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The goal of this study was to model the longitudinal progression of knee osteoarthritis (OA) and build a prognostic tool that uses data collected in one year to predict disease progression over eight years. We carried out functional data clustering with a mixed-effects mixture model to overcome the challenge of missing data in longitudinal studies.

License: OA Progression Model

To model OA progression, we used eight-year joint space width measurements from X-rays and pain scores from the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) questionnaire, clustering disease progression trajectories with a mixed-effects mixture model that was designed especially for functional data (trajectories) with missing portions. After clustering subjects based on radiographic and pain progression, we used clinical variables collected within the first year to build least absolute shrinkage and selection operator (LASSO) regression models for predicting the probabilities of belonging to each cluster.

For more details, please refer to the following article:

Halilaj E, Le Y, Hicks JL, Hastie TJ, Delp SL. Modeling and predicting osteoarthritis progression: data from the osteoarthritis initiative. Osteoarthritis Cartilage. 2018;26(12):1643-1650. doi:10.1016/j.joca.2018.08.003

Statistical modeling was based on the following articles:

James GM, Sugar CA. Clustering for Sparsely Sampled Functional Data. J Am Stat Assoc. 2003;98(462):397-408.

James GM, Hastie TJ. Functional linear discriminant analysis for irregularly sampled curves. J R Stat Soc Ser B Stat Methodol. 2001;63(3):533-550.

James GM, Hastie TJ, Sugar CA. Principal component models for sparse functional data. Biometrika. 2000;87(3):587-602.