arXiv subjects

Francisco Javier Rubio

Publications and source records attributed to Francisco Javier Rubio.

5 recordsLinked to original sources

arXiv2026

Bayesian variable and hazard structure selection in the General Hazard model

The proportional hazards (PH) and accelerated failure time (AFT) models are the most widely used hazard structures for analysing time-to-event data. When the goal is to identify variables associated with event times, variable selection is typically performed within a single hazard structure, imposing strong assumptions on how covariates affect the hazard function. To allow simultaneous selection of relevant variables and the hazard structure itself, we develop a Bayesian variable selection approach within the general hazard (GH) model, which includes the PH, AFT, and other structures as special cases. We propose two types of g-priors for the regression coefficients that enable tractable computation and show that both lead to consistent model selection. We also introduce a hierarchical prior on the model space that accounts for multiplicity and penalises model complexity. To efficiently explore the GH model space, we extend the Add-Delete-Swap algorithm to jointly sample variable inclusion indicators and hazard structures. Simulation studies show accurate recovery of both the true hazard structure and active variables across different sample sizes and censoring levels. Two real-data applications are presented to illustrate the use of the proposed methodology and to compare it with existing variable selection methods.

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arXiv2023

Extended Excess Hazard Models for Spatially Dependent Survival Data

Relative survival represents the preferred framework for the analysis of population cancer survival data. The aim is to model the survival probability associated to cancer in the absence of information about the cause of death. Recent data linkage developments have allowed for incorporating the place of residence into the population cancer data bases; however, modeling this spatial information has received little attention in the relative survival setting. We propose a flexible parametric class of spatial excess hazard models (along with inference tools), named "Relative Survival Spatial General Hazard" (RS-SGH), that allows for the inclusion of fixed and spatial effects in both time-level and hazard-level components. We illustrate the performance of the proposed model using an extensive simulation study, and provide guidelines about the interplay of sample size, censoring, and model misspecification. We present a case study using real data from colon cancer patients in England. This case study illustrates how a spatial model can be used to identify geographical areas with low cancer survival, as well as how to summarize such a model through marginal survival quantities and spatial effects.

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arXiv2021

Additive Bayesian variable selection under censoring and misspecification

We discuss the role of misspecification and censoring on Bayesian model selection in the contexts of right-censored survival and concave log-likelihood regression. Misspecification includes wrongly assuming the censoring mechanism to be non-informative. Emphasis is placed on additive accelerated failure time, Cox proportional hazards and probit models. We offer a theoretical treatment that includes local and non-local priors, and a general non-linear effect decomposition to improve power-sparsity trade-offs. We discuss a fundamental question: what solution can one hope to obtain when (inevitably) models are misspecified, and how to interpret it? Asymptotically, covariates that do not have predictive power for neither the outcome nor (for survival data) censoring times, in the sense of reducing a likelihood-associated loss, are discarded. Misspecification and censoring have an asymptotically negligible effect on false positives, but their impact on power is exponential. We show that it can be advantageous to consider simple models that are computationally practical yet attain good power to detect potentially complex effects, including the use of finite-dimensional basis to detect truly non-parametric effects. We also discuss algorithms to capitalize on sufficient statistics and fast likelihood approximations for Gaussian-based survival and binary models.

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arXiv2021

A tractable Bayesian joint model for longitudinal and survival data

We introduce a numerically tractable formulation of Bayesian joint models for longitudinal and survival data. The longitudinal process is modelled using generalised linear mixed models, while the survival process is modelled using a parametric general hazard structure. The two processes are linked by sharing fixed and random effects, separating the effects that play a role at the time scale from those that affect the hazard scale. This strategy allows for the inclusion of non-linear and time-dependent effects while avoiding the need for numerical integration, which facilitates the implementation of the proposed joint model. We explore the use of flexible parametric distributions for modelling the baseline hazard function which can capture the basic shapes of interest in practice. We discuss prior elicitation based on the interpretation of the parameters. We present an extensive simulation study, where we analyse the inferential properties of the proposed models, and illustrate the trade-off between flexibility, sample size, and censoring. We also apply our proposal to two real data applications in order to demonstrate the adaptability of our formulation both in univariate time-to-event data and in a competing risks framework. The methodology is implemented in rstan.

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arXiv2017

Natural (non-)informative priors for skew-symmetric distributions

In this paper, we present an innovative method for constructing proper priors for the skewness (shape) parameter in the skew-symmetric family of distributions. The proposed method is based on assigning a prior distribution on the perturbation effect of the shape parameter, which is quantified in terms of the Total Variation distance. We discuss strategies to translate prior beliefs about the asymmetry of the data into an informative prior distribution of this class. We show via a Monte Carlo simulation study that our noninformative priors induce posterior distributions with good frequentist properties, similar to those of the Jeffreys prior. Our informative priors yield better results than their competitors from the literature. We also propose a scale- and location-invariant prior structure for models with unknown location and scale parameters and provide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrative examples are presented using simulated and real data.

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