Exponentiated Discrete Weibull Distribution for Censored Data

Abstract

This paper further develops the statistical inference procedure of the exponentiated discrete Weibull distribution (EDW) for data with the presence of censoring. This generalization of the discrete Weibull distribution has the advantage of being suitable to model non-monotone failure rates, such as those with bathtub and unimodal distributions. Inferences about EDW distribution are presented using both frequentist and bayesian approaches. In addition, the classical Likelihood Ratio Test and a Full Bayesian Significance Test (FBST) were performed to test the parameters of EDW distribution. The method presented is applied to simulated data and illustrated with a real dataset regarding patients diagnosed with head and neck cancer.

Proportional Odds Hazard Model for Discrete Time-to-Event Data

“…In addition, for the parameters of the probability distributions (q and η), which are limited in parametric space, it is interesting to transform them to make them unrestricted. The appropriate transformations were made to the following parameters to construct the confidence intervals, as described by [13].…”

“…To estimate this hazard function informatively (i.e., smoothly), a parametric model may be appropriate. In this context, parametric models in which the response variable is discrete to inform the baseline hazard of the model efficiently become fundamental, and in recent years a large number of research articles dealing with discrete distributions arising from the discretization of distributions of continuous random variables in a survival analysis context have emerged among these are: discrete Weibull distribution (DW) in [10,11], discrete Weibull geometric in [12], exponentiated discrete Weibull (EDW) in [13], discrete Gumbel in [14], discrete Burr in [15] and discrete log-logistic in [16].…”

Discrete Bilal distribution with right-censored data

“…# Reading data (Wang et al, 2015) t <-c (3,7,11,18,22,25,28,32,34,35,35,36,40,40,41,54,66,76,84,88,92) d <-c(1,1,0,1,0,1,1,0,0,1,0,0,0,0,1,0,0,0,0,0,0) n <-length(t) # the sample size K <-2 # number of parameters # Loading the maxLik package library(maxLik) # The likelihood function log.f <-function(parms…”

“…The parametric models assume that the time-toevent variable follows a known probability distribution, such as Weibull, gamma, or the log-normal distributions. Among the discrete distributions proposed in the statistical literature to model time-to-event data, we have the discrete Weibull distribution (Nakagawa and Osaki, 1975), the discrete Lindley distribution (Gómez-Déniz and Calderín-Ojeda, 2012), the exponentiated discrete Weibull distribution (Nekoukhou and Bidram, 2015;Cardial et al, 2020;Freitas et al, 2021), the discrete generalized Let us assume the parameter transformation p = e − 1 θ , 0 < p < 1. From (2) and, following the notation of Altun et al (2020), the pmf of the discrete Bilal distribution is given by…”

Classical and Bayesian inference approaches for the exponentiated discrete Weibull model with censored data and a cure fraction

“…were S(t) = 1 − F (t) = P (T > t) is the survival function, defined in the context of survival analysis as the probability that an individual will be surviving at least until time t. The EDW distribution was studied by authors as Cardial et al(2020), and a bivariate version was proposed by El-Morshedy et al (2020). Some existing discrete distributions can be obtained as special cases of the EDW distribution (El-Morshedy et al,2020), as listed below:…”