arXiv subjects

Denis Rustand

Publications and source records attributed to Denis Rustand.

9 recordsLinked to original sources

arXiv2026

Informative Distance-Based Priors for Correlation Matrices Centred on a Target Reference

Specifying a prior over the space of correlation matrices is a persistent challenge in Bayesian analysis. The space is a curved manifold whose dimension grows quadratically with the number of variables, making substantive prior beliefs difficult to encode.\\ We propose a distance-based prior that assigns mass decaying exponentially in the Fisher arc-length distance from a user-specified reference correlation matrix, enabling shrinkage toward any target correlation structure rather than being confined to the identity matrix. Formally, this is constructed as a Penalised Complexity prior, but its interpretation shifts accordingly: unless the chosen target represents a structurally simpler state, the shrinkage penalises deviation rather than complexity in the usual sense. To accommodate conditional independence constraints, we introduce a parameterisation that constructs the correlation matrix via the Cholesky factor of the inverse correlation matrix with respect to a user-supplied graph, thereby reducing the number of free parameters from one per variable pair to one per graph edge. The prior is proper for every positive value of its rate parameter, accommodates correlations of either sign under any graph structure, and reduces to a fully unstructured prior when the graph is complete. A direct sampling algorithm is provided, enabling prior predictive checks and sensitivity analysis, implemented within the \texttt{graphpcor} package.

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arXiv2026

Efficient Bayesian inference for non-linear association structures in joint models: A hierarchical approach via INLA

Joint models for longitudinal and time-to-event data are increasingly used in health research to characterize the association between biomarker trajectories and the risk of clinical events. However, these models usually assume a linear relationship between the longitudinal marker and the log-hazard of the event. This assumption is rarely verified and often fails to capture complex biological mechanisms, such as U-shaped risk profiles or plateau effects. In this paper, we propose a fast and stable hierarchical framework for non-linear association structures in joint models using Integrated Nested Laplace Approximations (INLA), implemented in the INLAjoint R package. Our approach builds upon a unified framework where the scaling effect of the marker is decomposed into a parametric baseline (constant and linear components) and a data-driven smooth deviation modeled via an orthogonal basis derived from a second-order random walk. This natural hierarchy allows researchers to adapt model flexibility directly and verify the linearity assumption using standard information criteria. Through simulation studies, we demonstrate that the proposed method accurately recovers complex non-linear trajectories. We illustrate the practical utility of our framework by analyzing the joint association of the current value and current slope of body mass index (BMI) with all-cause mortality in the Health and Retirement Study. This analysis reveals a U-shaped mortality risk for the BMI value, and a non-linear effect for the rate of weight change, where a declining weight trajectory is associated with higher mortality risk.

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arXiv2025

A new approach for Bayesian joint modeling of longitudinal and cure-survival outcomes using the defective Gompertz distribution

In recent medical studies, the combination of longitudinal measurements with time-to-event data has increased the demand for more sophisticated models without unbiased estimates. Joint models for longitudinal and survival data have been developed to address such problems. One complex issue that may arise in the clinical trials is the presence of individuals who are statistically immune to the event of interest, those who may not experience the event even after extended follow-up periods. So far, the literature has addressed joint modeling with the presence of cured individuals mainly through mixture models for cure fraction and their extensions. In this study, we propose a joint modeling framework that accommodates the existence or absence of a cure fraction in an integrated way, using the defective Gompertz distribution. Our aim is to provide a more parsimonious alternative within an estimation process that involves a parameter vector with multiple components. Parameter estimation is performed using Bayesian inference via the efficient integrated nested Laplace approximation algorithm, by formulating the model as a latent Gaussian model. A simulation study is conducted to evaluate the frequentist properties of the proposed method under low-information prior settings. The model is further illustrated using a publicly available, yet underexplored, dataset on antiepileptic drug failure, where quality-of-life scores serve as longitudinal biomarkers. This application allows us to estimate the proportion of patients achieving seizure control under both traditional and modern antiepileptic therapies, demonstrating the model's ability to assess and compare long-term treatment effectiveness within a clinical trial context.

