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Supplemental material, sj-pdf-1-smm-10.1177_0962280220909986 for Quantile regression for incomplete longitudinal data with selection by death by Hélène Jacqmin-Gadda, Anaïs Rouanet, Robert D Mba, Viviane Philipps and Jean-François Dartigues in Statistical Methods in Medical Research

Supplemental material, sj-pdf-1-smm-10.1177_0962280220909986 for Quantile regression for incomplete longitudinal data with selection by death by Hélène Jacqmin-Gadda, Anaïs Rouanet, Robert D Mba, Viviane Philipps and Jean-François Dartigues in Statistical Methods in Medical Research

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.

International audience; 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 dynamic IRT model which exploits the information provided at item-level for a measurement scale while simultaneously handling observation times that may vary across individuals. 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 dynamic IRT 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 on 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.

International audience; Quantifying the association between lifetime exposures and the risk of developing a chronic disease is a recurrent challenge in epidemiology. Individual exposure trajectories are often heterogeneous and studying their associations with the risk of disease is not straightforward. We propose to use a latent class mixed model (LCMM) to identify profiles (latent classes) of exposure trajectories and estimate their association with the risk of disease. The methodology is applied to study the association between lifetime trajectories of smoking or occupational exposure to asbestos and the risk of lung cancer in males of the ICARE population-based case-control study. Asbestos exposure was assessed using a job exposure matrix. The classes of exposure trajectories were identified using two separate LCMM for smoking and asbestos, and the association between the identified classes and the risk of lung cancer was estimated in a second stage using weighted logistic regression and all subjects. A total of 2026/2610 cases/controls had complete information on both smoking and asbestos exposure, including 1938/1837 cases/controls ever smokers, and 1417/1520 cases/controls ever exposed to asbestos. The LCMM identified four latent classes of smoking trajectories which had different risks of lung cancer, all much stronger than never smokers. The most frequent class had moderate constant intensity over lifetime while the three others had either long-term, distant or recent high intensity. The latter had the strongest risk of lung cancer. We identified five classes of asbestos exposure trajectories which all had higher risk of lung cancer compared to men never occupationally exposed to asbestos, whatever the dose and the timing of exposure. The proposed approach opens new perspectives for the analyses of dose-time-response relationships between protracted exposures and the risk of developing a chronic disease, by providing a complete picture of exposure history in terms of intensity, duration, and timing of exposure.

Les tests psychométriques ont souvent des propriétés métrologiques (effets plafond/plancher, curvilinéarité) qui font que les méthodes classiques d'analyse ne sont pas adaptées. C'est le cas en particulier pour le Mini-Mental State Examination (MMSE), un test psychométrique très utilisé en épidémiologie pour décrire le déclin cognitif chez les personnes âgées. Ces propriétés sont corrigées par le modèle mixte à processus latent, qui définit une transformation reliant les observations au processus latent sous-jacent au test et décrit simultanément la trajectoire du processus latent en fonction de variables explicatives et de fonctions du temps par un modèle linéaire mixte. Mais ce type de modèle reste compliqué à mettre en place dans les analyses statistiques des études épidémiologiques. L'objectif du stage était donc de déterminer s'il était possible de définir une fois pour toutes une transformation du MMSE pour corriger ses propriétés métrologiques, permettant ainsi d'utiliser un modèle linéaire mixte sur données pré-transformées pour étudier l'impact de covariables sur le déclin cognitif. La variabilité de ces transformations estimées sur des populations différentes et des structures de régression différentes a pu être appréciée sur 3 grands jeux de données de vieillissement cognitif : PAQUID, 3~Cités et REAL. Nous avons observé que les transformations issues de structures de modèles différentes et estimées sur une même population étaient très similaires. Par contre, une plus grande variabilité a été observée entre les populations. À partir de ces cohortes, nous avons montré par validation croisée que la variabilité de la transformation a néanmoins un impact modéré sur l'estimation des coefficients de régression. Nous avons alors proposé la pré-transformation du MMSE comme la moyenne, pour chaque score, des valeurs transformées estimées dans la validation croisée. Une validation externe de cette transformation a enfin été effectuée. Elle a montré que l'utilisation de la pré-transformation du MMSE sur des cohortes en population générale n'engendre pas de biais très importants, les écarts entre les estimations du modèle mixte à processus latent et celles d'un modèle linéaire mixte sur les données pré-transformées n'étant pas très importants. De plus, en comparaison avec les autres méthodes généralement utilisées, la pré-transformation proposée améliore les résultats. Pour une cohorte de sujets déjà déments, son utilisation semble moins pertinente.