Package 'GofCens' reference manual

Title:	Goodness-of-Fit Methods for Complete and Right-Censored Data
Description:	Graphical tools and goodness-of-fit tests for complete and right-censored data: 1. Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling tests, which use the empirical distribution function for complete data and are extended for right-censored data. 2. Generalized chi-squared-type test, which is based on the squared differences between observed and expected counts using random cells with right-censored data. 3. A series of graphical tools such as probability or cumulative hazard plots to guide the decision about the most suitable parametric model for the data.
Authors:	Klaus Langohr [aut, cre], Mireia Besalú [aut], Matilde Francisco [aut], Arnau Garcia [aut], Guadalupe Gómez [aut]
Maintainer:	Klaus Langohr <[email protected]>
License:	GPL (>= 2)
Version:	1.2
Built:	2024-10-26 03:33:55 UTC
Source:	CRAN

Goodness-of-Fit Methods for Complete and Right-Censored Data.

Description

This package implements both graphical tools and goodness-of-fit tests for complete and right-censored data. It has implemented:

Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling tests, which use the empirical distribution function for complete data and are extended for right-censored data.
Generalized chi-squared-type test, which is based on the squared differences between observed and expected counts using random cells with right-censored data.
A series of graphical tools such as probability or cumulative hazard plots to guide the decision about the most suitable parametric model for the data.

Details

The GofCens package can be used to check the goodness of fit of the following 8 distributions. The list shows the parametrizations of the survival functions.

Exponential Distribution [Exp $(\beta)$ ]

$S(t)=e^{-\frac{t}{\beta}}$
Weibull Distribution [Wei( $\alpha,\,\beta$ )]

$S(t)=e^{-(\frac{t}{\beta})^\alpha}$
Gumbel Distribution [Gum( $\mu,\,\beta$ )]

$S(t)=1 - e^{-e^{-\frac{t-\mu}{\beta}}}$
Log-Logistic Distribution [LLogis( $\alpha, \beta$ )]

$S(t)=\frac{1}{1 + \left(\frac{t}{\beta}\right)^\alpha}$
Logistic Distribution [Logis( $\mu,\beta$ )]

$S(t)=\frac{e^{-\frac{t -\mu}{\beta}}}{1 + e^{-\frac{t - \mu}{\beta}}}$
Log-Normal Distribution [LN( $\mu,\beta$ )]

$S(t)=\int_{\frac{\log t - \mu}{\beta}}^\infty \!\frac{1}{\sqrt{2 \pi}}$
Normal Distribution [N( $\mu,\beta$ )]

$S(t)=\int_t^\infty \! \frac{1}{\beta\sqrt{2\pi}}e^{-\frac{(x - \mu)^2}{2 \beta^2}} dx$
4-Param. Beta Distribution [Beta( $\alpha, \gamma, a, b$ )]

$S(t)=1 - \frac{B_{(\alpha, \gamma, a, b)}(t)}{B(\alpha, \gamma)}$

The list of the parameters of the theoretical distribution can be set manually using the argument params of each function. In that case, the correspondence is: $\alpha$ is the shape value, $\gamma$ is the shape2 value, $\mu$ is the location value and $\beta$ is the scale value.

Package:	GofCens
Type:	Package
Version:	1.2
Date:	2024-10-25
License:	GPL (>= 2)

Author(s)

Klaus Langohr, Mireia Besalú, Matilde Francisco, Arnau Garcia, Guadalupe Gómez

Maintainer: Klaus Langohr <[email protected]>

Anderson-Darling test for complete and right-censored data

Description

Function ADcens computes the Anderson-Darling test statistic and p-value for complete and right-censored data against eight possible distributions using bootstrapping.

Usage

## Default S3 method:
ADcens(times, cens = rep(1, length(times)),
       distr = c("exponential", "gumbel", "weibull", "normal",
                 "lognormal", "logistic", "loglogistic", "beta"),
       betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
       params0 = list(shape = NULL, shape2 = NULL,
                      location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
ADcens(formula, data, ...)
## Default S3 method:
ADcens(times, cens = rep(1, length(times)),
       distr = c("exponential", "gumbel", "weibull", "normal",
                 "lognormal", "logistic", "loglogistic", "beta"),
       betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
       params0 = list(shape = NULL, shape2 = NULL,
                      location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
ADcens(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.
`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.
`tol`	Precision of survival times.
`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

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

To avoid long computation times due to bootstrapping, an alternative with complete data is the function ad.test of the goftest package.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

Value

ADcens returns an object of class "ADcens".

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

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the Anderson-Darling statistic (`AD`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

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, A. Garcia, G. Gómez.

