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The use of semiparametric or transformation models has been considered by many authors in the analysis of lifetime data in the presence of censoring and covariates as an alternative and generalization of the usual proportional hazards, the proportional odds models, and the accelerated failure time models, extensively used in lifetime data analysis. The inferences for the proportional hazards model introduced by Cox (1972) are usually obtained by maximum likelihood estimation methods assuming the partial likelihood function introduced by Cox (Cox, 1975). In this study, we consider a hierarchical Bayesian analysis of the proportional hazards model assuming the complete likelihood function obtained from a transformation model considering the unknown hazard function as a latent unknown variable under a Bayesian approach. Some applications with real time medical data illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

The statistical literature presents many continuous probability distributions with only one parameter, which are extensively used in the analysis of lifetime data, such as the exponential, the Lindley, and the Rayleigh distributions. Alternatively, the use of discretized versions of these distributions can provide a better fit for the data in many applications. As the novelty of this study, we present inferences for the discrete Bilal distribution (DB) with one parameter introduced by Altun et al. (2020) in the presence of right-censored data and cure fraction. We assume standard maximum likelihood methods based on asymptotic normality of the maximum likelihood estimators and also a Bayesian approach based on MCMC (Markov Chain Monte Carlo) simulation methods to get inferences for the parameters of the discrete BD distribution. The use of the proposed model was illustrated with three examples considering real medical lifetime data sets. From these applications, we concluded that the proposed model based on the discrete DB distribution has good performance even with the inclusion of a cure fraction in comparison to other existing discrete models, such as the DsFx-I, Lindley, Rayleigh, and Burr-Hatke probability distributions. Moreover, the model can be easily implemented in standard existing software, such as the R package. Under a Bayesian approach, we assumed a gamma prior distribution for the parameter of the DB discrete distribution. We also provided a brief sensitivity analysis assuming the half-normal distribution in place of the gamma distribution for the parameter of the DB distribution. From the obtained results of this study, we can conclude that the proposed methodology can be very useful for researchers dealing with medical discrete lifetime data in the presence of right-censored data and cure fraction. [ABSTRACT FROM AUTHOR]

In this paper, we introduce maximum likelihood and Bayesian parameter estimation for the exponentiated discrete Weibull (EDW) distribution in the presence of randomly right-censored data. We also consider the inclusion of a cure fraction in the model. The performance of the maximum likelihood estimation approach is assessed by conducting an extensive simulation study with different sample sizes and different values for the parameters of the EDW distribution. The uselfuness of the proposed model is illustrated with two examples considering real data sets. [ABSTRACT FROM AUTHOR]

Multivariate lifetime data are common in many applications, especially in medical and engineering studies. In this paper, we consider a trivariate Marshall-Olkin-Weibull distribution to model trivariate data in presence of right censored data. Maximum likelihood and Bayesian methods are used to get the parameter estimators of interest. An extensive simulation study was performed to verify the effectiveness of the maximum likelihood estimators. Reliability data sets related to fiber failure strengths were considered to illustrate the performance of the proposed model under the classical and Bayesian approaches. As a result, note that the trivariate Marshall-Olkin-Weibull model could be considered as a good alternative to model trivariate lifetime data, especially under a Bayesian approach which could be of interest for the reliability analysis, as observed with the real data application in industrial engineering presented in the study or any other area of interest. [ABSTRACT FROM AUTHOR]

Some computational aspects to obtain classical and Bayesian inferences for the Basu and Dhar (1995) bivariate geometric distribution in presence of censored data and covariates are discussed in this paper. The posterior summaries of interest are obtained using standard existing MCMC (Markov Chain Monte Carlo) simulation methods available in popular free softwares as the OpenBugs software and the R software. Numerical illustrations are introduced considering simulated and real datasets showing that the use of discrete bivariate distributions may be a good alternative to the use of continuous bivariate distributions, in many areas of application. [ABSTRACT FROM AUTHOR]

Simulation studies are important statistical tools used to inves-tigate the performance, properties and adequacy of statistical models. The simulation of rightcensored time-to-event data involves the generation of two independent survival distributions, where the rst distribution repre-sents the uncensored survival times and the second distribution represents the censoring mechanism. In this brief report we discuss how we can make it so that the percentage of censored data is previously de ned. The described method was used to generate data from a Weibull distribution, but it can be adapted to any other lifetime distribution. We further presented an R code function for generating random samples, considering the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we introduce bivariate lifetime models derived from copula functions considering two copula functions, the Farlie Gumbel Morgenstern (FGM) commonly used to model very weak linear dependences and the Gumbel-Barnett copula which models very weak non necessarily linear dependences. Considering the presence of cure fractions for both lifetimes, censored data and covariates, we use standard MCMC (Markov Chain Monte Carlo) methods to get a Bayesian analysis for the proposed models. This new modelling approach gives a great flexibility of fit for bivariate data, since we could assume any existing parametric marginal lifetime distribution for the bivariate lifetimes as standard Weibull, log-normal, gamma, generalized gamma, generalized Weibull or generalized F distributions. An example, considering a medical data set is introduced to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a Bayesian analysis for bivariate geometric distributions applied to lifetime data in the presence of covariates, censored data and cure fraction using Markov Chain Monte Carlo (MCMC) methods. We show that the use of a discrete bivariate geometric distribution could bring us some computational advantages when compared to standard existing bivariate exponential lifetime distributions introduced in the literature assuming continuous lifetime data as for example, the exponential Block and Basu bivariate distribution. Posterior summaries of interest are obtained using the popular OpenBUGS software. A numerical illustration is introduced considering a medical data set related to the analysis of a diabetic retinopathy data set. [ABSTRACT FROM AUTHOR]