arXiv subjects

Cécile Proust-Lima

Publications and source records attributed to Cécile Proust-Lima.

At least 19 recordsLinked to original sources

arXiv2026

Neural ODE enhanced linear mixed effect models for estimating complex association patterns of time-varying covariates with the marker trajectory

Longitudinal cohort studies produce repeated data that enable the assessment of time-varying association patterns between exposures and health outcomes. Classical linear mixed-effects models (LMMs) can accommodate a large variety of association patterns while accounting for the irregularly spaced, partially observed measurement. But they require the analyst to pre-specify the functional form linking the exposure history to the outcome. We propose the Neural ODE-LMM, which embeds a Neural Ordinary Differential Equation (Neural ODE) within the linear mixed-effects framework: a learned vector field encodes covariate trajectories into a continuous-time latent state that drives both the fixed- and random-effect design, while preserving the standard LMM observation model. This retains classical likelihood-based inference while learning complex, potentially cumulative, covariate effects flexibly. All parameters are estimated by maximising a penalised marginal likelihood. To quantify covariate effects, we introduce contrasts of counterfactual predictions that compare the expected outcome under alternative covariate trajectories with variance estimated via the delta method. In simulations, the model recovers both instantaneous and cumulative-burden effects without prior specification of the functional form. Applied to the Trois-Cités (3C) cohort, a population-based study of 7{,}324 participants, the method reveals trajectory-dependent associations of BMI and fasting glucose with cognitive decline.

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arXiv2025

A regularized multi-state model for covariate selection with interval-censored survival data

In population-based cohorts, disease diagnoses are typically censored by intervals as made during scheduled follow-up visits. The exact disease onset time is thus unknown, and in the presence of semi-competing risk of death, subjects may also die in between two visits before any diagnosis can be made. Illness-death models can be used to handle uncertainty about illness timing and the possible absence of diagnosis due to death. However, they are so far limited in the number of covariates. We developed a regularized estimation procedure for illness-death models with interval-censored illness diagnosis that performs variable selection in the case of high-dimensional predictors. We considered a proximal gradient hybrid algorithm maximizing the regularized likelihood with an elastic-net penalty. The algorithm simultaneously estimates the regression parameters of the three transitions under proportional transition intensities with transition-specific penalty parameters determined in an outer gridsearch. The algorithm, implemented in the R package HIDeM, shows high performances in predicting illness probability, as well as correct selection of transition-specific risk factors across different simulation scenarios. In comparison, the cause-specific competing risk model neglecting interval-censoring systematically showed worse predictive ability and tended to select irrelevant illness predictors, originally associated with death. Applied to the population-based cohort Three-City, the method identified predictors of clinical dementia onset among a large set of brain imaging, cognitive and clinical markers. Keywords: Interval censoring; Multi-state model; Semi-competing risk; Survival Analysis; Variable Selection.

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arXiv2025

Structuring, Sequencing, Staging, Selecting: the 4S method for the longitudinal analysis of multidimensional questionnaires in chronic diseases

In clinical studies, questionnaires are often used to report disease-related manifestations from clinician and/or patient perspectives. Their analysis can help identify relevant manifestations throughout the disease course, enhancing knowledge of disease progression and guiding clinicians in appropriate care provision. However, the analysis of questionnaires in health studies is not straightforward as made of repeated, ordinal, and potentially multidimensional item data. Sum-score summaries may considerably reduce information and hamper interpretation; item changes over time occur along clinical progression; and as many other longitudinal processes, observations may be truncated by events. This work establishes a comprehensive strategy in four consecutive steps to leverage repeated ordinal data from multidimensional questionnaires. The 4S method successively (1) identifies the questionnaire structure into dimensions satisfying three calibration assumptions (unidimensionality, conditional independence, increasing monotonicity), (2) describes each dimension progression using a joint latent process model which includes a continuous-time item response theory model for the longitudinal subpart, (3) aligns each dimension progression with disease stages through a projection approach, and (4) identifies the most informative items across disease stages using the Fisher information. The method is applied to multiple system atrophy (MSA), a rare neurodegenerative disease, with the analysis of daily activity and motor impairments over disease progression. The 4S method provides an effective and complete analytical strategy for questionnaires repeatedly collected in health studies.

