event.history: Produces event.history graph for survival data

Description

Produces an event history graph for right-censored survival data, including time-dependent covariate status, as described in Dubin, Muller, and Wang (2001). Effectively, a Kaplan-Meier curve is produced with supplementary information regarding individual survival information, censoring information, and status over time of an individual time-dependent covariate or time-dependent covariate function for both uncensored and censored individuals.

Usage

event.history(data, survtime.col, surv.col,
              surv.ind = c(1, 0), subset.rows = NULL,
              covtime.cols = NULL, cov.cols = NULL,
              num.colors = 1, cut.cov = NULL, colors = 1,
              cens.density = 10, mult.end.cens = 1.05,
              cens.mark.right =FALSE, cens.mark = "-",
              cens.mark.ahead = 0.5, cens.mark.cutoff = -1e-08,
              cens.mark.cex = 1,
              x.lab = "time under observation",
              y.lab = "estimated survival probability",
              title = "event history graph", ...)

Arguments

data: A matrix or data frame with rows corresponding to units (often individuals) and columns corresponding to survival time, event/censoring indicator. Also, multiple columns may be devoted to time-dependent covariate level and time change.
survtime.col: Column (in data) representing minimum of time-to-event or right-censoring time for individual.
surv.col: Column (in data) representing event indicator for an individual. Though, traditionally, such an indicator will be 1 for an event and 0 for a censored observation, this indicator can be represented by any two numbers, made explicit by the surv.ind argument.
surv.ind: Two-element vector representing, respectively, the number for an event, as listed in surv.col, followed by the number for a censored observation. Default is traditional survival data represention, i.e., c(1,0).
subset.rows: Subset of rows of original matrix or data frame (data) to place in event history graph. Logical arguments may be used here (e.g., treatment.arm == "a", if the data frame, data, has been attached to the search directory;
covtime.cols: Column(s) (in data) representing the time when change of time-dependent covariate (or time-dependent covariate function) occurs. There should be a unique non-NA entry in the column for each such change (along with corresponding cov.cols column entry representing the value of the covariate or function at that change time). Default is NULL, meaning no time-dependent covariate information will be presented in the graph.
cov.cols: Column(s) (in data) representing the level of the time-dependent covariate (or time-dependent covariate function). There should be a unique non-NA column entry representing each change in the level (along with a corresponding covtime.cols column entry representing the time of the change). Default is NULL, meaning no time-dependent covariate information will be presented in the graph.
num.colors: Colors are utilized for the time-dependent covariate level for an individual. This argument provides the number of unique covariate levels which will be displayed by mapping the number of colors (via num.colors) to the number of desired covariate levels. This will divide the covariate span into roughly equally-sized intervals, via the S-Plus cut function. Default is one color, meaning no time-dependent information will be presented in the graph. Note that this argument will be ignored/superceded if a non-NULL argument is provided for the cut.cov parameter.
cut.cov: This argument allows the user to explicitly state how to define the intervals for the time-dependent covariate, such that different colors will be allocated to the user-defined covariate levels. For example, for plotting five colors, six ordered points within the span of the data's covariate levels should be provided. Default is NULL, meaning that the num.colors argument value will dictate the number of breakpoints, with the covariate span defined into roughly equally-sized intervals via the S-Plus cut function. However, if is.null(cut.cov) == FALSE, then this argument supercedes any entry for the num.colors argument.
colors: This is a vector argument defining the actual colors used for the time-dependent covariate levels in the plot, with the index of this vector corresponding to the ordered levels of the covariate. The number of colors (i.e., the length of the colors vector) should correspond to the value provided to the num.colors argument or the number of ordered points - 1 as defined in the cut.cov argument (with cut.cov superceding num.colors if is.null(cut.cov) == FALSE). The function, as currently written, allows for as much as twenty distinct colors. This argument effectively feeds into the col argument for the S-Plus polygon function. Default is colors = 1. See the col argument for the both the S-Plus par function and polygon function for more information.
cens.density: This will provide the shading density at the end of the individual bars for those who are censored. For more information on shading density, see the density argument in the S-Plus polygon function. Default is cens.density=10.
mult.end.cens: This is a multiplier that extends the length of the longest surviving individual bar (or bars, if a tie exists) if right-censored, presuming that no event times eventually follow this final censored time. Default extends the length 5 percent beyond the length of the observed right-censored survival time.
cens.mark.right: A logical argument that states whether an explicit mark should be placed to the right of the individual right-censored survival bars. This argument is most useful for large sample sizes, where it may be hard to detect the special shading via cens.density, particularly for the short-term survivors.
cens.mark: Character argument which describes the censored mark that should be used if cens.mark.right = TRUE. Default is "-".
cens.mark.ahead: A numeric argument, which specifies the absolute distance to be placed between the individual right-censored survival bars and the mark as defined in the above cens.mark argument. Default is 0.5 (that is, a half of day, if survival time is measured in days), but may very well need adjusting depending on the maximum survival time observed in the dataset.
cens.mark.cutoff: A negative number very close to 0 (by default cens.mark.cutoff = -1e-8) to ensure that the censoring marks get plotted correctly. See event.history code in order to see its usage. This argument typically will not need adjustment.
cens.mark.cex: Numeric argument defining the size of the mark defined in the cens.mark argument above. See more information by viewing the cex argument for the S-Plus par function. Default is cens.mark.cex = 1.0.
x.lab: Single label to be used for entire x-axis. Default is "time under observation".
y.lab: Single label to be used for entire y-axis. Default is "estimated survival probability".
title: Title for the event history graph. Default is "event history graph".
...: This allows arguments to the plot function call within the event.history function. So, for example, the axes representations can be manipulated with appropriate arguments, or particular areas of the event.history graph can be “zoomed”. See the details section for more comments about zooming.

