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```
#' Obtain values for Kaplan-Meier plotting
#'
#' @param x Nx2 data matrix,first columen represents survival time of the i-th subject, second column represents censored flag (0 if not censored, 1 if censored)
#'
#' @usage kmvalue(x)
#' @return
#' Values used for Kaplan-Meier plotting
#' @export
#'
#' @examples
#' t1 <- c(2,3,4,5.5,7,10,12,15)
#' c1 <- c(0,0,1,0,0,1,0,0)
#' x1<-cbind(t1,c1)
#' kmvalue(x1)
kmvalue <- function(x){
# sort data by survival time
x = x[order(x[,1]),]
# table of patients observed for each survival time
# the TABULATE function sets up this matrix:
# table1=[time count]
# get frequent list for survival time
frequent <- table(x[,1])
# convert frequency list to matrix
y <- matrix(c(as.numeric(names(frequent)), frequent), ncol=2, byrow=FALSE,
dimnames=NULL)
# add (0,size) to the first row of matrix y
table1 = rbind(c(0,sum(y[,2])),y)
# Table of censored data
# list of censored data, "0" represent censored
cenData = x[which(x[,2]==0)]
freqCen <- table(cenData)
# convert censor data frequency list to matrix
table12 <- matrix(c(as.numeric(names(freqCen)), freqCen), ncol=2, byrow=FALSE,
dimnames=NULL)
# setup the vector of the censored data (function is.element() return T or F whether elements in first
# vector contained in second vector
cens <- as.numeric(is.element(table1[,1],table12[,1]))
# loc return index in vector 2 of matched element
loc <- match(table1[,1],table12[,1])
# replace NA with 0
loc[is.na(loc)] <- 0
# place in the third column how many subjects are still alive at the
# beginning of the i-th interval.
a1 = c(table1[1,2], -1*table1[-1,2])
table1 <- cbind(table1,cumsum(a1))
end1 <- dim(table1)[1]
table1[-1,3] = table1[-end1,3]
# number of deaths in the intervals (don't take in account the censored
# data)
table1[which(cens==1),2] = table1[which(cens==1),2]-table12[loc[which(cens == 1)],2]
# finally, delete the first row that is now useless
table1<- table1[-1,]
# this is the x variable (time);
t1 = c(0,table1[,1])
# this is the y variable (survival function)
T1 = c(1, cumprod(( 1-(table1[,2]/table1[,3]) )))
# censored data plotting
# if there are censored data after max(t1), add a new cell into the t1,T1
end12 <- dim(table12)[1]
if (table12[end12, 1] >= t1[length(t1)]){
t1[length(t1)+1] = table12[end12,1]+1
T1[length(T1)+1] = T1[length(T1)]
}
# data of censored points
# vectors preallocation
xcg = rep(0, sum(table12[,2]))
ycg = xcg
J = 1
# for each censored data into the i-th time interval...
for (I in 1:end12)
{
# compute how many position into the array they must occupy
JJ = J + table12[I,2]-1
#find the correct time interval in which censored data must be placed
B = min(which(t1>=table12[I,1]))
A = B-1
# equally divide this interval
int = seq(from = table12[I,1], to = t1[B], len = table12[I,2]+2)
xcg[J:JJ] = int[2:(length(int)-1)]
ycg[J:JJ] = T1[A]
# update the counter
J = JJ + 1
}
# compute the hazard rate
c1 = T1*dim(x)[1]*dim(x)[2]
c2 = -(diff(log(c1[-length(c1)]))/diff(t1[-length(t1)]))
lambda = mean(c2[which(c2 != 0)])
# output
kmout = list("table1"=table1, "table12" = table12, "t1" = t1, "T1" = T1, "xcg" = xcg, "ycg" = ycg,
"lambda" = lambda)
return (kmout)
}
#x = cbind(time_p,cens_p)
```

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