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arXiv2025

Including an infrequently measured time-dependent error-prone covariate in survival analyses: a simulation-based comparison of methods

Epidemiologic studies often evaluate the association between an exposure and an event risk. When time-varying, exposure updates usually occur at discrete visits although changes are in continuous time and survival models require values to be constantly known. Moreover, exposures are likely measured with error, and their observation truncated at the event time. We aimed to quantify in a Cox regression the bias in the association resulting from intermittent measurements of an error-prone exposure. Using simulations under various scenarios, we compared five methods: last observation carried-forward (LOCF), classical two-stage regression-calibration using measurements up to the event (RC) or also after (PE-RC), multiple imputation (MI) and joint modeling of the exposure and the event (JM). The LOCF, and to a lesser extent the classical RC, showed substantial bias in almost all 43 scenarios. The RC bias was avoided when considering post-event information. The MI performed relatively well, as did the JM. Illustrations exploring the association of Body Mass Index and Executive Functioning with dementia risk showed consistent conclusions. Accounting for measurement error and discrete updates is critical when studying time-varying exposures. MI and JM techniques may be applied in this context, while classical RC should be avoided due to the informative truncation.

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arXiv2024

Functional principal component analysis as an alternative to mixed-effect models for describing sparse repeated measures in presence of missing data

Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address these challenges, they remain parametric models and may incur computational costs. In contrast, Functional Principal Component Analysis (FPCA) is a non-parametric approach developed for regular and dense functional data that flexibly describes temporal trajectories at a potentially lower computational cost. This paper presents an empirical simulation study evaluating the behaviour of FPCA with sparse and error-prone repeated measures and its robustness under different missing data schemes in comparison with MM. The results show that FPCA is well-suited in the presence of missing at random data caused by dropout, except in scenarios involving most frequent and systematic dropout. Like MM, FPCA fails under missing not at random mechanism. The FPCA was applied to describe the trajectories of four cognitive functions before clinical dementia and contrast them with those of matched controls in a case-control study nested in a population-based aging cohort. The average cognitive declines of future dementia cases showed a sudden divergence from those of their matched controls with a sharp acceleration 5 to 2.5 years prior to diagnosis.

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arXiv2024

Random Forests for time-fixed and time-dependent predictors: The DynForest R package

The R package DynForest implements random forests for predicting a continuous, a categorical or a (multiple causes) time-to-event outcome based on time-fixed and time-dependent predictors. The main originality of DynForest is that it handles time-dependent predictors that can be endogeneous (i.e., impacted by the outcome process), measured with error and measured at subject-specific times. At each recursive step of the tree building process, the time-dependent predictors are internally summarized into individual features on which the split can be done. This is achieved using flexible linear mixed models (thanks to the R package lcmm) which specification is pre-specified by the user. DynForest returns the mean for continuous outcome, the category with a majority vote for categorical outcome or the cumulative incidence function over time for survival outcome. DynForest also computes variable importance and minimal depth to inform on the most predictive variables or groups of variables. This paper aims to guide the user with step-by-step examples for fitting random forests using DynForest.

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arXiv2023

Patient-perceived progression in multiple system atrophy: natural history of quality of life

Health-related quality of life (Hr-QoL) scales provide crucial information on neurodegenerative disease progression, help improving patient care, and constitute a meaningful endpoint for therapeutic research. However, Hr-QoL progression is usually poorly documented, as for multiple system atrophy (MSA), a rare and rapidly progressing alpha-synucleinopathy. This work aimed to describe Hr-QoL progression during the natural course of MSA, explore disparities between patients, and identify informative items using a four-step statistical strategy.We leveraged the data of the French MSA cohort comprising annual assessments with the MSA-QoL questionnaire for more than 500 patients over up to 11 years. The four-step strategy (1) determined the subdimensions of Hr-QoL in MSA; (2) modelled the subdimension trajectories over time, accounting for the risk of death; (3) mapped the sequence of item impairments with disease stages; and (4) identified the most informative items specific to each disease stage.Among the 536 patients included, 50% were women and they were aged on average 65.1 years old at entry. Among them, 63.1% died during the follow-up. Four dimensions were identified. In addition to the original motor, nonmotor, and emotional domains, an oropharyngeal component was highlighted. While the motor and oropharyngeal domains deteriorated rapidly, the nonmotor and emotional aspects were already slightly to moderately impaired at cohort entry and deteriorated slowly over the course of the disease. Impairments were associated with sex, diagnosis subtype, and delay since symptom onset. Except for the emotional domain, each dimension was driven by key identified items.Hr-QoL is a multidimensional concept that deteriorates progressively over the course of MSA and brings essential knowledge for improving patient care. As exemplified with MSA, the thorough description of Hr-QoL using the 4-step original analysis can provide new perspectives on neurodegenerative diseases' management to ultimately deliver better support focused on the patient's perspective.