Author

Joel Dubin
jdubin@uwaterloo.ca

WARNING

This function has been tested thoroughly, but only within a restricted version and environment, i.e., only within S-Plus 2000, Version 3, and within S-Plus 6.0, version 2, both on a Windows 2000 machine. Hence, we cannot currently vouch for the function's effectiveness in other versions of S-Plus (e.g., S-Plus 3.4) nor in other operating environments (e.g., Windows 95, Linux or Unix). The function has also been verified to work on R under Linux.

Details

In order to focus on a particular area of the event history graph, zooming can be performed. This is best done by specifying appropriate xlim and ylim arguments at the end of the event.history function call, taking advantage of the ... argument link to the plot function. An example of zooming can be seen in Plate 4 of the paper referenced below.

Please read the reference below to understand how the individual covariate and survival information is provided in the plot, how ties are handled, how right-censoring is handled, etc.

References

Dubin, J.A., Muller, H.-G., and Wang, J.-L. (2001). Event history graphs for censored survival data. Statistics in Medicine, 20, 2951-2964.

Examples

Run this code

# Code to produce event history graphs for SIM paper
#
# before generating plots, some pre-processing needs to be performed,
#  in order to get dataset in proper form for event.history function;
#  need to create one line per subject and sort by time under observation, 
#  with those experiencing event coming before those tied with censoring time;
require('survival')
data(heart)

# creation of event.history version of heart dataset (call heart.one):

heart.one <- matrix(nrow=length(unique(heart$id)), ncol=8)
for(i in 1:length(unique(heart$id)))
 {
  if(length(heart$id[heart$id==i]) == 1)
   heart.one[i,] <- as.numeric(unlist(heart[heart$id==i, ]))
  else if(length(heart$id[heart$id==i]) == 2)
   heart.one[i,] <- as.numeric(unlist(heart[heart$id==i,][2,]))
 }

heart.one[,3][heart.one[,3] == 0] <- 2 	## converting censored events to 2, from 0
if(is.factor(heart$transplant))
 heart.one[,7] <- heart.one[,7] - 1
 ## getting back to correct transplantation coding
heart.one <- as.data.frame(heart.one[order(unlist(heart.one[,2]), unlist(heart.one[,3])),])
names(heart.one) <- names(heart)
# back to usual censoring indicator:
heart.one[,3][heart.one[,3] == 2] <- 0 
# note: transplant says 0 (for no transplants) or 1 (for one transplant)
#        and event = 1 is death, while event = 0 is censored

# plot single Kaplan-Meier curve from heart data, first creating survival object
heart.surv <- survfit(Surv(stop, event) ~ 1, data=heart.one, conf.int = FALSE)

