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

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

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)
#> Parameter estimates
#>   
#> weibull
#>    Shape (se): 5.934 (0.136)
#>    Scale (se): 53.593 (0.302)
#>    AIC: 7287.137 
#>    BIC: 7296.952 
#> 
#> loglogistic
#>    Shape (se): 9.732 (0.258)
#>    Scale (se): 49.592 (0.277)
#>    AIC: 7258.912 
#>    BIC: 7268.728 
#> 
#> lognormal
#> Location (se): 3.892 (0.006)
#>    Scale (se): 0.197 (0.004)
#>    AIC: 7374.022 
#>    BIC: 7383.838 
#> 
#> gumbel
#> Location (se): 45.364 (0.334)
#>    Scale (se): 9.963 (0.205)
#>    AIC: 7512.212 
#>    BIC: 7522.028 
#> 
#> logistic
#> Location (se): 49.919 (0.272)
#>    Scale (se): 4.962 (0.131)
#>    AIC: 7207.713 
#>    BIC: 7217.529 
#> 
#> normal
#> Location (se): 49.899 (0.285)
#>    Scale (se): 9.002 (0.201)
#>    AIC: 7236.688 
#>    BIC: 7246.504 
#> 


# Censored data comparing three distributions
data(nba)
cumhazPlot(Surv(survtime, cens) ~ 1, nba, distr = c("expo", "normal", "gumbel"))
#> Parameter estimates
#>   
#> exponential
#>    Scale (se): 123.133 (4.189)
#>    AIC: 10047.32 
#>    BIC: 10053.6 
#> 
#> normal
#> Location (se): 53.004 (0.518)
#>    Scale (se): 16.977 (0.368)
#>    AIC: 8512.579 
#>    BIC: 8525.148 
#> 
#> gumbel
#> Location (se): 47.493 (0.626)
#>    Scale (se): 22.362 (0.489)
#>    AIC: 8773.697 
#>    BIC: 8786.266 
#>