Title: Longitudinal data analysis using matrix completion,
Abstract: In clinical practice and biomedical research, measurements are often
collected sparsely and irregularly in time while the data acquisition is
expensive and inconvenient. Examples include measurements of spine bone mineral
density, cancer growth through mammography or biopsy, a progression of defect
of vision, or assessment of gait in patients with neurological disorders. Since
the data collection is often costly and inconvenient, estimation of progression
from sparse observations is of great interest for practitioners.
From the statistical standpoint, such data is often analyzed in the context
of a mixed-effect model where time is treated as both random and fixed effect.
Alternatively, researchers analyze Gaussian processes or functional data where
observations are assumed to be drawn from a certain distribution of processes.
These models are flexible but rely on probabilistic assumptions and require
very careful implementation.
In this study, we propose an alternative elementary framework for analyzing
longitudinal data, relying on matrix completion. Our method yields point
estimates of progression curves by iterative application of the SVD. Our
framework covers multivariate longitudinal data, regression and can be easily
extended to other settings.
We apply our methods to understand trends of progression of motor impairment
in children with Cerebral Palsy. Our model approximates individual progression
curves and explains 30% of the variability. Low-rank representation of
progression trends enables discovering that subtypes of Cerebral Palsy exhibit
different progression trends.