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#' Simulate quantities of interest for covariates from Cox Proportional Hazards
#' models that are not interacted with time or nonlinearly transformed
#'
#' \code{coxsimLinear} simulates relative hazards, first differences, and
#' hazard ratios for linear covariates that are not interacted with time or
#' nonlinearly transformed from models estimated with \code{\link{coxph}} using
#' the multivariate normal distribution. These can be plotted with
#' \code{\link{simGG}}.
#' @param obj a \code{\link{coxph}} class fitted model object.
#' @param b character string name of the coefficient you would like to simulate.
#' @param qi quantity of interest to simulate. Values can be
#' \code{"Relative Hazard"}, \code{"First Difference"}, \code{"Hazard Ratio"},
#' and \code{"Hazard Rate"}. The default is \code{qi = "Relative Hazard"}. If
#' \code{qi = "Hazard Rate"} and the \code{coxph} model has strata, then hazard
#' rates for each strata will also be calculated.
#' @param Xj numeric vector of fitted values for \code{b} to simulate for.
#' @param Xl numeric vector of values to compare \code{Xj} to. Note if
#' \code{code = "Relative Hazard"} only \code{Xj} is relevant.
#' @param means logical, whether or not to use the mean values to fit the
#' hazard rate for covaraiates other than \code{b}. Note: EXPERIMENTAL.
#' \code{lines} are not currently supported in \code{\link{simGG}} if
#' \code{means = TRUE}.
#' @param nsim the number of simulations to run per value of X. Default is
#' \code{nsim = 1000}. Note: it does not currently support models that include
#' polynomials created by \code{\link{I}}.
#' @param ci the proportion of simulations to keep. The default is
#' \code{ci = 0.95}, i.e. keep the middle 95 percent. If \code{spin = TRUE}
#' then \code{ci} is the confidence level of the shortest probability interval.
#' Any value from 0 through 1 may be used.
#' @param spin logical, whether or not to keep only the shortest probability
#' interval rather than the middle simulations. Currently not supported for
#' Hazard Rates.
#' @param extremesDrop logical whether or not to drop simulated quantity of
#' interest values that are \code{Inf}, \code{NA}, \code{NaN} and
#' \eqn{> 1000000} for \code{spin = FALSE} or \eqn{> 800} for
#' \code{spin = TRUE}. These values are difficult to plot \code{\link{simGG}}
#' and may prevent \code{spin} from finding the central interval.
#'
#' @return a \code{simlinear}, \code{coxsim} object
#'
#' @description Simulates relative hazards, first differences, hazard ratios,
#' and hazard rates for linear, non-time interacted covariates from Cox
#' Proportional Hazard models. These can be plotted with \code{\link{simGG}}.
#'
#'
#' @examples
#' # Load Carpenter (2002) data
#' data("CarpenterFdaData")
#'
#' # Load survival package
#' library(survival)
#'
#' # Run basic model
#' M1 <- coxph(Surv(acttime, censor) ~ prevgenx + lethal +
#' deathrt1 + acutediz + hosp01 + hhosleng +
#' mandiz01 + femdiz01 + peddiz01 + orphdum +
#' vandavg3 + wpnoavg3 + condavg3 + orderent +
#' stafcder, data = CarpenterFdaData)
#'
#' # Simulate Hazard Ratios
#' Sim1 <- coxsimLinear(M1, b = "stafcder",
#' Xj = c(1237, 1600),
#' Xl = c(1000, 1000),
#' qi = "Hazard Ratio",
#' spin = TRUE, ci = 0.99)
#'
#' \dontrun{
#' # Simulate Hazard Rates
#' Sim2 <- coxsimLinear(M1, b = "stafcder",
#' Xj = 1237,
#' ci = 0.99)
#' }
#'
#' @seealso \code{\link{simGG.simlinear}}, \code{\link{survival}},
#' \code{\link{strata}}, and \code{\link{coxph}}
#'
#' @references Gandrud, Christopher. 2015. simPH: An R Package for Illustrating
#' Estimates from Cox Proportional Hazard Models Including for Interactive and
#' Nonlinear Effects. Journal of Statistical Software. 65(3)1-20.
#'
#' Licht, Amanda A. 2011. ''Change Comes with Time: Substantive
#' Interpretation of Nonproportional Hazards in Event History Analysis.''
#' Political Analysis 19: 227-43.
#'
#' King, Gary, Michael Tomz, and Jason Wittenberg. 2000. ''Making the Most of
#' Statistical Analyses: Improving Interpretation and Presentation.'' American
#' Journal of Political Science 44(2): 347-61.
#'
#' Liu, Ying, Andrew Gelman, and Tian Zheng. 2013. ''Simulation-Efficient
#' Shortest Probability Intervals.'' Arvix.
