Denis Rustand

Modèles conjoints pour un biomarqueur semi-continu et un événement terminal avec application aux essais cliniques en cancérologie: Evaluer l’efficacité des traitements dans les essais cliniques en oncologie soulève de multiples problèmes méthodologiques qui doivent être correctement traités afin de produire une estimation fiable des effets du traitement. Le but de ce projet de recherche est de proposer une nouvelle stratégie de modélisation dans le cadre de la modélisation conjointe pour étudier simultanément l’évolution de la taille tumorale (biomarqueur) et le risque de décès (évènement terminal). Un excès de zéros caractérise la distribution des mesures de taille tumorale, correspondant à des patients ayant une réponse au traitement qui se traduit par la disparition des tumeurs. Le modèle two-part a été proposé avec l’idée de décomposer la distribution du biomarqueur en une partie binaire (zéros vs. valeurs positives) et une partie continue, les deux étant généralement modélisés avec des modèles de régression à effets mixtes. Nous avons développé un modèle conjoint two-part pour lequel la partie binaire donne l’effet de covariables sur la probabilité de valeur nulle du biomarqueur tandis que la partie continue donne l’effet de covariables soit sur la valeur du biomarqueur parmi les positifs (forme conditionnelle) ou la valeur marginale du biomarqueur (forme marginale), tous deux répondant à différentes questions cliniques d’intérêt. Nous avons établi à l’aide de simulations que ce modèle fournit des estimations de paramètres non biaisées et nous l’avons comparé avec des approches alternatives telles qu’ignorer l’excès de zéro en ne décomposant pas la distribution du biomarqueur ou considérer les zéros comme des valeurs censurées (i.e., trop petites pour être mesurées). Nous montrons comment l’approche two-part est plus appropriée en présence de vrais zéros (i.e., non censurés). Ce nouveau modèle permet d’utiliser à la fois les mesures répétées de taille tumorale et les temps de survie pour comparer plusieurs lignes de traitement, ce qui pourrait impacter les décisions cliniques finales. Nous avons illustré ces développements sur la base de données réelles issues d’essais cliniques randomisés en cancérologie. Enfin, nous avons étendu l’estimation fréquentiste que nous avons implémentée dans le package R frailtypack à un cadre Bayésien avec le package R INLA afin de réduire le temps de calcul et résoudre les problèmes de convergence observés pour des structures de corrélation plus complexes. Les logiciels et codes pour l’estimation fréquentiste et Bayésienne de ce nouveau modèle sont publiquement disponibles pour s’assurer que ces outils sont facilement diffusés aux épidémiologistes, aux statisticiens ou chercheurs en sciences biomédicales. Les distributions semi-continues sont courantes dans la recherche biomédicale, par exemple lorsque l’on quantifie une exposition ou mesure les symptômes d’une maladie, notamment en génomique (microbiome, épigénétique), de sorte que le modèle proposé pourrait ouvrir un large spectre d’applications au-delà de la recherche relative au cancer.

Implement some models for correlation/covariance matrices including two approaches to model correlation matrices from a graphical structure. One use latent parent variables as proposed in Sterrantino et. al. (2024) . The other uses a graph to specify conditional relations between the variables. The graphical structure makes correlation matrices interpretable and avoids the quadratic increase of parameters as a function of the dimension. In the first approach a natural sequence of simpler models along with a complexity penalization is used. The second penalizes deviations from a base model. These can be used as prior for model parameters, considering C code through the 'cgeneric' interface for the 'INLA' package (). This allows one to use these models as building blocks combined and to other latent Gaussian models in order to build complex data models.

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.

The sum of the longest diameter (SLD) of the target lesions is a longitudinal biomarker used to assess tumor response in cancer clinical trials, which can inform about early treatment effect. This biomarker is semicontinuous, often characterized by an excess of zeros and right skewness. Conditional two‐part joint models were introduced to account for the excess of zeros in the longitudinal biomarker distribution and link it to a time‐to‐event outcome. A limitation of the conditional two‐part model is that it only provides an effect of covariates, such as treatment, on the conditional mean of positive biomarker values, and not an overall effect on the biomarker, which is often of clinical relevance. As an alternative, we propose in this article, a marginalized two‐part joint model (M‐TPJM) for the repeated measurements of the SLD and a terminal event, where the covariates affect the overall mean of the biomarker. Our simulation studies assessed the good performance of the marginalized model in terms of estimation and coverage rates. Our application of the M‐TPJM to a randomized clinical trial of advanced head and neck cancer shows that the combination of panitumumab in addition with chemotherapy increases the odds of observing a disappearance of all target lesions compared to chemotherapy alone, leading to a possible indirect effect of the combined treatment on time to death.

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 with alternative estimation strategies. We further apply the methodology to analyze five 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.

