scholarly journals Estimating Growth in Height from Limited Longitudinal Growth Data Using Full-Curves Training Dataset: A Comparison of Two Procedures of Curve Optimization—Functional Principal Component Analysis and SITAR

Children ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 934
Author(s):  
Miroslav Králík ◽  
Ondřej Klíma ◽  
Martin Čuta ◽  
Robert M. Malina ◽  
Sławomir M. Kozieł ◽  
...  

A variety of models are available for the estimation of parameters of the human growth curve. Several have been widely and successfully used with longitudinal data that are reasonably complete. On the other hand, the modeling of data for a limited number of observation points is problematic and requires the interpolation of the interval between points and often an extrapolation of the growth trajectory beyond the range of empirical limits (prediction). This study tested a new approach for fitting a relatively limited number of longitudinal data using the normal variation of human empirical growth curves. First, functional principal components analysis was done for curve phase and amplitude using complete and dense data sets for a reference sample (Brno Growth Study). Subsequently, artificial curves were generated with a combination of 12 of the principal components and applied for fitting to the newly analyzed data with the Levenberg–Marquardt optimization algorithm. The approach was tested on seven 5-points/year longitudinal data samples of adolescents extracted from the reference sample. The samples differed in their distance from the mean age at peak velocity for the sample and were tested by a permutation leave-one-out approach. The results indicated the potential of this method for growth modeling as a user-friendly application for practical applications in pediatrics, auxology and youth sport.

2018 ◽  
Vol 28 (4) ◽  
pp. 1216-1229
Author(s):  
Xiao Lin ◽  
Ruosha Li ◽  
Fangrong Yan ◽  
Tao Lu ◽  
Xuelin Huang

Optimal therapeutic decisions can be made according to disease prognosis, where the residual lifetime is extensively used because of its straightforward interpretation and formula. To predict the residual lifetime in a dynamic manner, a longitudinal biomarker that is repeatedly measured during the post-baseline follow-up period should be included. In this article, we use functional principal component analysis, a powerful and flexible tool, to handle irregularly measured longitudinal data and extract the dominant features over a specific time interval. To capture the time-dependent trajectory pattern, a series of moving time windows are used to estimate window-specific functional principal component analysis scores, which are then combined with a quantile residual lifetime regression model to facilitate dynamic prediction. Estimation of this regression model can be achieved by solving estimating equations with the help of locating the minimizer of the L1-type function. Simulation studies demonstrate the advantages of our proposed method in both calibration and discrimination under various scenarios. The proposed method is applied to data from patients with chronic myeloid leukemia to illustrate its practicality, where we dynamically predict quantile residual lifetimes with longitudinal expression levels of an oncogene, BCR-ABL.


Author(s):  
Zhenhua Lin ◽  
Hongtu Zhu

We consider the problem of performing dimension reduction on heteroscedastic functional data where the variance is in different scales over entire domain. The aim of this paper is to propose a novel multiscale functional principal component analysis (MFPCA) approach to address such heteroscedastic issue. The key ideas of MFPCA are to partition the whole domain into several subdomains according to the scale of variance, and then to conduct the usual functional principal component analysis (FPCA) on each individual subdomain. Both theoretically and numerically, we show that MFPCA can capture features on areas of low variance without estimating high-order principal components, leading to overall improvement of performance on dimension reduction for heteroscedastic functional data. In contrast, traditional FPCA prioritizes optimizing performance on the subdomain of larger data variance and requires a practically prohibitive number of components to characterize data in the region bearing relatively small variance.


2014 ◽  
Vol 48 (4) ◽  
pp. 408-415 ◽  
Author(s):  
Nan Hu ◽  
Laura Cerviño ◽  
Paul Segars ◽  
John Lewis ◽  
Jinlu Shan ◽  
...  

Abstract Background. With the rapidly increasing application of adaptive radiotherapy, large datasets of organ geometries based on the patient’s anatomy are desired to support clinical application or research work, such as image segmentation, re-planning, and organ deformation analysis. Sometimes only limited datasets are available in clinical practice. In this study, we propose a new method to generate large datasets of organ geometries to be utilized in adaptive radiotherapy. Methods. Given a training dataset of organ shapes derived from daily cone-beam CT, we align them into a common coordinate frame and select one of the training surfaces as reference surface. A statistical shape model of organs was constructed, based on the establishment of point correspondence between surfaces and non-uniform rational B-spline (NURBS) representation. A principal component analysis is performed on the sampled surface points to capture the major variation modes of each organ. Results. A set of principal components and their respective coefficients, which represent organ surface deformation, were obtained, and a statistical analysis of the coefficients was performed. New sets of statistically equivalent coefficients can be constructed and assigned to the principal components, resulting in a larger geometry dataset for the patient’s organs. Conclusions. These generated organ geometries are realistic and statistically representative


2014 ◽  
Vol 30 (6) ◽  
pp. 732-736 ◽  
Author(s):  
Chris Richter ◽  
Kevin McGuinness ◽  
Noel E. O’Connor ◽  
Kieran Moran

In functional principal component analysis (fPCA) a threshold is chosen to define the number of retained principal components, which corresponds to the amount of preserved information. A variety of thresholds have been used in previous studies and the chosen threshold is often not evaluated. The aim of this study is to identify the optimal threshold that preserves the information needed to describe a jump height accurately utilizing vertical ground reaction force (vGRF) curves. To find an optimal threshold, a neural network was used to predict jump height from vGRF curve measures generated using different fPCA thresholds. The findings indicate that a threshold from 99% to 99.9% (6–11 principal components) is optimal for describing jump height, as these thresholds generated significantly lower jump height prediction errors than other thresholds.


2020 ◽  
Vol 29 (11) ◽  
pp. 3205-3217
Author(s):  
Yaeji Lim ◽  
Ying Kuen Cheung ◽  
Hee-Seok Oh

This paper presents a new model-based generalized functional clustering method for discrete longitudinal data, such as multivariate binomial and Poisson distributed data. For this purpose, we propose a multivariate functional principal component analysis (MFPCA)-based clustering procedure for a latent multivariate Gaussian process instead of the original functional data directly. The main contribution of this study is two-fold: modeling of discrete longitudinal data with the latent multivariate Gaussian process and developing of a clustering algorithm based on MFPCA coupled with the latent multivariate Gaussian process. Numerical experiments, including real data analysis and a simulation study, demonstrate the promising empirical properties of the proposed approach.


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