Joint models for the longitudinal analysis of measurement scales in the presence of informative dropout
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 the time of occurrence of an event of interest for subject i (). 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 where is the censoring time, and the event indicator such that when the event of cause p occurs first and before censoring (), and 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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