References

G. Marsaglia and J. Marsaglia. Evaluating the Aderson-Darling Distrinution. In: Journal os Statistical Software, Articles, 9 (2) (2004), 1-5.

Examples

# Complete data
set.seed(123)
ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
       BS = 199)
print(ADcens(times = rweibull(100, 12, scale = 4), distr = "exponential",
       BS = 199), outp = "table", print.BIC = FALSE, print.infoBoot = TRUE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
ADcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)
# Complete data
set.seed(123)
ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
       BS = 199)
print(ADcens(times = rweibull(100, 12, scale = 4), distr = "exponential",
       BS = 199), outp = "table", print.BIC = FALSE, print.infoBoot = TRUE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
ADcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)

General chi-squared statistics for right-censored data.

Description

Function chisqcens computes the general chi-squared test statistic for right-censored data introduced by Kim (1993) and the respective p-value using bootstrapping.

Usage

## Default S3 method:
chisqcens(times, cens = rep(1, length(times)), M,
          distr = c("exponential", "gumbel", "weibull", "normal",
                    "lognormal", "logistic", "loglogistic", "beta"),
          betaLimits=c(0, 1), igumb = c(10, 10), BS = 999,
          params0 = list(shape = NULL, shape2 = NULL,
                         location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
chisqcens(formula, data,...)
## Default S3 method:
chisqcens(times, cens = rep(1, length(times)), M,
          distr = c("exponential", "gumbel", "weibull", "normal",
                    "lognormal", "logistic", "loglogistic", "beta"),
          betaLimits=c(0, 1), igumb = c(10, 10), BS = 999,
          params0 = list(shape = NULL, shape2 = NULL,
                         location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
chisqcens(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.
`M`	Number indicating the number of cells that will be considered.
`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.
`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.
`tol`	Precision of survival times.
`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

The function implements the test introduced by Kim (1993) and returns the value of the test statistic.

The cell boundaries of the test are obtained via the quantiles, which are based on the Kaplan-Meier estimate of the distribution function. In the presence of right-censored data, it is possible that not all quantiles are estimated, and in this case, the value of M provided by the user is reduced.

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

Value

chisqcens returns an object of class "chisqcens".

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

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the test statistic (`Statistic`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`CellNumber`	Vector with two values: the original cell number introduced by the user and the final cell number used.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

Author(s)

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

References

J. H. Kim. Chi-Square Goodness-of-Fit Tests for Randomly Censored Data. In: The Annals of Statistics, 21 (3) (1993), 1621-1639.

Examples

# Complete data
set.seed(123)
chisqcens(times = rgumbel(100, 12, scale = 4), M = 8, distr = "gumbel",
          BS = 99)
print(chisqcens(times = rlogis(100, 20, scale = 3), M = 8, distr = "loglogistic",
          BS = 105), print.AIC = FALSE, print.infoBoot = TRUE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
chisqcens(Surv(time, status) ~ 1, colonsamp, M = 6, distr = "normal")

## End(Not run)
# Complete data
set.seed(123)
chisqcens(times = rgumbel(100, 12, scale = 4), M = 8, distr = "gumbel",
          BS = 99)
print(chisqcens(times = rlogis(100, 20, scale = 3), M = 8, distr = "loglogistic",
          BS = 105), print.AIC = FALSE, print.infoBoot = TRUE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
chisqcens(Surv(time, status) ~ 1, colonsamp, M = 6, distr = "normal")

## End(Not run)

Cumulative hazard plots to check the goodness of fit of parametric models

Description

Function cumhazPlot uses the cumulative hazard plot to check if a certain distribution is an appropiate choice for the data.

Usage

## Default S3 method:
cumhazPlot(times, cens = rep(1, length(times)), distr = "all6", colour = 1,
           betaLimits = c(0, 1), igumb = c(10, 10), ggp = FALSE, m = NULL,
           prnt = TRUE, degs = 3, print.AIC = TRUE, print.BIC = TRUE,...)
## S3 method for class 'formula'
cumhazPlot(formula, data, ...)
## Default S3 method:
cumhazPlot(times, cens = rep(1, length(times)), distr = "all6", colour = 1,
           betaLimits = c(0, 1), igumb = c(10, 10), ggp = FALSE, m = NULL,
           prnt = TRUE, degs = 3, print.AIC = TRUE, print.BIC = TRUE,...)
## S3 method for class 'formula'
cumhazPlot(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 names of the distributions 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. By default, `distr` is set to `"all6"`, which means that the cumulative hazard plots are drawn for the Weibull, loglogistic, lognormal, Gumbel, logistic, and normal distributions.
`colour`	Colour of the points. Default colour: black.
`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.
`ggp`	Logical to use or not the ggplot2 package to draw the plots. Default is `FALSE`.
`m`	Optional layout for the plots to be displayed.
`prnt`	Logical to indicate if the maximum likelihood estimates of the parameters of all distributions considered should be printed. Default is `TRUE`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`formula`	A formula with a numeric vector as response (which assumes no censoring) or `Surv` object.
`data`	Data frame for variables in `formula`.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`...`	Optional arguments for function `par`, if `ggplo = FALSE`.

