  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
defective 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 a fixed-effect
(population progression curve) and a random-effect (individual variability).
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, require very
careful implementation, specific to the given problem, and tend to be slow in
practice.
  In this study, we propose an alternative elementary framework for analyzing
longitudinal data, relying on matrix completion. Our method yields estimates of
progression curves by iterative application of the Singular Value
Decomposition. Our framework covers multivariate longitudinal data, regression,
and can be easily extended to other settings. As it relies on existing tools
for matrix algebra it is efficient and easy to implement.
  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 identification of different progression trends in
subtypes of Cerebral Palsy.
