A Bayesian semiparametric partially PH model for clustered time‐to‐event data

Nipoti, Bernardo; Jara, Alejandro; Guindani, Michele

doi:10.1111/sjos.12332

Cited by 5 publications

(3 citation statements)

References 38 publications

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“…These approaches are reviewed by Hanson and Jara (2013). Other approaches to nonproportional hazards include Nieto-Barajas (2014) who introduces a semiparametric model based on increasing additive processes, Nipoti et al (2018) who propose a partially proportional hazards model using cluster-dependent random hazards, and Fernández et al (2016) who model the hazard as a logistic transform of a sum of Gaussian processes.…”

Section: = ∞mentioning

confidence: 99%

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Riva-Palacio

Leisen

Griffin

2021

Journal of the American Statistical Association

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We present a novel Bayesian nonparametric model for regression in survival analysis. Our model builds on the classical neutral to the right model of Doksum (1974) and on the Cox proportional hazards model of Kim and Lee (2003). The use of a vector of dependent Bayesian nonparametric priors allows us to efficiently * Fabrizio Leisen was supported by the European Community's Seventh Framework Programme [FP7/2007[FP7/ -2013 under grant agreement no: 630677. model the hazard as a function of covariates whilst allowing nonproportionality. The model can be seen as having competing latent risks. We characterize the posterior of the underlying dependent vector of completely random measures and study the asymptotic behavior of the model. We show how an MCMC scheme can provide Bayesian inference for posterior means and credible intervals. The method is illustrated using simulated and real data.

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Section: = ∞mentioning

confidence: 99%

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Riva-Palacio

Leisen

Griffin

2021

Journal of the American Statistical Association

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“…Nonparametric mixtures have been tailored to model survival data by choosing suitable kernels, such as gamma (Hanson, 2006), Weibull (Kottas, 2006) and Burr (Bohlouri Hajjar and Khazaei, 2018). Alternatively, nonparametric mixtures based on the use of mixing completely random measures have been deployed to model hazard functions (Dykstra and Laud, 1981;Nieto-Barajas and Walker, 2004), possibly accounting for the presence of covariates (see, e.g., Nieto- Barajas and Walker, 2005;Nipoti et al, 2018). Nonparametric mixtures for accelerated life models in the presence of covariates have been considered in Argiento et al (2014) and Liverani et al (2020), with the goal of producing cluster-specific posterior inference.…”

Section: Introductionmentioning

confidence: 99%

Optimal stratification of survival data via Bayesian nonparametric mixtures

Corradin¹,

Nieto‐Barajas²,

Nipoti³

2021

Preprint

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The stratified proportional hazards model represents a simple solution to account for heterogeneity within the data while keeping the multiplicative effect on the hazard function. Strata are typically defined a priori by resorting to the values taken by a categorical covariate. A general framework is proposed, which allows for the stratification of a generic accelerated life time model, including as a special case the Weibull proportional hazard model. The stratification is determined a posteriori by taking into account that strata might be characterized by different baseline survivals as well as different effects of the predictors. This is achieved by considering a Bayesian nonparametric mixture model and the posterior distribution it induces on the space of data partitions. The optimal stratification is then identified by means of the variation of information criterion and, in turn, stratum-specific inference is carried out. The performance of the proposed method and its robustness to the presence of right-censored observations are investigated by means of an extensive simulation study. A further illustration is provided by the analysis of a data set extracted from

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“…These works paved the way for another active line of research that defines priors for the hazard rates by relaxing the dependence structure between the observables, going beyond the exchangeability assumption. For example, Pennell and Dunson [45], De Iorio et al [13] and Hanson, Jara and Zhao [25] model subject specific hazards based on continuous covariates; Lijoi and Nipoti [35] and Zhou et al [53] define priors for cluster specific hazards, while Nipoti, Jara and Guindani [43] account for both individual and cluster covariates simultaneously. In this work we rather focus on priors for the hazard rates of exchangeable time-to-event data.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Bayesian models for time-to-event data

Catalano¹,

Lijoi²,

Prünster³

2020

Electron. J. Statist.

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Random measures are the key ingredient for effective nonparametric Bayesian modeling of time-to-event data. This paper focuses on priors for the hazard rate function, a popular choice being the kernel mixture with respect to a gamma random measure. Sampling schemes are usually based on approximations of the underlying random measure, both a priori and conditionally on the data. Our main goal is the quantification of approximation errors through the Wasserstein distance. Though easy to simulate, the Wasserstein distance is generally difficult to evaluate, making tractable and informative bounds essential. Here we accomplish this task on the wider class of completely random measures, yielding a measure of discrepancy between many noteworthy random measures, including the gamma, generalized gamma and beta families. By specializing these results to gamma kernel mixtures, we achieve upper and lower bounds for the Wasserstein distance between hazard rates, cumulative hazard rates and survival functions.

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A Bayesian semiparametric partially PH model for clustered time‐to‐event data

Cited by 5 publications

References 38 publications

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Survival Regression Models With Dependent Bayesian Nonparametric Priors

Optimal stratification of survival data via Bayesian nonparametric mixtures

Approximation of Bayesian models for time-to-event data

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