Details

The cumulative hazard plot is based on transforming the cumulative hazard function $\Lambda$ in such a way that it becomes linear in $t$ or $\log(t)$ . This transformation is specific for each distribution. The function uses the data to compute the Nelson-Aalen estimator of the cumulative hazard function, $\widehat{\Lambda}$ , and the maximum likelihood estimators of the parameters of the theoretical distribution under study. If the distribution fits the data, the plot is expected to be a straight line.

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

Value

If prnt = TRUE, the following output is returned:

`Distribution`	Distribution under study.
`Estimates`	A list with the maximum likelihood estimates of the parameters of all distributions considered.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).

In addition, a list with the same contents is returned invisibly.

Author(s)

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

Examples

# Complete data and default distributions
set.seed(123)
x <- rlogis(1000, 50, 5)
cumhazPlot(x, lwd = 2)

# Censored data comparing three distributions
data(nba)
cumhazPlot(Surv(survtime, cens) ~ 1, nba, distr = c("expo", "normal", "gumbel"))
# Complete data and default distributions
set.seed(123)
x <- rlogis(1000, 50, 5)
cumhazPlot(x, lwd = 2)

# Censored data comparing three distributions
data(nba)
cumhazPlot(Surv(survtime, cens) ~ 1, nba, distr = c("expo", "normal", "gumbel"))

Cramér-von Mises test for complete and right-censored data

Description

Function CvMcens computes the Cramér-von Mises statistic and p-value for complete and right-censored data against eight possible distributions.

Usage

## Default S3 method:
CvMcens(times, cens = rep(1, length(times)),
        distr = c("exponential", "gumbel", "weibull", "normal",
                  "lognormal", "logistic", "loglogistic", "beta"),
        betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
        params0 = list(shape = NULL, shape2 = NULL,
                       location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
CvMcens(formula, data,...)
## Default S3 method:
CvMcens(times, cens = rep(1, length(times)),
        distr = c("exponential", "gumbel", "weibull", "normal",
                  "lognormal", "logistic", "loglogistic", "beta"),
        betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
        params0 = list(shape = NULL, shape2 = NULL,
                       location = NULL, scale = NULL), tol = 1e-04, ...)
## S3 method for class 'formula'
CvMcens(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.
`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.
`tol`	Precision of survival times.
`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

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.

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

To avoid long computation times due to bootstrapping, an alternative with complete data is the function cvm.test of the goftest package.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

Value

CvMcens returns an object of class "CvMcens".

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

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the Cramér-von Mises statistic (`CvM`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

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, A. Garcia, G. Gómez.

References

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.

Examples

# Complete data
set.seed(123)
CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 199)
print(CvMcens(times = rweibull(100, 12, scale = 4), distr = "normal",
        BS = 99), degs = 4, print.AIC = FALSE, print.BIC = FALSE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
CvMcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)
# Complete data
set.seed(123)
CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 199)
print(CvMcens(times = rweibull(100, 12, scale = 4), distr = "normal",
        BS = 99), degs = 4, print.AIC = FALSE, print.BIC = FALSE)

## Not run: 
# Censored data
set.seed(123)
colonsamp <- colon[sample(nrow(colon), 300), ]
CvMcens(Surv(time, status) ~ 1, colonsamp, distr = "normal")

## End(Not run)

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 using bootstrapping.

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), BS = 999,
        params0 = list(shape = NULL, shape2 = NULL, location = NULL,
                       scale = NULL),
        tol = 1e-04, ...)
## S3 method for class 'formula'
gofcens(formula, data,...)
## 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), BS = 999,
        params0 = list(shape = NULL, shape2 = NULL, location = NULL,
                       scale = NULL),
        tol = 1e-04, ...)
## 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.
`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.
`tol`	Precision of survival times.
`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

All p-values are calculated via bootstrapping methods. For the three hypothesis tests, the same data generated with the bootstrapping method are used.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

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.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the values of the Kolmogovor-Smirnov (`KS`), Cramér-von Mises (`CvM`), and Anderson-Darling (`AD`) test statistics and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

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, A. Garcia, G. Gómez.