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arXiv2023

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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arXiv2023

Random survival forests with multivariate longitudinal endogenous covariates

Predicting the individual risk of a clinical event using the complete patient history is still a major challenge for personalized medicine. Among the methods developed to compute individual dynamic predictions, the joint models have the assets of using all the available information while accounting for dropout. However, they are restricted to a very small number of longitudinal predictors. Our objective was to propose an innovative alternative solution to predict an event probability using a possibly large number of longitudinal predictors. We developed DynForest, an extension of competing-risk random survival forests that handles endogenous longitudinal predictors. At each node of the tree, the time-dependent predictors are translated into time-fixed features (using mixed models) to be used as candidates for splitting the subjects into two subgroups. The individual event probability is estimated in each tree by the Aalen-Johansen estimator of the leaf in which the subject is classified according to his/her history of predictors. The final individual prediction is given by the average of the tree-specific individual event probabilities. We carried out a simulation study to demonstrate the performances of DynForest both in a small dimensional context (in comparison with joint models) and in a large dimensional context (in comparison with a regression calibration method that ignores informative dropout). We also applied DynForest to (i) predict the individual probability of dementia in the elderly according to repeated measures of cognitive, functional, vascular and neuro-degeneration markers, and (ii) quantify the importance of each type of markers for the prediction of dementia. Implemented in the R package DynForest, our methodology provides a novel and appropriate solution for the prediction of events from any number of longitudinal endogenous predictors.

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arXiv2023

Describing complex disease progression using joint latent class models for multivariate longitudinal markers and clinical endpoints

Neurodegenerative diseases are characterized by numerous markers of progression and clinical endpoints. For instance, Multiple System Atrophy (MSA), a rare neurodegenerative synucleinopathy, is characterized by various combinations of progressive autonomic failure and motor dysfunction, and a very poor prognosis. Describing the progression of such complex and multi-dimensional diseases is particularly difficult. One has to simultaneously account for the assessment of multivariate markers over time, the occurrence of clinical endpoints, and a highly suspected heterogeneity between patients. Yet, such description is crucial for understanding the natural history of the disease, staging patients diagnosed with the disease, unravelling subphenotypes, and predicting the prognosis. Through the example of MSA progression, we show how a latent class approach modeling multiple repeated markers and clinical endpoints can help describe complex disease progression and identify subphenotypes for exploring new pathological hypotheses. The proposed joint latent class model includes class-specific multivariate mixed models to handle multivariate repeated biomarkers possibly summarized into latent dimensions and class-and-cause-specific proportional hazard models to handle time-to-event data. Maximum likelihood estimation procedure, validated through simulations is available in the lcmm R package. In the French MSA cohort comprising data of 598 patients during up to 13 years, five subphenotypes of MSA were identified that differ by the sequence and shape of biomarkers degradation, and the associated risk of death. In posterior analyses, the five subphenotypes were used to explore the association between clinical progression and external imaging and fluid biomarkers, while properly accounting for the uncertainty in the subphenotypes membership.

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arXiv2023

Disease progression model anchored around clinical diagnosis in longitudinal cohorts: example of Alzheimer's disease and related dementia

Background. Alzheimer's disease and related dementia (ADRD) are characterized by multiple and progressive anatomo clinical changes. Yet, modeling changes over disease course from cohort data is challenging as the usual timescales are inappropriate and time-to-clinical diagnosis is available on small subsamples of participants with short follow-up durations prior to diagnosis. One solution to circumvent this challenge is to define the disease time as a latent variable. Methods: We developed a multivariate mixed model approach that realigns individual trajectories into the latent disease time to describe disease progression. Our methodology exploits the clinical diagnosis information as a partially observed and approximate reference to guide the estimation of the latent disease time. The model estimation was carried out in the Bayesian Framework using Stan. We applied the methodology to 2186 participants of the MEMENTO study with 5-year follow-up. Repeated measures of 12 ADRD markers stemmed from cerebrospinal fluid (CSF), brain imaging and cognitive tests were analyzed. Result: The estimated latent disease time spanned over twenty years before the clinical diagnosis. Considering the profile of a woman aged 70 with a high level of education and APOE4 carrier (the main genetic risk factor for ADRD), CSF markers of tau proteins accumulation preceded markers of brain atrophy by 5 years and cognitive decline by 10 years. We observed that individual characteristics could substantially modify the sequence and timing of these changes. Conclusion: Our disease progression model does not only realign trajectories into the most homogeneous way. It accounts for the inherent residual inter-individual variability in dementia progression to describe the long-term changes according to the years preceding clinical diagnosis, and to provide clinically meaningful information on the sequence of events.