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arXiv2024

Joint Modeling of Multivariate Longitudinal and Survival Outcomes with the R package INLAjoint

This paper introduces the R package INLAjoint, designed as a toolbox for fitting a diverse range of regression models addressing both longitudinal and survival outcomes. INLAjoint relies on the computational efficiency of the integrated nested Laplace approximations methodology, an efficient alternative to Markov chain Monte Carlo for Bayesian inference, ensuring both speed and accuracy in parameter estimation and uncertainty quantification. The package facilitates the construction of complex joint models by treating individual regression models as building blocks, which can be assembled to address specific research questions. Joint models are relevant in biomedical studies where the collection of longitudinal markers alongside censored survival times is common. They have gained significant interest in recent literature, demonstrating the ability to rectify biases present in separate modeling approaches such as informative censoring by a survival event or confusion bias due to population heterogeneity. We provide a comprehensive overview of the joint modeling framework embedded in INLAjoint with illustrative examples. Through these examples, we demonstrate the practical utility of INLAjoint in handling complex data scenarios encountered in biomedical research.

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arXiv2023

A graphical framework for interpretable correlation matrix models

In this work, we present a new approach for constructing models for correlation matrices with a user-defined graphical structure. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of parameters as a function of the dimension. We suggest an automatic approach to define a prior using a natural sequence of simpler models within the Penalized Complexity framework for the unknown parameters in these models. We illustrate this approach with three applications: a multivariate linear regression of four biomarkers, a multivariate disease mapping, and a multivariate longitudinal joint modelling. Each application underscores our method's intuitive appeal, signifying a substantial advancement toward a more cohesive and enlightening model that facilitates a meaningful interpretation of correlation matrices.

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arXiv2022

Bayesian survival analysis with INLA

This tutorial shows how various Bayesian survival models can be fitted using the integrated nested Laplace approximation in a clear, legible, and comprehensible manner using the INLA and INLAjoint R-packages. Such models include accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data, originally presented in the article "Bayesian survival analysis with BUGS" (Alvares et al., 2021). In addition, we illustrate the implementation of a new joint model for a longitudinal semicontinuous marker, recurrent events, and a terminal event. Our proposal aims to provide the reader with syntax examples for implementing survival models using a fast and accurate approximate Bayesian inferential approach.

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arXiv2022

A new avenue for Bayesian inference with INLA

Integrated Nested Laplace Approximations (INLA) has been a successful approximate Bayesian inference framework since its proposal by Rue et al. (2009). The increased computational efficiency and accuracy when compared with sampling-based methods for Bayesian inference like MCMC methods, are some contributors to its success. Ongoing research in the INLA methodology and implementation thereof in the R package R-INLA, ensures continued relevance for practitioners and improved performance and applicability of INLA. The era of big data and some recent research developments, presents an opportunity to reformulate some aspects of the classic INLA formulation, to achieve even faster inference, improved numerical stability and scalability. The improvement is especially noticeable for data-rich models. We demonstrate the efficiency gains with various examples of data-rich models, like Cox's proportional hazards model, an item-response theory model, a spatial model including prediction, and a 3-dimensional model for fMRI data.

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arXiv2022

Fast and flexible inference for joint models of multivariate longitudinal and survival data using Integrated Nested Laplace Approximations

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the Integrated Nested Laplace Approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared to alternative estimation strategies. We further apply the methodology to analyze 5 longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.

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arXiv2020

Bayesian Estimation of Two-Part Joint Models for a Longitudinal Semicontinuous Biomarker and a Terminal Event with R-INLA: Interests for Cancer Clinical Trial Evaluation

Two-part joint models for a longitudinal semicontinuous biomarker and a terminal event have been recently introduced based on frequentist estimation. The biomarker distribution is decomposed into a probability of positive value and the expected value among positive values. Shared random effects can represent the association structure between the biomarker and the terminal event. The computational burden increases compared to standard joint models with a single regression model for the biomarker. In this context, the frequentist estimation implemented in the R package frailtypack can be challenging for complex models (i.e., large number of parameters and dimension of the random effects). As an alternative, we propose a Bayesian estimation of two-part joint models based on the Integrated Nested Laplace Approximation (INLA) algorithm to alleviate the computational burden and fit more complex models. Our simulation studies confirm that INLA provides accurate approximation of posterior estimates and to reduced computation time and variability of estimates compared to frailtypack in the situations considered. We contrast the Bayesian and frequentist approaches in the analysis of two randomized cancer clinical trials (GERCOR and PRIME studies), where INLA has a reduced variability for the association between the biomarker and the risk of event. Moreover, the Bayesian approach was able to characterize subgroups of patients associated with different responses to treatment in the PRIME study. Our study suggests that the Bayesian approach using INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

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