References

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.

Examples

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

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

## End(Not run)
## Not run: 
# Complete data
set.seed(123)
gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 499)
print(gofcens(times = rweibull(100, 12, scale = 4), distr = "exponential"),
              outp = "table", print.infoBoot = TRUE)

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

## End(Not run)

Plot of the Kaplen-Meier and parametric estimations

Description

Function kmPlot is a function that generates a plot that combines a Kaplan-Meier survival curve and a parametric survival curve in the same graph. It is useful for comparing non-parametric survival estimates with the fitted parametric survival model.

Usage

## Default S3 method:
kmPlot(times, cens = rep(1, length(times)), distr = "all6",
       colour = c("black", "blue", "cornflowerblue"),
       betaLimits = c(0, 1), igumb = c(10, 10), ggp = FALSE, m = NULL,
       prnt = TRUE, degs = 3, print.AIC = TRUE, print.BIC = TRUE,...)
## S3 method for class 'formula'
kmPlot(formula, data, ...)
## Default S3 method:
kmPlot(times, cens = rep(1, length(times)), distr = "all6",
       colour = c("black", "blue", "cornflowerblue"),
       betaLimits = c(0, 1), igumb = c(10, 10), ggp = FALSE, m = NULL,
       prnt = TRUE, degs = 3, print.AIC = TRUE, print.BIC = TRUE,...)
## S3 method for class 'formula'
kmPlot(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 Weibull (`"weibull"`), the Gumbel (`"gumbel"`), the normal (`"normal"`), the lognormal (`"lognormal"`), the logistic (`"logistic"`), the loglogistic (`"loglogistic"`), the exponential (`"exponential"`) and the beta (`"beta"`) distribution. Default is `"all6"` and includes the fisrt 6 listed which are the most used distributions.
`colour`	Vector with three components indicating the colours of the displayed plots. The first element is for the survival curve, the second for the Kaplan-Meier curve, and the last one for the confidence intervals.
`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.
`ggp`	Logical to use or not the ggplot2 package to draw the plots. Default is `FALSE`.
`m`	Optional layout for the plots to be displayed.
`prnt`	Logical to indicate if the maximum likelihood estimates of the parameters should be printed. Default is `TRUE`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`formula`	A formula with a numeric vector as response (which assumes no censoring) or `Surv` object.
`data`	Data frame for variables in `formula`.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`...`	Optional arguments for function `par`, if `ggp = FALSE`.

Details

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

Value

If prnt = TRUE, the following output is returned:

`Distribution`	Distribution under study.
`Estimates`	A list with the maximum likelihood estimates of the parameters of all distributions considered.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).

In addition, a list with the same contents is returned invisibly.

Author(s)

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

References

Peterson Jr, Arthur V. Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions. In: Journal of the American Statistical Association 72.360a (1977): 854-858.

Examples

# Plots for complete data and default distributions
set.seed(123)
x <- rexp(1000, 0.1)
kmPlot(x)

# Plots for censored data using ggplot2
kmPlot(Surv(time, status) ~ 1, colon, distr= "lognormal", ggp = TRUE)

# Plots for censored data from three distributions
data(nba)
kmPlot(Surv(survtime, cens) ~ 1, nba, distr = c("normal", "weibull", "lognormal"),
       prnt = FALSE)
# Plots for complete data and default distributions
set.seed(123)
x <- rexp(1000, 0.1)
kmPlot(x)

# Plots for censored data using ggplot2
kmPlot(Surv(time, status) ~ 1, colon, distr= "lognormal", ggp = TRUE)

# Plots for censored data from three distributions
data(nba)
kmPlot(Surv(survtime, cens) ~ 1, nba, distr = c("normal", "weibull", "lognormal"),
       prnt = FALSE)

Kolmogorov-Smirnov test for complete and right-censored data

Description

Function KScens computes the Kolmogorov-Smirnov statistic and p-value for complete and right-censored data against eight possible distributions using either bootsrapping or a modified test.