#' \url{https://arxiv.org/pdf/1302.2142v1.pdf}.
#'
#' @import data.table
#' @importFrom stats vcov model.frame
#' @importFrom survival basehaz
#' @importFrom MASS mvrnorm
#' @export
coxsimLinear <- function(obj, b, qi = "Relative Hazard", Xj = NULL, Xl = NULL,
means = FALSE, nsim = 1000, ci = 0.95, spin = FALSE,
extremesDrop = TRUE)
{
HRValue <- strata <- QI <- SimID <- time <- NULL
if (qi != "Hazard Rate" & isTRUE(means)){
stop("means can only be TRUE when qi = 'Hazard Rate'.", call. = FALSE)
}
if (is.null(Xl) & qi != "Hazard Rate"){
Xl <- rep(0, length(Xj))
message("All Xl set to 0.")
} else if (!is.null(Xl) & qi == "Relative Hazard") {
message("All Xl set to 0.")
}
# Ensure that qi is valid
qiOpts <- c("Relative Hazard", "First Difference", "Hazard Rate",
"Hazard Ratio")
TestqiOpts <- qi %in% qiOpts
if (!isTRUE(TestqiOpts)){
stop("Invalid qi type. qi must be 'Relative Hazard', 'Hazard Rate',
'First Difference', or 'Hazard Ratio'.", call. = FALSE)
}
MeansMessage <- NULL
if (isTRUE(means) & length(obj$coefficients) == 3){
means <- FALSE
MeansMessage <- FALSE
message("Note: means reset to FALSE. The model only includes the interaction variables.")
} else if (isTRUE(means) & length(obj$coefficients) > 3){
MeansMessage <- TRUE
}
# Create simulation ID variable
SimID <- 1:nsim
# Parameter estimates & Variance/Covariance matrix
Coef <- matrix(obj$coefficients)
VC <- vcov(obj)
# Draw covariate estimates from the multivariate normal distribution
Drawn <- mvrnorm(n = nsim, mu = Coef, Sigma = VC)
DrawnDF <- data.frame(Drawn)
dfn <- names(DrawnDF)
# If all values aren't set for calculating the hazard rate
if (!isTRUE(means)){
# Subset simulations to only include b
bpos <- match(b, dfn)
Simb <- data.frame(SimID, DrawnDF[, bpos])
names(Simb) <- c("SimID", "Coef")
# Find quantity of interest
if (qi == "Relative Hazard"){
Xs <- data.frame(Xj)
names(Xs) <- c("Xj")
Xs$Comparison <- paste(Xs[, 1])
Simb <- merge(Simb, Xs)
Simb$QI <- exp(Simb$Xj * Simb$Coef)
} else if (qi == "First Difference"){
if (length(Xj) != length(Xl)){
stop("Xj and Xl must be the same length.", call. = FALSE)
}
else {
Xs <- data.frame(Xj, Xl)
Simb <- merge(Simb, Xs)
Simb$QI<- (exp((Simb$Xj - Simb$Xl) * Simb$Coef) - 1) * 100
}
}
else if (qi == "Hazard Ratio"){
Xs <- data.frame(Xj, Xl)
Simb <- merge(Simb, Xs)
Simb$QI<- exp((Simb$Xj - Simb$Xl) * Simb$Coef)
}
else if (qi == "Hazard Rate"){
if (!is.null(Xl)) {
Xl <- NULL
message("Xl is ignored.")
}
if (isTRUE(MeansMessage)){
message("All variables values other than b are fitted at 0.")
}
Xs <- data.frame(Xj)
Xs$HRValue <- paste(Xs[, 1])
Simb <- merge(Simb, Xs)
Simb$HR <- exp(Simb$Xj * Simb$Coef)
bfit <- basehaz(obj)
bfit$FakeID <- 1
Simb$FakeID <- 1
bfitDT <- data.table(bfit, key = "FakeID", allow.cartesian = TRUE)
SimbDT <- data.table(Simb, key = "FakeID", allow.cartesian = TRUE)
Simb <- SimbDT[bfitDT, allow.cartesian = TRUE]
# Create warning message
Rows <- nrow(Simb)
if (Rows > 2000000){
message(paste("There are", Rows, "simulations. This may take awhile. Consider using nsim to reduce the number of simulations."))
