gofcens {GofCens}

Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics for complete and right-censored data

Description

Function gofcens computes the Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics ans p-values for complete and right-censored data against eight possible distributions.

Usage

## Default S3 method:
gofcens(times, cens = rep(1, length(times)), 
        distr = c("exponential", "gumbel", "weibull", "normal", 
                  "lognormal", "logistic", "loglogistic", "beta"), 
        betaLimits = c(0, 1), igumb = c(10, 10), degs = 3, BS = 999, 
        params0 = list(shape = NULL, shape2 = NULL, location = NULL, 
                       scale = NULL), ...)
## S3 method for class 'formula'
gofcens(formula, data,...)

Arguments

times

Numeric vector of times until the event of interest.

cens

Status indicator (1, exact time; 0, right-censored time). If not provided, all times are assumed to be exact.

distr

A string specifying the name of the distribution to be studied. The possible distributions are the exponential ("exponential"), the Weibull ("weibull"), the Gumbel ("gumbel"), the normal ("normal"), the lognormal ("lognormal"), the logistic ("logistic"), the loglogistic ("loglogistic"), and the beta ("beta") distribution.

betaLimits

Two-components vector with the lower and upper bounds of the Beta distribution. This argument is only required, if the beta distribution is considered.

igumb

Two-components vector with the initial values for the estimation of the Gumbel distribution parameters.

degs

Integer indicating the number of decimal places of the numeric results of the output.

BS

Number of bootstrap samples.

params0

List specifying the parameters of the theoretical distribution. By default, parameters are set to NULL and estimated with the maximum likelihood method. This argument is only considered, if all parameters of the studied distribution are specified.

formula

A formula with a numeric vector as response (which assumes no censoring) or Surv object.

data

Data frame for variables in formula.

...

Additional arguments.

Details

Fleming et al. (1980) proposed a modified Kolmogorov-Smirnov test to be used with right-censored data. Koziol and Green (1976) proposed a Cramér-von Mises statistic for randomly censored data. This function reproduces this test for a given survival data and a theorical distribution. In presence of ties, different authors provide slightly different definitions of the product-limit estimator, what might provide different values of the test statistic.

When dealing with complete data, we recommend the use of functions ks.test of the stats package and cvm.test and ad.test of the goftest package.

Value

gofcens returns an object of class "gofcens".

An object of class "gofcens" is a list containing the following components:

Distribution

Null distribution.

Null hypothesis

Parameters under the null hypothesis (if params0 is provided).

Tests statistics

Values of the Kolmogovor-Smirnov, Cramér-von Mises, and Anderson-Darling test statistics.

p-value

P-values associated with each test.

Parameters

List with the maximum likelihood estimates of the parameters of the distribution under study.

Warning

If the amount of data is large, the execution time of the function can be elevated. The parameter BS can limit the number of random censored samples generated and reduce the execution time.

Author(s)

K. Langohr, M. Besalú, M. Francisco, G. Gómez.

References

T. R. Fleming et al. Modified Kolmogorov-Smirnov test procedure with application to arbitrarily right-censored data. In: Biometrics 36 (1980), 607-625.

J. A. Koziol and S. B. Green. A Cramér-von Mises statistic for randomly censored data. In: Biometrika, 63 (3) (1976), 465-474.

A. N. Pettitt and M. A. Stephens. Modified Cramér-von Mises statistics for censored data. In: Biometrika, 63 (2) (1976), 291-298.

See Also

ks.test (Package stats), cvm.test (Package goftest), and ad.test (Package goftest) for complete data, and KScens for the Kolmogorov-Smirnov test for right-censored data, which returns the p-value.

Examples

## Not run: 
# Complete data
set.seed(123)
gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 499)

# Censored data
data(colon)
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
gofcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)