Usage

## Default S3 method:
KScens(times, cens = rep(1, length(times)),
       distr = c("exponential", "gumbel", "weibull", "normal",
                 "lognormal", "logistic", "loglogistic", "beta"),
       betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
       params0 = list(shape = NULL, shape2 = NULL, location = NULL,
                      scale = NULL),
       tol = 1e-04, boot = TRUE, ...)
## S3 method for class 'formula'
KScens(formula, data, ...)
## Default S3 method:
KScens(times, cens = rep(1, length(times)),
       distr = c("exponential", "gumbel", "weibull", "normal",
                 "lognormal", "logistic", "loglogistic", "beta"),
       betaLimits = c(0, 1), igumb = c(10, 10), BS = 999,
       params0 = list(shape = NULL, shape2 = NULL, location = NULL,
                      scale = NULL),
       tol = 1e-04, boot = TRUE, ...)
## S3 method for class 'formula'
KScens(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.
`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.
`tol`	Precision of survival times.
`formula`	A formula with a numeric vector as response (which assumes no censoring) or `Surv` object.
`data`	Data frame for variables in `formula`.
`boot`	Logical to indicate if the p-value is computed using bootstrapping or using the the modified Kolmogorov-Smirnov test (see details). Default is `TRUE`.
`...`	Additional arguments.

Details

By default the p-value is computed via bootstrapping methods.

The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

To avoid long computation times due to bootstrapping, an alternative with complete data is the function ks.test of the stats package.

The precision of the survival times is important mainly in the data generation step of the bootstrap samples.

If boot = FALSE a modified test is used to compute the p-value. Fleming et al. (1980) proposed a modified Kolmogorov-Smirnov test to use with right-censored data. This function reproduces this test for a given survival data and a theorical distribution. The approximation for the p-value is acceptable when it is smaller than 0.8 and excellent when it is smaller than 0.2. The output of the function follows the notation of Fleming et al. (1980).

In presence of ties, different authors provide slightly different definitions of $\widehat{F}_n(t)$ , with which other values of the test statistic might be obtained.

Value

KScens returns an object of class "KScens".

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

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the modified Kolmogorov-Smirnov statistic (`A`), the estimated p-value (`p-value`), the estimation of the image of the last recorded time (`F(y_m)`) and the last recorded time (`y_m`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used. If the modified test is used, a 0 is returned.

Author(s)

K. Langohr, M. Besalú, M. Francisco, A. Garcia, 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.

Examples

# Complete data with bootstrapping
set.seed(123)
KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99)

# Censored data with bootstrapping
KScens(Surv(time, status) ~ 1, colon, distr = "norm", BS = 99)

# Censored data using the modified test
KScens(Surv(time, status) ~ 1, colon, distr = "norm", boot = FALSE)

data(nba)
print(KScens(Surv(survtime, cens) ~ 1, nba, "logis", boot = FALSE), degs = 2)
KScens(Surv(survtime, cens) ~ 1, nba, "beta", betaLimits = c(0, 80),
       boot = FALSE)
# Complete data with bootstrapping
set.seed(123)
KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99)

# Censored data with bootstrapping
KScens(Surv(time, status) ~ 1, colon, distr = "norm", BS = 99)

# Censored data using the modified test
KScens(Surv(time, status) ~ 1, colon, distr = "norm", boot = FALSE)

data(nba)
print(KScens(Surv(survtime, cens) ~ 1, nba, "logis", boot = FALSE), degs = 2)
KScens(Surv(survtime, cens) ~ 1, nba, "beta", betaLimits = c(0, 80),
       boot = FALSE)

Survival times of former NBA players.

Description

Survival times of former NBA players after their NBA career.

Usage

data("nba")data("nba")

Format

A data frame with 3962 observations on the following 3 variables.

id: Player ID
survtime: Time (in years) from end of NBA career until either death or July 31, 2019.
cens: Death indicator (1, exact survival time; 0, right-censored survival time).

Details

The survival times of former NBA players were analyzed by Martínez et al. (2022).

Source

J. A. Martínez, K. Langohr, J. Felipo, L. Consuegra and M. Casals. Data set on mortality of national basketball association (NBA) players. In: Data in Brief, 45 (2022).

Examples

data(nba)
cumhazPlot(Surv(survtime, cens) ~ 1, nba)
data(nba)
cumhazPlot(Surv(survtime, cens) ~ 1, nba)

Printing method for `ADcens` object.

Description

Printing method for ADcens object.

Usage

## S3 method for class 'ADcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)
## S3 method for class 'ADcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)

Arguments

`x`	An object of class `ADcens`.
`prnt`	Logical to indicate if the estimations of the Anderson-Darling statistic and p-value should be printed. Default is `TRUE`.
`outp`	Indicator of how the output will be displayed. The possible formats are `list` and `table`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`print.infoBoot`	Logical to indicate if the number of bootstrap samples used should be printed. Default is `FALSE`
`...`	Additional arguments.

Value

If prnt = TRUE, a list or table (if outp = "table") containing the following components:

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the Anderson-Darling statistic (`AD`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

The list is also returned invisibly.

