.covars, with = FALSE]
            else
                add.list$newdata <- newdata[, all.covars, drop=FALSE]
      }
      out[names(add.list)] <- add.list
      class(out) <- "predictCox"

        ## ** confidence intervals/bands
      if(confint){
          out <- stats::confint(out)
      }
      if(band[1] && se[1]==FALSE){
          out[paste0(type,".se")] <- NULL
      }
      if(band[1] && iid[1]==FALSE){
          out[paste0(type,".iid")] <- NULL
      }
      
      return(out)
  }
  
}