Survival Regression Models With Dependent Bayesian Nonparametric Priors

Riva-Palacio, Alan; Leisen, Fabrizio; Griffin, Jim E.

doi:10.1080/01621459.2020.1864381

Cited by 4 publications

(2 citation statements)

References 67 publications

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“…In addition to the three models described in the paper, the proposed technique can be extended to other generalised linear models and survival models. Two possible extensions are the Gamma generalised linear model [ 74 ] and various Bayesian non-parametric approaches to survival analysis [ 75 ]. It is still a challenging problem to reduce the computational cost of simulating samples when a data-set contains a large number of observations.…”

Section: Discussionmentioning

confidence: 99%

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

Liang,

Livingstone,

Griffin

2023

Entropy

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Developing an efficient computational scheme for high-dimensional Bayesian variable selection in generalised linear models and survival models has always been a challenging problem due to the absence of closed-form solutions to the marginal likelihood. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) approach can be employed to jointly sample models and coefficients, but the effective design of the trans-dimensional jumps of RJMCMC can be challenging, making it hard to implement. Alternatively, the marginal likelihood can be derived conditional on latent variables using a data-augmentation scheme (e.g., Pólya-gamma data augmentation for logistic regression) or using other estimation methods. However, suitable data-augmentation schemes are not available for every generalised linear model and survival model, and estimating the marginal likelihood using a Laplace approximation or a correlated pseudo-marginal method can be computationally expensive. In this paper, three main contributions are presented. Firstly, we present an extended Point-wise implementation of Adaptive Random Neighbourhood Informed proposal (PARNI) to efficiently sample models directly from the marginal posterior distributions of generalised linear models and survival models. Secondly, in light of the recently proposed approximate Laplace approximation, we describe an efficient and accurate estimation method for marginal likelihood that involves adaptive parameters. Additionally, we describe a new method to adapt the algorithmic tuning parameters of the PARNI proposal by replacing Rao-Blackwellised estimates with the combination of a warm-start estimate and the ergodic average. We present numerous numerical results from simulated data and eight high-dimensional genetic mapping data-sets to showcase the efficiency of the novel PARNI proposal compared with the baseline add–delete–swap proposal.

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Section: Discussionmentioning

confidence: 99%

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

Liang,

Livingstone,

Griffin

2023

Entropy

Self Cite

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“…Hence, our work is an extension of [25] to some extent. However, the proposed GSFM is different from the Linear DDP model for a single group which is a generalization of the accelerated failure time model [42,43]. Furthermore, although we point out that there exists potentially dual dependence for dual stratification of treatment strata and recurrences, we just simply allow dependence in treatment strata and assume that the recurrences are independent in our methodology demonstration.…”

Section: Discussionmentioning

confidence: 99%

Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

Zhong¹,

Ma²,

Shen³

et al. 2022

Computational Statistics and Applications

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Bayesian paradigm takes advantage of well-fitting complicated survival models and feasible computing in survival analysis owing to the superiority in tackling the complex censoring scheme, compared with the frequentist paradigm. In this chapter, we aim to display the latest tendency in Bayesian computing, in the sense of automating the posterior sampling, through a Bayesian analysis of survival modeling for multivariate survival outcomes with the complicated data structure. Motivated by relaxing the strong assumption of proportionality and the restriction of a common baseline population, we propose a generalized shared frailty model which includes both parametric and nonparametric frailty random effects to incorporate both treatment-wise and temporal variation for multiple events. We develop a survival-function version of the ANOVA dependent Dirichlet process to model the dependency among the baseline survival functions. The posterior sampling is implemented by the No-U-Turn sampler in Stan, a contemporary Bayesian computing tool, automatically. The proposed model is validated by analysis of the bladder cancer recurrences data. The estimation is consistent with existing results. Our model and Bayesian inference provide evidence that the Bayesian paradigm fosters complex modeling and feasible computing in survival analysis, and Stan relaxes the posterior inference.

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A general Bayesian bootstrap for censored data based on the beta-Stacy process

Arfè

Muliere

2023

Journal of Statistical Planning and Inference

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Survival Regression Models With Dependent Bayesian Nonparametric Priors

Cited by 4 publications

References 67 publications

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

Adaptive MCMC for Bayesian Variable Selection in Generalised Linear Models and Survival Models

Dependent Dirichlet Processes for Analysis of a Generalized Shared Frailty Model

A general Bayesian bootstrap for censored data based on the beta-Stacy process

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