Author(s)

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

Examples

# List output
set.seed(123)
ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
       BS = 149)

# Table output
set.seed(123)
print(ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
             BS = 99), outp = "table")
# List output
set.seed(123)
ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
       BS = 149)

# Table output
set.seed(123)
print(ADcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
             BS = 99), outp = "table")

Printing method for `chisqcens` object.

Description

Printing method for chisqcens object.

Usage

## S3 method for class 'chisqcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)
## S3 method for class 'chisqcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)

Arguments

`x`	An object of class `chisqcens`.
`prnt`	Logical to indicate if the estimations of the chi-squared statistic and p-value should be printed. Default is `TRUE`.
`outp`	Indicator of how the output will be displayed. The possible formats are `list` and `table`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`print.infoBoot`	Logical to indicate if the number of bootstrap samples used should be printed. Default is `FALSE`
`...`	Additional arguments.

Value

If prnt = TRUE, a list or table (if outp = "table") containing the following components:

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the test statistic (`Statistic`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`CellNumber`	Vector with two values: the original cell number introduced by the user and the final cell number used.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

The list is also returned invisibly.

Author(s)

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

Examples

# List output
set.seed(123)
chisqcens(times = rweibull(100, 12, scale = 4), M = 8, distr = "weibull",
          BS = 149)

# Table output
set.seed(123)
print(chisqcens(times = rweibull(100, 12, scale = 4), M = 8, distr = "weibull",
                BS = 99), outp = "table")
# List output
set.seed(123)
chisqcens(times = rweibull(100, 12, scale = 4), M = 8, distr = "weibull",
          BS = 149)

# Table output
set.seed(123)
print(chisqcens(times = rweibull(100, 12, scale = 4), M = 8, distr = "weibull",
                BS = 99), outp = "table")

Printing method for `CvMcens` object.

Description

Printing method for CvMcens object.

Usage

## S3 method for class 'CvMcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)
## S3 method for class 'CvMcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)

Arguments

`x`	An object of class `CvMcens`.
`prnt`	Logical to indicate if the estimations of the Cramér-von Mises statistic and p-value should be printed. Default is `TRUE`.
`outp`	Indicator of how the output will be displayed. The possible formats are `list` and `table`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`print.infoBoot`	Logical to indicate if the number of bootstrap samples used should be printed. Default is `FALSE`
`...`	Additional arguments.

Value

If prnt = TRUE, a list or table (if outp = "table") containing the following components:

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the Cramér-von Mises statistic (`CvM`) and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

The list is also returned invisibly.

Author(s)

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

Examples

# List output
set.seed(123)
CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 149)

# Table output
set.seed(123)
print(CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
              BS = 99), outp = "table")
# List output
set.seed(123)
CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 149)

# Table output
set.seed(123)
print(CvMcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
              BS = 99), outp = "table")

Printing method for `gofcens` object.

Description

Printing method for gofcens object.

Usage

## S3 method for class 'gofcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE,  ...)
## S3 method for class 'gofcens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE,  ...)

Arguments

`x`	An object of class `gofcens`.
`prnt`	Logical to indicate if the values of the Kolmogovor-Smirnov, Cramér-von Mises, and Anderson-Darling test statistics along with the p-values should be printed. Default is `TRUE`.
`outp`	Indicator of how the output will be displayed. The possible formats are `list` and `table`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`print.infoBoot`	Logical to indicate if the number of bootstrap samples used should be printed. Default is `FALSE`
`...`	Additional arguments.

Value

If prnt = TRUE, a list or table (if outp = "table") containing the following components:

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the values of the Kolmogovor-Smirnov (`KS`), Cramér-von Mises (`CvM`), and Anderson-Darling (`AD`) test statistics and the estimated p-value (`p-value`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used.

The list is also returned invisibly.

Author(s)

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

Examples

## Not run: 
# List output
set.seed(123)
gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 149)

# Table output
set.seed(123)
print(gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
              BS = 149), outp = "table")

## End(Not run)
## Not run: 
# List output
set.seed(123)
gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
        BS = 149)

# Table output
set.seed(123)
print(gofcens(times = rweibull(100, 12, scale = 4), distr = "weibull",
              BS = 149), outp = "table")

## End(Not run)

Printing method for `KScens` object.

Description

Printing method for KScens object.

Usage

## S3 method for class 'KScens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)
## S3 method for class 'KScens'
print(x, prnt = TRUE, outp = c("list", "table"),  degs = 3, print.AIC = TRUE,
                         print.BIC = TRUE, print.infoBoot = FALSE, ...)