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arXiv2022

Joint models for the longitudinal analysis of measurement scales in the presence of informative dropout

In health cohort studies, repeated measures of markers are often used to describe the natural history of a disease. Joint models allow to study their evolution by taking into account the possible informative dropout usually due to clinical events. However, joint modeling developments mostly focused on continuous Gaussian markers while, in an increasing number of studies, the actual quantity of interest is non-directly measurable; it constitutes a latent variable evaluated by a set of observed indicators from questionnaires or measurement scales. Classical examples include anxiety, fatigue, cognition. In this work,we explain how joint models can be extended to the framework of a latent quantity measured over time by indicators of different nature (e.g. continuous, binary, ordinal). The longitudinal submodel describes the evolution over time of the quantity of interest defined as a latent process in a structural mixed model, and links the latent process to each observation of the indicators through appropriate measurement models. Simultaneously, the risk of multi-cause event is modelled via a proportional cause-specific hazard model that includes a function of the mixed model elements as linear predictor to take into account the association between the latent process and the risk of event. Estimation, carried out in the maximum likelihood framework and implemented in the R-package JLPM, has been validated by simulations. The methodology is illustrated in the French cohort on Multiple-System Atrophy (MSA), a rare and fatal neurodegenerative disease, with the study of dysphagia progression over time stopped by the occurrence of death.

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arXiv2022

Individual dynamic prediction of clinical endpoint from large dimensional longitudinal biomarker history: a landmark approach

The individual data collected throughout patient follow-up constitute crucial information for assessing the risk of a clinical event, and eventually for adapting a therapeutic strategy. Joint models and landmark models have been proposed to compute individual dynamic predictions from repeated measures to one or two markers. However, they hardly extend to the case where the complete patient history includes much more repeated markers possibly. Our objective was thus to propose a solution for the dynamic prediction of a health event that may exploit repeated measures of a possibly large number of markers. We combined a landmark approach extended to endogenous markers history with machine learning methods adapted to survival data. Each marker trajectory is modeled using the information collected up to landmark time, and summary variables that best capture the individual trajectories are derived. These summaries and additional covariates are then included in different prediction methods. To handle a possibly large dimensional history, we rely on machine learning methods adapted to survival data, namely regularized regressions and random survival forests, to predict the event from the landmark time, and we show how they can be combined into a superlearner. Then, the performances are evaluated by cross-validation using estimators of Brier Score and the area under the Receiver Operating Characteristic curve adapted to censored data. We demonstrate in a simulation study the benefits of machine learning survival methods over standard survival models, especially in the case of numerous and/or nonlinear relationships between the predictors and the event. We then applied the methodology in two prediction contexts: a clinical context with the prediction of death for patients with primary biliary cholangitis, and a public health context with the prediction of death in the general elderly population at different ages. Our methodology, implemented in R, enables the prediction of an event using the entire longitudinal patient history, even when the number of repeated markers is large. Although introduced with mixed models for the repeated markers and methods for a single right censored time-to-event, our method can be used with any other appropriate modeling technique for the markers and can be easily extended to competing risks setting.

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arXiv2021

Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model

Item Response Theory (IRT) models have received growing interest in health science for analyzing latent constructs such as depression, anxiety, quality of life, or cognitive functioning from the information provided by each individual's items responses. However, in the presence of repeated item measures, IRT methods usually assume that the measurement occasions are made at the exact same time for all patients. In this paper, we show how the IRT methodology can be combined with the mixed model theory to provide a longitudinal IRT model which exploits the information of a measurement scale provided at the item level while simultaneously handling observation times that may vary across individuals and items. The latent construct is a latent process defined in continuous time that is linked to the observed item responses through a measurement model at each individual- and occasion-specific observation time; we focus here on a Graded Response Model for binary and ordinal items. The Maximum Likelihood Estimation procedure of the model is available in the R package lcmm. The proposed approach is contextualized in a clinical example in end-stage renal disease, the PREDIALA study. The objective is to study the trajectories of depressive symptomatology (as measured by 7 items of the Hospital Anxiety and Depression scale) according to the time from registration on the renal transplant waiting list and the renal replacement therapy. We also illustrate how the method can be used to assess Differential Item Functioning and lack of measurement invariance over time.

