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In clinical practice and biomedical research, measurements are oftencollected sparsely and irregularly in time while the data acquisition isexpensive and inconvenient. Examples include measurements of spine bone mineraldensity, cancer growth through mammography or biopsy, a progression ofdefective vision, or assessment of gait in patients with neurologicaldisorders. Since the data collection is often costly and inconvenient,estimation of progression from sparse observations is of great interest forpractitioners.  From the statistical standpoint, such data is often analyzed in the contextof a mixed-effect model where time is treated as both a fixed-effect(population progression curve) and a random-effect (individual variability).Alternatively, researchers analyze Gaussian processes or functional data whereobservations are assumed to be drawn from a certain distribution of processes.These models are flexible but rely on probabilistic assumptions, require verycareful implementation, specific to the given problem, and tend to be slow inpractice.  In this study, we propose an alternative elementary framework for analyzinglongitudinal data, relying on matrix completion. Our method yields estimates ofprogression curves by iterative application of the Singular ValueDecomposition. Our framework covers multivariate longitudinal data, regression,and can be easily extended to other settings. As it relies on existing toolsfor matrix algebra it is efficient and easy to implement.  We apply our methods to understand trends of progression of motor impairmentin children with Cerebral Palsy. Our model approximates individual progressioncurves and explains 30% of the variability. Low-rank representation ofprogression trends enables identification of different progression trends insubtypes of Cerebral Palsy.

Modeling longitudinal data using matrix completion