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A Bayesian Location‐Scale Joint Model for Time‐To‐Event and Multivariate Longitudinal Data With Association Based on Within‐Individual Variability
Abstract
Within‐individual variability of health indicators measured over time is becoming commonly used to inform about disease progression. Simple summary statistics (e.g., the standard deviation for each individual) are often used but they are not suited to account for time changes. In addition, when these summary statistics are used as covariates in a regression model for time‐to‐event outcomes, the estimates of the hazard ratios are subject to regression dilution. To overcome these issues, a joint model is built where the association between the time‐to‐event outcome and multivariate longitudinal markers is specified in terms of the within‐individual variability of the latter. A mixed‐effect location‐scale model is used to analyze the longitudinal biomarkers, their within‐individual variability and their correlation. The time to event is modeled using a proportional hazard regression model, with a flexible specification of the baseline hazard, and the information from the longitudinal biomarkers is shared as a function of the random effects. The model can be used to quantify within‐individual variability for the longitudinal markers and their association with the time‐to‐event outcome. We show through a simulation study the performance of the model in comparison with standard joint models with constant variance. The model is applied on a dataset of adult women from the UK cystic fibrosis registry, to evaluate the association between lung function, malnutrition and mortality.
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Metadata
- Authors
- Palma, M., El Makkaoui, O., Keogh, R. H., Carr, S. B., Szczesniak, R., Taylor‐Robinson, D., Wood, A. M., Muniz‐Terrera, G., & Barrett, J. K.
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2026-05
- Volume
- 45
- Issue
- 10-12
- ISSN
- 0277-6715
- 1097-0258
- Cited by
- 2
- Language
- en
- Licence
- creativecommons.org/licenses/by/4.0/ (vor, 16 d)
- doi.wiley.com/10.1002/tdm_license_1.1 (tdm)
- Funders
- Medical Research Council (MR/V020595/1, MC_UU_00002/5, MC_UU_00040/02)
- UK Research and Innovation (MR/X015017/1)
- National Institutes of Health (R01 HL141286)
- Cystic Fibrosis Foundation (Naren19R0, SZCZES22AB0)
- Osteopathic Heritage Foundation
- National Institute for Health and Care Research (NIHR 302438, NIHR 303137, NIHR 203312)
- British Heart Foundation (HDRUK2023.0239, RG/F/23/110103, CH/12/2/29428, RE/24/130011)
- Health Data Research UK (Big Data for Complex Disease‐HDR‐23012, HDRUK2023.0028)
- Ulverscroft Foundation
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- Palma, M., El Makkaoui, O., Keogh, R. H., Carr, S. B., Szczesniak, R., Taylor‐Robinson, D., Wood, A. M., Muniz‐Terrera, G., & Barrett, J. K. (2026). A Bayesian Location‐Scale Joint Model for Time‐To‐Event and Multivariate Longitudinal Data With Association Based on Within‐Individual Variability. Statistics in Medicine. https://doi.org/10.1002/sim.70596
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