Applications of functional data analysis: A systematic review

BACKGROUND: Functional data analysis (FDA) is increasingly being used to better analyze, model and predict time series data. Key aspects of FDA include the choice of smoothing technique, data reduction, adjustment for clustering, functional linear modeling and forecasting methods. METHODS: A systematic review using 11 electronic databases was conducted to identify FDA application studies published in the peer-review literature during 1995-2010. Papers reporting methodological considerations only were excluded, as were non-English articles. RESULTS: In total, 84 FDA application articles were identified; 75.0% of the reviewed articles have been published since 2005. Application of FDA has appeared in a large number of publications across various fields of sciences; the majority is related to biomedicine applications (21.4%). Overall, 72 studies (85.7%) provided information about the type of smoothing techniques used, with B-spline smoothing (29.8%) being the most popular. Functional principal component analysis (FPCA) for extracting information from functional data was reported in 51 (60.7%) studies. One-quarter (25.0%) of the published studies used functional linear models to describe relationships between explanatory and outcome variables and only 8.3% used FDA for forecasting time series data. CONCLUSIONS: Despite its clear benefits for analyzing time series data, full appreciation of the key features and value of FDA have been limited to date, though the applications show its relevance to many public health and biomedical problems. Wider application of FDA to all studies involving correlated measurements should allow better modeling of, and predictions from, such data in the future especially as FDA makes no a priori age and time effects assumptions.