Arguments

`x`	An object of class `KScens`.
`prnt`	Logical to indicate if the estimations of the Kolmogorov-Smirnov statistic and p-value should be printed. Default is `TRUE`.
`outp`	Indicator of how the output will be displayed. The possible formats are `list` and `table`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`print.infoBoot`	Logical to indicate if the number of bootstrap samples used should be printed. Default is `FALSE`
`...`	Additional arguments.

Value

If prnt = TRUE, a list or table (if outp = "table") containing the following components:

`Distribution`	Null distribution.
`Hypothesis`	Parameters under the null hypothesis (if `params0` is provided).
`Test`	Vector containing the value of the modified Kolmogorov-Smirnov statistic (`A`), the estimated p-value (`p-value`), the estimation of the image of the last recorded time (`F(y_m)`) and the last recorded time (`y_m`).
`Estimates`	Vector with the maximum likelihood estimates of the parameters of the distribution under study.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).
`BS`	The number of bootstrap samples used. If the modified test is used, a 0 is returned.

The list is also returned invisibly.

Author(s)

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

Examples

# List output
set.seed(123)
KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99)

# Table output
set.seed(123)
print(KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99),
      outp = "table")
# List output
set.seed(123)
KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99)

# Table output
set.seed(123)
print(KScens(times = rweibull(100, 12, scale = 4), distr = "weibull", BS = 99),
      outp = "table")

Probability plots to check the goodness of fit of parametric models

Description

probPlot provides four types of probability plots: P-P plot, Q-Q plot, Stabilised probability plot, and Empirically Rescaled plot to check if a certain distribution is an appropiate choice for the data.

Usage

## Default S3 method:
probPlot(times, cens = rep(1, length(times)),
         distr = c("exponential", "gumbel", "weibull", "normal",
                   "lognormal", "logistic", "loglogistic", "beta"),
         plots = c("PP", "QQ", "SP", "ER"),
         colour = c("green4", "deepskyblue4", "yellow3",
                    "mediumvioletred"), mtitle = TRUE, ggp = FALSE,
         m = NULL, betaLimits = c(0, 1), igumb = c(10, 10),
         prnt = TRUE, degs = 3,
         params0 = list(shape = NULL, shape2 = NULL,
                        location = NULL, scale = NULL), print.AIC = TRUE,
                        print.BIC = TRUE, ...)
## S3 method for class 'formula'
probPlot(formula, data, ...)
## Default S3 method:
probPlot(times, cens = rep(1, length(times)),
         distr = c("exponential", "gumbel", "weibull", "normal",
                   "lognormal", "logistic", "loglogistic", "beta"),
         plots = c("PP", "QQ", "SP", "ER"),
         colour = c("green4", "deepskyblue4", "yellow3",
                    "mediumvioletred"), mtitle = TRUE, ggp = FALSE,
         m = NULL, betaLimits = c(0, 1), igumb = c(10, 10),
         prnt = TRUE, degs = 3,
         params0 = list(shape = NULL, shape2 = NULL,
                        location = NULL, scale = NULL), print.AIC = TRUE,
                        print.BIC = TRUE, ...)
## S3 method for class 'formula'
probPlot(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.
`plots`	Vector stating the plots to be displayed. Possible choices are the P-P plot (`"PP"`), the Q-Q plot (`"QQ"`), the Stabilised Probability plot (`"SP"`), and the Empirically Rescaled plot (`"ER"`). By default, all four plots are displayed.
`colour`	Vector indicating the colours of the displayed plots. The vector will be recycled if its length is smaller than the number of plots to be displayed.
`mtitle`	Logical to add or not the title "Probability plots for a `distr` distribution" to the plot. Default is `TRUE`.
`ggp`	Logical to use or not the ggplot2 package to draw the plots. Default is `FALSE`.
`m`	Optional layout for the plots to be displayed.
`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.
`prnt`	Logical to indicate if the maximum likelihood estimates of the parameters should be printed. Default is `TRUE`.
`degs`	Integer indicating the number of decimal places of the numeric results of the output.
`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`.
`print.AIC`	Logical to indicate if the AIC of the model should be printed. Default is `TRUE`
`print.BIC`	Logical to indicate if the BIC of the model should be printed. Default is `TRUE`
`...`	Optional arguments for function `par`, if `ggp = FALSE`.

Details

By default, function probPlot draws four plots: P-P plot, SP plot, Q-Q plot, and EP plot. Following, a description is given for each plot.

The Probability-Probability plot (P-P plot) depicts the empirical distribution, $\widehat{F}(t)$ , which is obtained with the Kaplan-Meier estimator if data are right-censored, versus the theoretical cumulative distribution function (cdf), $\widehat{F_0}(t)$ . If the data come from the chosen distribution, the points of the resulting graph are expected to lie on the identity line.

