Joint modelling of longitudinal data: a scoping review of methodology and applications for non-time to event data

Joint models are powerful statistical models that allow us to define a joint likelihood for quantifying the association between two or more outcomes. Joint modelling has been shown to reduce bias in parameter estimates, increase the efficiency of statistical inference by incorporating the correlation between measurements, and allow borrowing of information in cases where data is missing for variables of interest. Most joint modelling methods and applications involve time-to-event data. There is less awareness about the amount of literature available for joint models of non-time-to-event data. Therefore, this review's main objective is to summarise the current state of joint modelling of non-time-to-event longitudinal data.

We conducted a search in PubMed, Embase, Medline, Scopus, and Web of Science following the PRISMA-ScR guidelines for articles published up to 28 January 2024. Studies were included if they focused on joint modelling of non-time-to-event longitudinal data and published in English. Exclusions were made for time-to-event articles, conference abstracts, book chapters, and studies without full text. We extracted information on statistical methods, association structure, estimation methods, software, etc. RESULTS: We identified 4,681 studies from the search. After removing 2,769 duplicates, 1,912 were reviewed by title and abstract, and 190 underwent full-text review. Ultimately, 74 studies met inclusion criteria and spanned from 2001 to 2024, with the majority (64 studies; 86%) published between 2014 and 2024. Most joint models were based on a frequentist approach (48 studies; 65%) and applied a linear mixed-effects model. The random effect was the most commonly applied association structure for linking two sub-models (63 studies; 85%). Estimation of model parameters was commonly done using Markov Chain Monte Carlo with Gibbs sampler algorithm (10 studies; 38%) for the Bayesian approach, whereas maximum likelihood was the most common (33 studies; 68.75%) for the frequentist approach. Most studies used R statistical software (33 studies; 40%) for analysis.

A wide range of methods for joint-modelling non-time-to-event longitudinal data exist and have been applied to various areas. An exponential increase in the application of joint modelling of non-time-to-event longitudinal data has been observed in the last decade. There is an opportunity to leverage potential benefits of joint modelling for non-time-to-event longitudinal data for reducing bias in parameter estimates, increasing efficiency of statistical inference by incorporating the correlation between measurements, and allowing borrowing of information in cases with missing data.