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Full article title A new numerical method for processing longitudinal data: Clinical applications
Journal Epidemiology Biostatistics and Public Health
Author(s) Stura, Ilaria; Perracchione, Emma; Migliaretti, Giuseppe; Cavallo, Franco
Author affiliation(s) Università di Torino, Università di Padova
Primary contact Email: Ilaria dot stura at unito dot it
Year published 2018
Volume and issue 15(2)
Page(s) e12881
DOI 10.2427/12881
ISSN 2282-0930
Distribution license Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Website https://ebph.it/index.php/ebph/article/view/12881
Download https://ebph.it/article/view/12881/11630 (PDF)

Abstract

Background: Processing longitudinal data is a computational issue that arises in many applications, such as in aircraft design, medicine, optimal control, and weather forecasting. Given some longitudinal data, i.e., scattered measurements, the aim consists in approximating the parameters involved in the dynamics of the considered process. For this problem, a large variety of well-known methods have already been developed.

Results: Here, we propose an alternative approach to be used as an effective and accurate tool for the parameters fitting and prediction of individual trajectories from sparse longitudinal data. In particular, our mixed model, that uses radial basis functions (RBFs) combined with stochastic optimization algorithms (SOMs), is here presented and tested on clinical data. Further, we also carry out comparisons with other methods that are widely used in this framework.

Conclusion: The main advantages of the proposed method are the flexibility with respect to the datasets, meaning that it is effective also for truly irregularly distributed data, and its ability to extract reliable information on the evolution of the dynamics.

Keywords: statistical method, radial basis function; stochastic optimization algorithm, longitudinal data

Introduction

Longitudinal data are often the object of study in many fields, e.g., sociology, meteorology, and medicine. In medicine, repeated measurements are used to monitor patients’ behaviors and also to adjust therapies accordingly. However, many problems occur when these data are analyzed. Indeed, each time series could have a different number of observations and not be equally spaced. In addition, the sampling period could vary from patient to patient, and measurement errors and also missing data often occur. Thus, since in these cases common methods such as linear regression usually fail, the recent research is directed towards more robust statistical methods. For instance, longitudinal data are commonly analyzed using parametric models such as Bayesian ones[1], as well as functional data analysis (FDA).[2][3] In both cases, many data are required in order to model the behavior of the studied variable(s). These methods, in fact, try to find an "average curve" using all the data, including truncated series and observations with missing information.

References

  1. Rao, C.R. (1987). "Prediction of Future Observations in Growth Curve Models". Statistical Science 2 (4): 434–47. doi:10.1214/ss/1177013119. 
  2. Ji, H; Müller, H.-G. (2017). "Optimal designs for longitudinal and functional data". Statistical Methodology Series B 79 (3): 859-876. doi:10.1111/rssb.12192. 
  3. Ramsay, J.; Silverman, B.W. (2005). Functional Data Analysis. Springer-Verlag. pp. 428. ISBN 9780387400808. 

Notes

This presentation is faithful to the original, with only a few minor changes to presentation, spelling, and grammar. We also added PMCID and DOI when they were missing from the original reference. No other modifications were made in accordance with the "no derivatives" portion of the distribution license.