Elsevier

Methods

Volume 203, July 2022, Pages 142-151
Methods

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

https://doi.org/10.1016/j.ymeth.2022.03.003Get rights and content

Highlights

  • Joint models (JM) are a useful tool to analyze longitudinal data with informative dropout .

  • Joint Latent Process Models (LPM) extend JM to markers (of possibly different nature) measuring the same underlying quantity.

  • Maximum Likelihood Estimation of the joint LPM is available in the R-package JLPM.

  • The case study quantifies the progression of dysphagia during Multiple-System Atrophy (MSA) and its association with death risk.

Abstract

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.

Introduction

In health cohort studies, markers measured at multiple times are often used to describe the natural history of a disease, monitor patients or predict the risk of clinical progression. Classical examples include T-cell CD4 counts and viral load for the progression of HIV [1] or PSA for prostate cancer evolution [2]. Due to the intrinsic intra-subject correlation between the repeated measures of markers, their evolution can not be modelled using classical regression models, and mixed models which include individual random effects to account for this serial correlation are now adopted worldwide [3].

During the follow-up, clinical events (e.g. diagnosis, recurrence, death) may disrupt the progression of the markers and induce a dropout. When this interruption of the follow-up is predictable by the observed marker data, the missing data mechanism is called missing-at-random (MAR), and inference provided by the mixed model is still valid [4]. However, in many cases, the dropout is likely to depend on the underlying (unobserved) disease mechanism rather than only on the strictly observed data. The missing data mechanism becomes missing-not-at-random (MNAR), and mixed models may not provide correct inference anymore [5], [6]. During the last twenty years, the statistical community has massively embraced the issue of dropout in longitudinal analysis which lead to the development of joint models for the simultaneous analysis of repeated markers and clinical events [7], [8], [1], [9]. Joint models combine a mixed model describing the progression of the markers and a survival model for the time of occurrence of the clinical events, while associating the two models through shared random variables, usually the random effects from the mixed model [7]. Beyond the study of the marker progression in the presence of MNAR dropout, this method also more generally assesses the association between a marker trajectory and an associated event of interest [10], [11], [2].

Despite many developments in joint models in the recent years [12], [13], most works are dedicated to classical continuous biomarkers stemmed from blood samples, MRI, etc. Yet, in an ever-increasing number of health studies, the actual quantity of interest is not directly measured. It is a latent construct which is assessed using a set of indicators measured with error, usually stemmed from questionnaires or measurement scales. Examples include health related quality of life in Cancer research and beyond [14], cognitive functioning and functional dependency in neurodegenerative diseases [15], [16], or many other constructs such as anxiety or depressive symptomatology [17], [18]. The analysis of latent constructs stemmed from measurement scales and questionnaires requires a specific attention. Measurement scales usually translate into multiple categorical and/or continuous items that measure different aspects of the underlying construct of interest. Furthermore, when aggregating the item information into a sumscore, the resulting univariate marker may not have classical Gaussian properties for continuous markers; they are usually bounded with floor/ceiling effects and possible unequal-interval scaling [16], [19].

In this contribution, we show how the joint modeling methodology can be extended to handle repeated data from measurement scales in the presence of an informative clinical event, and provide a software solution with the R package JLPM. We illustrate the methodology through simulations and in Multiple-System Atrophy (MSA), a rare and deadly neurodegenerative disease, which progression is almost exclusively described by measurement scales [20].

The article is organized as follows: Section 2 presents the methodology developed to handle previously mentioned challenges (multiple markers of different nature, competing risks, delayed entry), Section 3 reports simulation studies aiming at validating the inference procedure. Section 4 illustrates the methodology with the analysis of dysphagia progression in MSA, and Section 5 concludes.

Section snippets

Methodology

Let consider a cohort of N individuals followed up over time. We define Ti the time of occurrence of an event of interest for subject i (i=1,,N). This event may be due to P different causes, defining a competing risk setting. As some individuals may be censored before this occurrence, we observe Ti=min(Ti,Ci) where Ci is the censoring time, and δi the event indicator such that δi=p when the event of cause p occurs first and before censoring (TiCi), and δi=0 otherwise. We also collect

Simulation studies

Two simulation studies were performed to illustrate the methodology and validate the estimation procedure implemented in the R-package JLPM according to the type of markers and times-to-event included, and the nature of the dependency structure between the longitudinal and the survival submodels.

Illustration in Multiple-System Atrophy

We illustrate our methodology to the Multiple-System Atrophy (MSA), a rare neurodegenerative disease characterized by various combinations of parkinsonism, cerebellar ataxia and dysautonomic symptoms. The disease progresses very fast and is fatal with a median survival between 8 and 10 years after the first symptoms onset [20]. The occurrence of death suddenly interrupts the follow-up of MSA patients who are usually the most affected. This constitutes an informative dropout that needs to be

Concluding remarks

The joint modelling of longitudinal data and time-to-event data has become a standard methodology to address the problem of informative dropout and more generally investigate the association between longitudinal markers and clinical events [32]. In this work, we have shown how this methodology could be extended to longitudinal data of different natures by separating the longitudinal model for the quantity of interest defined as a latent process from the measurement model that links the quantity

Funding

This work was funded by the French National Research Agency 455 (Project DyMES - ANR-18-C36-0004-01).

CRediT authorship contribution statement

Tiphaine Saulnier: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing - original draft. Viviane Philipps: Methodology, Software, Validation. Wassilios G. Meissner: Investigation, Resources. Olivier Rascol: Investigation, Resources. Anne Pavy-Le Traon: Investigation, Resources. Alexandra Foubert-Samier: Conceptualization, Formal analysis, Investigation, Resources. Cécile Proust-Lima: Conceptualization, Methodology, Validation, Formal analysis, Writing - review &

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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