Related papers: Gaussian Processes for Survival Analysis
In Bayesian semi-parametric analyses of time-to-event data, non-parametric process priors are adopted for the baseline hazard function or the cumulative baseline hazard function for a given finite partition of the time axis. However, it…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…
Semi-parametric survival analysis methods like the Cox Proportional Hazards (CPH) regression (Cox, 1972) are a popular approach for survival analysis. These methods involve fitting of the log-proportional hazard as a function of the…
Bayesian inference for survival regression modeling offers numerous advantages, especially for decision-making and external data borrowing, but demands the specification of the baseline hazard function, which may be a challenging task. We…
We consider Bayesian nonparametric inference in the right-censoring survival model, where modeling is made at the level of the hazard rate. We derive posterior limiting distributions for linear functionals of the hazard, and then for `many'…
A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly-used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many…
Fully Bayesian methods for Cox models specify a model for the baseline hazard function. Parametric approaches generally provide monotone estimations. Semi-parametric choices allow for more flexible patterns but they can suffer from…
In this paper, we prove almost surely consistency of a Survival Analysis model, which puts a Gaussian process, mapped to the unit interval, as a prior on the so-called hazard function. We assume our data is given by survival lifetimes $T$…
This article presents an approach to Bayesian semiparametric inference for Gaussian multivariate response regression. We are motivated by various small and medium dimensional problems from the physical and social sciences. The statistical…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…
Survival models are used to analyze time-to-event data in a variety of disciplines. Proportional hazard models provide interpretable parameter estimates, but proportional hazards assumptions are not always appropriate. Non-parametric models…
We describe a new approach to estimating relative risks in time-to-event prediction problems with censored data in a fully parametric manner. Our approach does not require making strong assumptions of constant proportional hazard of the…
We overview Bayesian estimation, hypothesis testing, and model-averaging and illustrate how they benefit parametric survival analysis. We contrast the Bayesian framework to the currently dominant frequentist approach and highlight…
The main challenges that arise when adopting Gaussian Process priors in probabilistic modeling are how to carry out exact Bayesian inference and how to account for uncertainty on model parameters when making model-based predictions on…
There is increasing interest in flexible parametric models for the analysis of time-to-event data, yet Bayesian approaches that offer incorporation of prior knowledge remain underused. A flexible Bayesian parametric model has recently been…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
We propose a deep generative approach to nonparametric estimation of conditional survival and hazard functions with right-censored data. The key idea of the proposed method is to first learn a conditional generator for the joint conditional…
Prognostic models in survival analysis are aimed at understanding the relationship between patients' covariates and the distribution of survival time. Traditionally, semi-parametric models, such as the Cox model, have been assumed. These…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
Survival Analysis (SA) constitutes the default method for time-to-event modeling due to its ability to estimate event probabilities of sparsely occurring events over time. In this work, we show how to improve the training and inference of…