R: Plot of empirical and theoretical distributions for censored...

plotdistcens {fitdistrplus} | R Documentation

## 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, Turnbull.confint = FALSE, ...)

### 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 bound of the interval for interval censored observations, or the observed value for non-censored observations. The `right` column contains either `NA` for right censored observations, the right bound of the interval for interval censored observations, or the observed value for non-censored observations.
`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)
`Turnbull.confint` | if TRUE confidence intervals will be added to the Turnbull plot.
`...` | 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 if `Turnbull.confint` is `TRUE`, 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.

### Author(s)

Marie-Laure Delignette-Muller and Christophe Dutang.

### References

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

Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.

### See Also

`plotdist`, `survfit.formula`.

### Examples

    # (1) Plot of an empirical censored distribution (censored data) as a CDF
    # using the default Turnbull method
    #
    data(smokedfish)
    d1 <- as.data.frame(log10(smokedfish))
    plotdistcens(d1)

    # (2) Add the CDF of a normal distribution
    #
    plotdistcens(d1,"norm",para=list(mean=-1.6,sd=1.5))

    # (3) Various plots of the same empirical distribution
    #
    # default Turnbull plot
    plotdistcens(d1,Turnbull = TRUE)
    # Turnbull plot with confidence intervals
    plotdistcens(d1,Turnbull = TRUE,Turnbull.confint = TRUE)
    # with intervals and points
    plotdistcens(d1,rightNA=3, Turnbull = FALSE)
    # with intervals and points
    # defining a minimum value for left censored values
    plotdistcens(d1,leftNA=-3, Turnbull = FALSE)

[Package fitdistrplus version 1.0-9 Index]