# figure 3: traditional Kaplan-Meier curve
# postscript('ehgfig3.ps', horiz=TRUE)
# omi <- par(omi=c(0,1.25,0.5,1.25))
 plot(heart.surv, ylab='estimated survival probability',
      xlab='observation time (in days)')
 title('Figure 3: Kaplan-Meier curve for Stanford data', cex=0.8)
# dev.off()

## now, draw event history graph for Stanford heart data; use as Figure 4

# postscript('ehgfig4.ps', horiz=TRUE, colors = seq(0, 1, len=20))
# par(omi=c(0,1.25,0.5,1.25))
 event.history(heart.one, 
		survtime.col=heart.one[,2], surv.col=heart.one[,3],
		covtime.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,1]),
		cov.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,7]),
		num.colors=2, colors=c(6,10),
		x.lab = 'time under observation (in days)',
		title='Figure 4: Event history graph for\nStanford data',
		cens.mark.right =TRUE, cens.mark = '-', 
		cens.mark.ahead = 30.0, cens.mark.cex = 0.85)
# dev.off()



# now, draw age-stratified event history graph for Stanford heart data; 
#  use as Figure 5

# two plots, stratified by age status
# postscript('c:\temp\ehgfig5.ps', horiz=TRUE, colors = seq(0, 1, len=20))
# par(omi=c(0,1.25,0.5,1.25))
 par(mfrow=c(1,2))

 event.history(data=heart.one, subset.rows = (heart.one[,4] < 0),
		survtime.col=heart.one[,2], surv.col=heart.one[,3],
		covtime.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,1]),
		cov.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,7]),
		num.colors=2, colors=c(6,10),  
		x.lab = 'time under observation\n(in days)',
		title = 'Figure 5a:\nStanford data\n(age < 48)',
		cens.mark.right =TRUE, cens.mark = '-', 
		cens.mark.ahead = 40.0, cens.mark.cex = 0.85,
		xlim=c(0,1900))

 event.history(data=heart.one, subset.rows = (heart.one[,4] >= 0),
		survtime.col=heart.one[,2], surv.col=heart.one[,3],
		covtime.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,1]),
		cov.cols = cbind(rep(0, dim(heart.one)[1]), heart.one[,7]),
		num.colors=2, colors=c(6,10),
		x.lab = 'time under observation\n(in days)',
		title = 'Figure 5b:\nStanford data\n(age >= 48)',
		cens.mark.right =TRUE, cens.mark = '-', 
		cens.mark.ahead = 40.0, cens.mark.cex = 0.85,
		xlim=c(0,1900))
# dev.off()
# par(omi=omi)

# we will not show liver cirrhosis data manipulation, as it was 
#  a bit detailed; however, here is the 
#  event.history code to produce Figure 7 / Plate 1

# Figure 7 / Plate 1 : prothrombin ehg with color
if (FALSE) {
second.arg <- 1				### second.arg is for shading
third.arg <- c(rep(1,18),0,1)		### third.arg is for intensity

# postscript('c:\temp\ehgfig7.ps', horiz=TRUE, 
# colors = cbind(seq(0, 1, len = 20), second.arg, third.arg)) 
# par(omi=c(0,1.25,0.5,1.25), col=19)
 event.history(cirrhos2.eh, subset.rows = NULL,
               survtime.col=cirrhos2.eh$time, surv.col=cirrhos2.eh$event,
		covtime.cols = as.matrix(cirrhos2.eh[, ((2:18)*2)]),
		cov.cols = as.matrix(cirrhos2.eh[, ((2:18)*2) + 1]),
		cut.cov =  as.numeric(quantile(as.matrix(cirrhos2.eh[, ((2:18)*2) + 1]),
				c(0,.2,.4,.6,.8,1), na.rm=TRUE) + c(-1,0,0,0,0,1)),	
 		colors=c(20,4,8,11,14),
		x.lab = 'time under observation (in days)',
		title='Figure 7: Event history graph for liver cirrhosis data (color)',
		cens.mark.right =TRUE, cens.mark = '-', 
		cens.mark.ahead = 100.0, cens.mark.cex = 0.85)
# dev.off()
}

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