23º SINAPE - Simpósio Nacional de Probabilidade e Estatística

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Título

Bayesian superposition of pure-birth destructive cure processes for tumor latency

Resumo

In this paper, a new Bayesian stochastic cure rate model, based on the individual frailty as the total number of
descendent cells of each damaged cell (known as the volume of the tumor) up to speci c time and the repair mechanism (known as the destructive mechanism), is formulated as a superposition of pure-birth stochastic processes (Yule processes). The proposed model deals with combined modeling of long-term e ects (cure rate) and short-term e ects (tumor growth) which can be regarded as a Bayesian alternative to the Cox regression and promotion cure rate models when the proportional hazards assumption is violated, for example, in the case of crossing survival functions (Broet et al., 2001; Yang & Prentice, 2005; Bennett, 1983). A simulation study and an application to a clinical melanoma data, using the Bayesian RStan package, are provided to illustrate the usefulness of the proposed model and also to evaluate the impact of cancer treatment over the long-term e ect and the progression stage of the tumor (tumor growth). Besides this interesting new biological interpretation of the tumor growth, the model can be viewed as an extended Bayesian version of the destructive cure rate model of Rodrigues et al. (2010) and an alternative to the two-sample semiparametric model of Yang & Prentice (2005).

Palavras-chave

Frailty models, Cox regression models, Bayesian estimation, Stan sampler, Survival functions, Destruc-
tive random variables, Pure-birth processes, Yule process, Long-term e ects, Short-term e ffects.

Área

Análise de Sobrevivência

Autores

Josemar Rodrigues, Marco Henrique Almeida Inacio, Adriano Kimura Suzuki, Fernando Raimundo da Silva, N. Balakrishnan