plotdistcens: Plot of empirical and theoretical distributions for censored data

Description

Plots an empirical distribution for censored data with a theoretical one if specified.

Usage

plotdistcens(censdata,distr,para,leftNA=-Inf,rightNA=Inf,Turnbull=TRUE,...)

Arguments

censdata

A dataframe of two columns respectively named left and right, describing each observed value as an interval. The left column contains either NA for left censored observations, the left b

distr

A character string "name" naming a distribution, for which the corresponding density function dname and the corresponding distribution function pname must be defined, or directly the density function.

para

A named list giving the parameters of the named distribution. This argument may be omitted only if distr is omitted.

leftNA

the real value of the left bound of left censored observations : -Inf or a finite value such as 0 for positive data for example.

rightNA

the real value of the right bound of right censored observations : Inf or a finite value such as a realistic maximum value.

Turnbull

if TRUE the Turnbull algorithm is used to estimate the cdf curve of the censored data and previous arguments leftNA and rightNA are not used (see details)

...

further graphical arguments passed to other methods

Details

Empirical and, if specified, theoretical distributions are plotted in cdf. If Turnbull is TRUE, the EM approach of Turnbull (Turnbull, 1974) is used to compute the overall empirical cdf curve with confidence intervals, by calls to functions survfit and plot.survfit from the survival package. Else data are reported directly as segments for interval, left and right censored data, and as points for non-censored data. Before plotting, observations are ordered and a rank r is associated to each of them. Left censored observations are ordered first, by their right bounds. Interval censored and non censored observations are then ordered by their mid-points and, at last, right censored observations are ordered by their left bounds. If leftNA (resp. rightNA) is finite, left censored (resp. right censored) observations are considered as interval censored observations and ordered by mid-points with non-censored and interval censored data. It is sometimes necessary to fix rightNA or leftNA to a realistic extreme value, even if not exactly known, to obtain a reasonable global ranking of observations. After ranking, each of the n observations is plotted as a point (one x-value) or a segment (an interval of possible x-values), with an y-value equal to r/n, r being the rank of each observation in the global ordering previously described. This second method may be interesting but is certainly less rigorous than the Turnbull method that should be prefered.

References

Turnbull BW (1974) Nonparametric estimation of a survivorship function with doubly censored data.Journal of American Statistical Association, 69, 169-173.

Examples

Run this code

# (1) Plot of an empirical censored distribution (censored data) as a CDF
# using the default Turnbull method
#
d1<-data.frame(
left=c(1.73,1.51,0.77,1.96,1.96,-1.4,-1.4,NA,-0.11,0.55,
    0.41,2.56,NA,-0.53,0.63,-1.4,-1.4,-1.4,NA,0.13),
right=c(1.73,1.51,0.77,1.96,1.96,0,-0.7,-1.4,-0.11,0.55,
    0.41,2.56,-1.4,-0.53,0.63,0,-0.7,NA,-1.4,0.13))
plotdistcens(d1)
plotdistcens(d1,col="red")

# (2) Add the CDF of a normal distribution 
#
plotdistcens(d1,"norm",para=list(mean=0.12,sd=1.4))

# (3) Basic plot of the same empirical distribution with intervals and points
# defining a realistic maximum value for right censored values
# in the second plot
#
plotdistcens(d1,Turnbull = FALSE)
plotdistcens(d1,rightNA=3, Turnbull = FALSE)

# (4) Plot of the CDF of the same dataset after logarithmic transformation
#   with a lognormal distribution, successively using the two proposed methods
#
d3<-data.frame(left=10^(d1$left),right=10^(d1$right))
plotdistcens(d3,"lnorm",para=list(meanlog=0.27,sdlog=3.3))
plotdistcens(d3,"lnorm",para=list(meanlog=0.27,sdlog=3.3),Turnbull = FALSE, leftNA=0)