A Case Study Using the Beta-Danish Distribution

Introduction

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

library(BetaDanish)
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)
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  0.686576   0.795132 -0.871883  2.245035  0.8635 0.387877   
#> b  4.078205   1.478893  1.179575  6.976834  2.7576 0.005823 **
#> c  2.196505   2.576019 -2.852492  7.245502  0.8527 0.393840   
#> k  0.082973   0.076769 -0.067495  0.233441  1.0808 0.279782   
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> ---
#> Log-Likelihood: -409.9137 
#> AIC: 827.8274  | BIC: 839.2356

Three-parameter submodel

fit_sub <- fit_betadanish(Surv(time, status) ~ 1, data = remission, submodel = TRUE, n_starts = 1)
compare_models(fit, fit_sub)
#> 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) -409.9137 0.08081129  1   0.776201

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.