}
Simb$QI <- Simb$hazard * Simb$HR
if (!('strata' %in% names(Simb))){
Simb <- Simb[, list(SimID, time, Xj, QI, HRValue)]
} else if ('strata' %in% names(Simb)){
Simb <- Simb[, list(SimID, time, Xj, QI, HRValue, strata)]
}
Simb <- data.frame(Simb)
}
}
# If the user wants to calculate Hazard Rates using means for fitting
# all covariates other than b.
else if (isTRUE(means)){
Xl <- NULL
message("Xl ignored")
# Set all values of b at means for data used in the analysis
NotB <- setdiff(names(DrawnDF), b)
MeanValues <- data.frame(obj$means)
FittedMeans <- function(Z){
ID <- 1:nsim
Temp <- data.frame(ID)
for (i in Z){
BarValue <- MeanValues[i, ]
DrawnCoef <- DrawnDF[, i]
FittedCoef <- outer(DrawnCoef, BarValue)
FCMolten <- MatrixMelter(FittedCoef)
Temp <- cbind(Temp, FCMolten[,3])
}
Names <- c("ID", Z)
names(Temp) <- Names
Temp <- Temp[, -1]
return(Temp)
}
FittedComb <- FittedMeans(NotB)
ExpandFC <- do.call(rbind, rep(list(FittedComb), length(Xj)))
# Set fitted values for Xj
bpos <- match(b, dfn)
Simb <- data.frame(DrawnDF[, bpos])
Xs <- data.frame(Xj)
Xs$HRValue <- paste(Xs[, 1])
Simb <- merge(Simb, Xs)
Simb$CombB <- Simb[, 1] * Simb[, 2]
Simb <- Simb[, 2:4]
Simb <- cbind(Simb, ExpandFC)
Simb$Sum <- rowSums(Simb[, c(-1, -2)])
Simb$HR <- exp(Simb$Sum)
bfit <- basehaz(obj)
bfit$FakeID <- 1
Simb$FakeID <- 1
bfitDT <- data.table(bfit, key = "FakeID", allow.cartesian = TRUE)
SimbDT <- data.table(Simb, key = "FakeID", allow.cartesian = TRUE)
Simb <- SimbDT[bfitDT, allow.cartesian = TRUE]
# Create warning message
Rows <- nrow(Simb)
if (Rows > 2000000){
message(paste("There are", Rows,
"simulations. This may take awhile. Consider using nsim to reduce the number of simulations."))
}
Simb$QI <- Simb$hazard * Simb$HR
if (!('strata' %in% names(Simb))){
Simb <- Simb[, list(time, Xj, QI, HRValue)]
} else if ('strata' %in% names(Simb)){
Simb <- Simb[, list(time, Xj, QI, HRValue, strata)]
}
Simb <- data.frame(Simb)
}
# Drop simulations outside of 'confidence bounds'
if (qi != "Hazard Rate"){
SubVar <- "Xj"
} else if (qi == "Hazard Rate"){
SubVar <- c("time", "Xj")
}
# Drop simulations outside of the middle
SimbPerc <- IntervalConstrict(Simb = Simb, SubVar = SubVar,
qi = qi, spin = spin, ci = ci,
extremesDrop = extremesDrop)
# Final clean up
# Subset simlinear object & create a data frame of important variables
if (qi == "Hazard Rate" & !isTRUE(means)){
if (!('strata' %in% names(obj))){
SimbPercSub <- data.frame(SimbPerc$SimID,
SimbPerc$time, SimbPerc$QI,
SimbPerc$HRValue)
names(SimbPercSub) <- c("SimID", "Time", "HRate", "HRValue")
} else if ('strata' %in% names(SimbPerc)) {
SimbPercSub <- data.frame(SimbPerc$SimID, SimbPerc$time,
SimbPerc$QI, SimbPerc$strata,
SimbPerc$HRValue)
names(SimbPercSub) <- c("SimID", "Time", "HRate", "Strata",
"HRValue")
}
} else if (qi == "Hazard Rate" & isTRUE(means)){
if (!('strata' %in% names(obj))){
SimbPercSub <- data.frame(SimbPerc$time, SimbPerc$QI,
SimbPerc$HRValue)
names(SimbPercSub) <- c("Time", "HRate", "HRValue")
} else if ('strata' %in% names(SimbPerc)) {
SimbPercSub <- data.frame(SimbPerc$SimID, SimbPerc$time,
SimbPerc$QI, SimbPerc$strata,
SimbPerc$HRValue)
names(SimbPercSub) <- c("SimID", "Time", "HRate",
"Strata", "HRValue")
}
} else if (qi == "Hazard Ratio" | qi == "Relative Hazard" |
qi == "First Difference"){
SimbPercSub <- data.frame(SimbPerc$SimID, SimbPerc$Xj, SimbPerc$QI)
names(SimbPercSub) <- c("SimID", "Xj", "QI")
}
# Add in distribution of b
rug <- model.frame(obj)[, b]
out <- list(sims = SimbPercSub, rug = rug)
class(out) <- c("simlinear", qi, "coxsim")
attr(out, 'xaxis') <- b
out
}
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