Background: Lyme borreliosis (LB) is the most widespread hard tick-borne zoonosis in the northern hemisphere. Existing studies in Europe have focused mainly on acarological risk assessment, with few investigations exploring human LB occurrence. Aim: We explored the determinants of spatial and seasonal LB variations in France from 2016 to 2021 by integrating environmental, animal, meteorological and anthropogenic factors, and then mapped seasonal LB risk predictions. Methods: We fitted 2016–19 LB national surveillance data to a two-part spatio-temporal statistical model. Spatial and temporal random effects were specified using a Besag-York-Mollie model and a seasonal model, respectively. Coefficients were estimated in a Bayesian framework using integrated nested Laplace approximation. Data from 2020–21 were used for model validation. Results: A high vegetation index (≥ 0.6) was positively associated with seasonal LB presence, while the index of deer presence (> 60%), mild soil temperature (15–22 °C), moderate air saturation deficit (1.5–5 mmHg) and higher tick bite frequency were associated with increased incidence. Prediction maps show a higher risk of LB in spring and summer (April–September), with higher incidence in parts of eastern, midwestern and south-western France. Conclusion: We present a national level spatial assessment of seasonal LB occurrence in Europe, disentangling factors associated with the presence and increased incidence of LB. Our findings yield quantitative evidence for national public health agencies to plan targeted prevention campaigns to reduce LB burden, enhance surveillance and identify further data needs. This approach can be tested in other LB endemic areas.

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., a 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 the INLA algorithm enables to fit complex joint models that might be of interest in a wide range of clinical applications.

Summary: Background: Lyme Borreliosis (LB) is the most widespread hard tick-borne zoonosis in the Northern Hemisphere and shows a seasonal pattern. Existing studies in Europe mainly focused on acarological risk assessment, with very limited investigations exploring human LB occurrence. We aimed to highlight areas and seasons of higher risk for LB occurrence in mainland France, integrating information on meteorological, environmental, animal hosts and human exposure to quantify the associated spatial and temporal risk factors. Methods: We fitted 2016–19 French LB surveillance data to a two-part spatiotemporal statistical model, defined with binomial and gamma distributions, to explore the factors associated with the presence and increased LB incidence. Shared spatial and temporal random effects were specified using a Besag-York-Mollie model and a seasonal model, respectively. Coefficients were estimated in a Bayesian framework using integrated nested Laplace approximation. Projections and data for 2020 were used for model validation. Findings: LB presence was associated with a high vegetation index (≥0·6). LB incidence increased in areas highly suitable for deer (≥80% cover per area), with mild soil temperatures (10–15°C) in the season preceding the onset, moderate air saturation deficits (3–5 mmHg), and higher proportion of tick bite reports. Prediction maps showed a higher risk of LB in spring and summer (April-September). Substantial geographical variation in LB incidence was found. Higher incidence was reported in parts of eastern, midwestern, and southwestern France. Interpretation: This is the first national-level assessment of seasonal human LB occurrence in Europe allowing to disentangle factors associated with LB presence and increased incidence. This model illustrates a spatial integrated analysis of meteorological, hosts, and anthropogenic factors for a zoonotic and vector-borne infection of major public health concern, and can be used as a reference model to be calibrated in other LB-affected areas. Funding: WF is funded by a Sorbonne University PhD fellowship, JD is supported by a grant overseen by the French National Research Agency (ANR) as part of the «Investissements d’Avenir» program (ANR-11-LABX-0002-01, Lab of Excellence ARBRE).

Summary: Joint models for a longitudinal biomarker and a terminal event have gained interests for evaluating cancer clinical trials because the tumor evolution reflects directly the state of the disease. A biomarker characterizing the tumor size evolution over time can be highly informative for assessing treatment options and could be taken into account in addition to the survival time. The biomarker often has a semicontinuous distribution, i.e., it is zero inflated and right skewed. An appropriate model is needed for the longitudinal biomarker as well as an association structure with the survival outcome. In this article, we propose a joint model for a longitudinal semicontinuous biomarker and a survival time. The semicontinuous nature of the longitudinal biomarker is specified by a two-part model, which splits its distribution into a binary outcome (first part) represented by the positive versus zero values and a continuous outcome (second part) with the positive values only. Survival times are modeled with a proportional hazards model for which we propose three association structures with the biomarker. Our simulation studies show some bias can arise in the parameter estimates when the semicontinuous nature of the biomarker is ignored, assuming the true model is a two-part model. An application to advanced metastatic colorectal cancer data from the GERCOR study is performed where our two-part model is compared to one-part joint models. Our results show that treatment arm B (FOLFOX6/FOLFIRI) is associated to higher SLD values over time and its positive association with the terminal event leads to an increased risk of death compared to treatment arm A (FOLFIRI/FOLFOX6).