4.6 Article

SURVIVAL ANALYSIS VIA HIERARCHICALLY DEPENDENT MIXTURE HAZARDS

期刊

ANNALS OF STATISTICS
卷 49, 期 2, 页码 863-884

出版社

INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/20-AOS1982

关键词

Bayesian Nonparametrics; completely random measures; generalized gamma processes; hazard rate mixtures; hierarchical processes; meta-analysis; partial exchangeability

资金

  1. European Research Council (ERC) [817257]
  2. Italian Ministry of Education, University and Research (MIUR)
  3. MIUR, PRIN Project [2015SNS29B]
  4. European Research Council (ERC) [817257] Funding Source: European Research Council (ERC)

向作者/读者索取更多资源

The article introduces a novel hierarchical nonparametric process for defining priors on collections of probability distributions to model hazard rates and induce dependence through mixing random measures. The theoretical results allow for the development of a comprehensive Bayesian analysis for this class of models, which can also consider right-censored survival data and covariates.
Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems, one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here, we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures whose distribution acts as a prior for the vector of sample-specific baseline hazard rates. The dependence is induced through a hierarchical specification of the mixing random measures that ultimately corresponds to a composition of random discrete combinatorial structures. Our theoretical results allow to develop a full Bayesian analysis for this class of models, which can also account for right-censored survival data and covariates, and we also show posterior consistency. In particular, we emphasize that the posterior characterization we achieve is the key for devising both marginal and conditional algorithms for evaluating Bayesian inferences of interest. The effectiveness of our proposal is illustrated through some synthetic and real data examples.

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