The Stabilised Probability plot (SP plot), proposed by Michael (1983), is a transformation of the P-P plot. It stabilises the variance of the plotted points. If $F_0 = F$ and the parameters of $F_0$ are known, $\widehat{F_0}(t)$ corresponds to the cdf of a uniform order statistic, and the arcsin transformation stabilises its variance. If the data come from distribution $F_0$ , the SP plot will resemble the identity line.

The Quartile-Quartile plot (Q-Q plot) is similar to the P-P plot, but it represents the sample quantiles versus the theoretical ones, that is, it plots $t$ versus $\widehat{F}_0^{-1}(\widehat{F}(t))$ . Hence, if $F_0$ fits the data well, the resulting plot will resemble the identity line.

A drawback of the Q-Q plot is that the plotted points are not evenly spread. Waller and Turnbull (1992) proposed the Empirically Rescaled plot (EP plot), which plots $\widehat{F}_u(t)$ against $\widehat{F}_u(\widehat{F}_0^{-1}(\widehat{F}(t)))$ , where $\widehat{F}_u(t)$ is the empirical cdf of the points corresponding to the uncensored observations. Again, if $\widehat{F}_0$ fits the data well, the ER plot will resemble the identity line.

By default, all four probability plots are drawn and the maximum likelihood estimates of the parameters of the chosen parametric model are returned. The parameter estimation is acomplished with the fitdistcens function of the fitdistrplus package.

Value

If prnt = TRUE, the following output is returned:

`Distribution`	Distribution under study.
`Parameters`	Parameters used to draw the plots (if `params0` is provided).
`Estimates`	A list with the maximum likelihood estimates of the parameters of all distributions considered.
`StdErrors`	Vector containing the estimated standard errors.
`aic`	The Akaike information criterion.
`bic`	The so-called BIC or SBC (Schwarz Bayesian criterion).

In addition, a list with the same contents is returned invisibly.

Author(s)

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

References

J. R. Michael. The Stabilized Probability Plot. In: Biometrika 70 (1) (1983), 11-17.

L.A. Waller and B.W. Turnbull. Probability Plotting with Censored Data. In: American Statistician 46 (1) (1992), 5-12.

Examples

# P-P, Q-Q, SP, and EP plots for complete data
set.seed(123)
x <- rlnorm(1000, 3, 2)
probPlot(x)
probPlot(x, distr = "lognormal")

# P-P, Q-Q, SP, and EP plots for censored data using ggplot2
probPlot(Surv(time, status) ~ 1, colon, "weibull", ggp = TRUE)

# P-P, Q-Q and SP plots for censored data and lognormal distribution
data(nba)
probPlot(Surv(survtime, cens) ~ 1, nba, "lognorm", plots = c("PP", "QQ", "SP"),
         ggp = TRUE, m = matrix(1:3, nr = 1))
# P-P, Q-Q, SP, and EP plots for complete data
set.seed(123)
x <- rlnorm(1000, 3, 2)
probPlot(x)
probPlot(x, distr = "lognormal")

# P-P, Q-Q, SP, and EP plots for censored data using ggplot2
probPlot(Surv(time, status) ~ 1, colon, "weibull", ggp = TRUE)

# P-P, Q-Q and SP plots for censored data and lognormal distribution
data(nba)
probPlot(Surv(survtime, cens) ~ 1, nba, "lognorm", plots = c("PP", "QQ", "SP"),
         ggp = TRUE, m = matrix(1:3, nr = 1))

Package 'GofCens'

Help Index

Goodness-of-Fit Methods for Complete and Right-Censored Data.

Description

Details

Author(s)

Anderson-Darling test for complete and right-censored data

Description

Usage

Arguments

Details

Value

Warning

Author(s)

References

See Also

Examples

General chi-squared statistics for right-censored data.

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Cumulative hazard plots to check the goodness of fit of parametric models

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Cramér-von Mises test for complete and right-censored data

Description

Usage

Arguments

Details

Value

Warning

Author(s)

References

See Also

Examples

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

Description

Usage

Arguments

Details

Value

Warning

Author(s)

References

See Also

Examples

Plot of the Kaplen-Meier and parametric estimations

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Kolmogorov-Smirnov test for complete and right-censored data

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Survival times of former NBA players.

Description

Usage

Format

Details

Printing method for `ADcens` object.

Printing method for `chisqcens` object.

Printing method for `CvMcens` object.

Printing method for `gofcens` object.

Printing method for `KScens` object.