Abstract
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.
Highlights
In medical, engineering or other lifetime data applications, we could have more than one lifetime associated to each unit
We explore the use of a bivariate geometric distribution to analyze bivariate lifetime data
This paper is organized as follows: in section 2, we introduce the presence of censored data; in section 3, we introduce the presence of cure fraction; in section 4, we introduce an analysis of a diabetic retinopathy data set; in section 5, we present some concluding remarks
Summary
In medical, engineering or other lifetime data applications, we could have more than one lifetime associated to each unit. This is the case, for example, considering X1 and X2 the timing of failure of paired organs like kidney, lungs, eyes, ears, dental implants among many others In this situation, we could consider some existing bivariate lifetime distributions that has been introduced in the literature for continuous bivariate lifetime data (see for example, Arnold and Strauss, 1988; Marshall and Olkin, 1967; Sarkar, 1987; Block and Basu, 1974). It is important to point out, that despite discrete measuring of medical or engineering lifetime data is very common in applications, few papers related to discrete lifetime data are introduced in the literature, (see for example, Grimshaw and et al, 2005; Davarzani and Parsian, 2013) In this way, Arnold (1975) introduced a general multivariate geometric distribution which showed that it leads in a natural way to the Marshall-Olkin multivariate exponential distribution. This paper is organized as follows: in section 2, we introduce the presence of censored data; in section 3, we introduce the presence of cure fraction; in section 4, we introduce an analysis of a diabetic retinopathy data set; in section 5, we present some concluding remarks
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