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A Case Study Using the Beta-Danish Distribution

Introduction

This vignette demonstrates a typical survival analysis workflow using the BetaDanish package.

library(BetaDanish)
#> BetaDanish 0.1.0: see ?BetaDanish for help.
library(survival)
#> Warning: package 'survival' was built under R version 4.5.3
#> 
#> Attaching package: 'survival'
#> The following objects are masked from 'package:BetaDanish':
#> 
#>     leukemia, transplant
data('remission', package = 'BetaDanish')
head(remission)
#>   time status
#> 1 0.08      1
#> 2 2.09      1
#> 3 3.48      1
#> 4 4.87      1
#> 5 6.94      1
#> 6 8.66      1

Fitting the Beta-Danish model

fit <- fit_betadanish(Surv(time, status) ~ 1, data = remission, n_starts = 1)
#> Warning in dbetadanish(time, a_par, b_par, c_par, k_par, log = TRUE):
#> Parameters a, b, c, and k must be strictly positive.
summary(fit)
#> 
#> Call:
#> fit_betadanish(formula = Surv(time, status) ~ 1, data = remission, 
#>     n_starts = 1)
#> 
#> Beta-Danish Distribution Fit
#> Model: Full 4-Parameter Model 
#> 
#>      Estimate  Std. Error   Lower 95%   Upper 95% z value Pr(>|z|)  
#> a  189.106079  173.021934 -150.016912  528.229071  1.0930  0.27441  
#> b    4.672827    2.251973    0.258961    9.086693  2.0750  0.03799 *
#> c    0.013018    0.012241   -0.010974    0.037011  1.0635  0.28755  
#> k    0.033940    0.031263   -0.027335    0.095214  1.0856  0.27765  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> ---
#> Log-Likelihood: -410.5329 
#> AIC: 829.0658  | BIC: 840.4739

Three-parameter submodel

fit_sub <- fit_betadanish(Surv(time, status) ~ 1, data = remission, submodel = TRUE, n_starts = 1)
compare_models(fit, fit_sub)
#> Warning in compare_models(fit, fit_sub): Full model log-likelihood is lower
#> than submodel. Check convergence.
#> Likelihood Ratio Test (a = 1 vs a != 1)
#> 
#>                  Model    LogLik Chisq Df Pr(>Chisq)
#> 1   Submodel (3-param) -409.9541    NA NA         NA
#> 2 Full Model (4-param) -410.5329     0  1          1

Diagnostic plots

plot(fit, type = 'survival')

plot(fit, type = 'hazard')

Interpretation

The fitted model can be used to estimate survival probabilities, hazard behavior, and overall model fit. Users should compare the Beta-Danish model with alternative lifetime distributions and inspect diagnostic plots before drawing final conclusions.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.