Abstract
This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a three-parameter Burr XII distribution, which includes the popular Weibull mixture model as a special case. Classical and Bayesian procedures are used to get point estimates and confidence intervals for the unknown parameters. We consider a general survival model where the scale and shape parameters of the Burr XII distribution are dependent of some covariates. To illustrate the proposed methodology, we consider an application considering a leukaemia data set where the proposed model gives better fit for the data when compared to other existing models.
Highlights
A long-term survivor mixture model, known as standard cure rate model, assumes that the studied population is a mixture of susceptible individuals, who experience the event of interest and non-susceptible individuals that will never experience it
The paper is organized as follows: in Section 2, we introduce the likelihood function assuming the Burr XII distribution distribution for the susceptible individuals; in Section 3, we present a Bayesian analysis assuming the mixture and non-mixture models in presence or absence of covariates; in Section 4, we present an application with the leukaemia data of Kersey et al (1999) in various aspects of statistical inference, in particular, the comparison between the effects of the allogeneic and autologous treatments; in Section 5, we introduce some comments and remarks
In the analysis of lifetime data we could have the presence of a cure fraction, where a proportion of the patients will never experiment the event of interest, in many cases, death of the patient
Summary
A long-term survivor mixture model, known as standard cure rate model, assumes that the studied population is a mixture of susceptible individuals, who experience the event of interest and non-susceptible individuals that will never experience it. Shao and Zhou (2004) proposed a mixture parametric model for survival data with long-term survivors considering the Burr XII distribution. From (1.6), the survival and hazard function for the non-mixture cure rate model can be written, respectively, as:. The paper is organized as follows: in Section 2, we introduce the likelihood function assuming the Burr XII distribution distribution for the susceptible individuals; in Section 3, we present a Bayesian analysis assuming the mixture and non-mixture models in presence or absence of covariates; in Section 4, we present an application with the leukaemia data of Kersey et al (1999) in various aspects of statistical inference, in particular, the comparison between the effects of the allogeneic and autologous treatments; we introduce some comments and remarks The paper is organized as follows: in Section 2, we introduce the likelihood function assuming the Burr XII distribution distribution for the susceptible individuals; in Section 3, we present a Bayesian analysis assuming the mixture and non-mixture models in presence or absence of covariates; in Section 4, we present an application with the leukaemia data of Kersey et al (1999) in various aspects of statistical inference, in particular, the comparison between the effects of the allogeneic and autologous treatments; in Section 5, we introduce some comments and remarks
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