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A CURE RATE FRAILTY REGRESSION MODEL BASED ON THE BIRNBAUM-SAUNDERS DISTRIBUTION
Cure rate models have been widely studied to analyze time-to-event data with a cured fraction of patients. We incorporate frailty into a cure rate model as an alternative approach to the description of such data based on the Birnbaum-Saunders distribution. This distribution has theoretical arguments to model medical data and has shown empirically to be an option to analyze this kind
of data. An important advantage of the proposed model is the possibility to jointly consider the heterogeneity among patients by their frailties and the presence of a cured fraction of them. In addition, the number of competing causes is modeled by the negative binomial distribution, which absorbs several particular cases. We consider likelihood-based methods to estimate the model parameters and to derive influence diagnostics for this model. We assess local influence on the parameter estimates under different perturbation schemes. Diagnostic tools are important in all statistical modeling, which is another novel aspect of the paper when deriving it in frailty-based cure rate models. Numerical evaluation of the proposed model is performed by Monte Carlo simulations and by an illustration with melanoma medical data, which shows its potential applications.
Censored data; Cure rate models; Frailty models; Likelihood methods; Local influence; Medical data; Monte Carlo simulation; Negative binomial distribution.
Análise de Sobrevivência
Jeremias Leao, Helton Saulo, Victor Leiva, Vera Tomazella