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arXiv2021

Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg

Implementations in R of classical general-purpose algorithms for local optimization generally have two major limitations which cause difficulties in applications to complex problems: too loose convergence criteria and too long calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a Newton-like method particularly robust for solving local optimization problems, we provide with marqLevAlg package an efficient and general-purpose local optimizer which (i) prevents convergence to saddle points by using a stringent convergence criterion based on the relative distance to minimum/maximum in addition to the stability of the parameters and of the objective function; and (ii) reduces the computation time in complex settings by allowing parallel calculations at each iteration. We demonstrate through a variety of cases from the literature that our implementation reliably and consistently reaches the optimum (even when other optimizers fail), and also largely reduces computational time in complex settings through the example of maximum likelihood estimation of different sophisticated statistical models.

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arXiv2021

A multistate approach for mediation analysis in the presence of semi-competing risks with application in cancer survival disparities

We propose a novel methodology to quantify the effect of stochastic interventions on non-terminal time-to-events that lie on the pathway between an exposure and a terminal time-to-event outcome. Investigating these effects is particularly important in health disparities research when we seek to quantify inequities in timely delivery of treatment and its impact on patients survival time. Current approaches fail to account for semi-competing risks arising in this setting. Under the potential outcome framework, we define and provide identifiability conditions for causal estimands for stochastic direct and indirect effects. Causal contrasts are estimated in continuous time within a multistate modeling framework and analytic formulae for the estimators of the causal contrasts are developed. We show via simulations that ignoring censoring in mediator and or outcome time-to-event processes, or ignoring competing risks may give misleading results. This work demonstrates that rigorous definition of the direct and indirect effects and joint estimation of the outcome and mediator time-to-event distributions in the presence of semi-competing risks are crucial for valid investigation of mechanisms in continuous time. We employ this novel methodology to investigate the role of delaying treatment uptake in explaining racial disparities in cancer survival in a cohort study of colon cancer patients.

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arXiv2021

Time-varying exposure history and subsequent health outcomes: a two-stage approach to identify critical windows

Long-term behavioral and health risk factors constitute a primary focus of research on the etiology of chronic diseases. Yet, identifying critical time-windows during which risk factors have the strongest impact on disease risk is challenging. To assess the trajectory of association of an exposure history with an outcome, the weighted cumulative exposure index (WCIE) has been proposed, with weights reflecting the relative importance of exposures at different times. However, WCIE is restricted to a complete observed error-free exposure whereas exposures are often measured with intermittent missingness and error. Moreover, it rarely explores exposure history that is very distant from the outcome as usually sought in life-course epidemiology. We extend the WCIE methodology to (i) exposures that are intermittently measured with error, and (ii) contexts where the exposure time-window precedes the outcome time-window using a landmark approach. First, the individual exposure history up to the landmark time is estimated using a mixed model that handles missing data and error in exposure measurement, and the predicted complete error-free exposure history is derived. Then the WCIE methodology is applied to assess the trajectory of association between the predicted exposure history and the health outcome collected after the landmark time. In our context, the health outcome is a longitudinal marker analyzed using a mixed model. A simulation study first demonstrates the correct inference obtained with this approach. Then, applied to the Nurses' Health Study (19,415 women) to investigate the association between BMI history (collected from midlife) and subsequent cognitive decline after age 70. In conclusion, this approach, easy to implement, provides a flexible tool for studying complex dynamic relationships and identifying critical time windows while accounting for exposure measurement errors.

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arXiv2019

Dynamic Modelling of Multivariate Dimensions and Their Temporal Relationships using Latent Processes: Application to Alzheimer's Disease

Alzheimer's disease gradually affects several components including the cerebral dimension with brain atrophies, the cognitive dimension with a decline in various functions and the functional dimension with impairment in the daily living activities. Understanding how such dimensions interconnect is crucial for AD research. However it requires to simultaneously capture the dynamic and multidimensional aspects, and to explore temporal relationships between dimensions. We propose an original dynamic structural model that accounts for all these features. The model defines dimensions as latent processes and combines a multivariate linear mixed model and a system of difference equations to model trajectories and temporal relationships between latent processes in finely discrete time. Dimensions are simultaneously related to their observed (possibly multivariate) markers through nonlinear equations of observation. Parameters are estimated in the maximum likelihood framework enjoying a closed form for the likelihood. We demonstrate in a simulation study that this dynamic model in discrete time benefits the same causal interpretation of temporal relationships as models defined in continuous time as long as the discretization step remains small. The model is then applied to the data of the Alzheimer's Disease Neuroimaging Initiative. Three longitudinal dimensions (cerebral anatomy, cognitive ability and functional autonomy) measured by 6 markers are analyzed and their temporal structure is contrasted between different clinical stages of Alzheimer's disease. Keywords: causality, difference equations, latent process, longitudinal data, mixed models, multivariate data.

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