Functional principal component analysis for identifying the child growth pattern using longitudinal birth cohort data

Abstract

Background: Longitudinal studies are important to understand patterns of growth in children and limited in India. It is important to identify an approach for characterising growth trajectories to distinguish between children who have healthy growth and those growth is poor. Many statistical approaches are available to assess the longitudinal growth data and which are difficult to recognize the pattern. In this research study, we employed functional principal component analysis (FPCA) as a statistical method to find the pattern of growth data. The purpose of this study is to describe the longitudinal child growth trajectory pattern under 3 years of age using functional principal component method.

Methods: Children born between March 2002 and August 2003 (n = 290) were followed until their third birthday in three neighbouring slums in Vellore, South India. Field workers visited homes to collect details of morbidity twice a week. Height and weight were measured monthly from 1 month of age in a study-run clinic. Longitudinal child growth trajectory pattern were extracted using Functional Principal Component analysis using B-spline basis functions with smoothing parameters. Functional linear model was used to assess the factors association with the growth functions.

Results: We have obtained four FPCs explained by 86.5, 3.9, 3.1 and 2.2% of the variation respectively for the height functions. For height, 38% of the children's had poor growth trajectories. Similarly, three FPCs explained 76.2, 8.8, and 4.7% respectively for the weight functions and 44% of the children's had poor growth in their weight trajectories. Results show that gender, socio-economic status, parent's education, breast feeding, and gravida are associated and, influence the growth pattern in children.

Conclusions: The FPC approach deals with subjects' dynamics of growth and not with specific values at given times. FPC could be a better alternate approach for both dimension reduction and pattern detection. FPC may be used to offer greater insight for classification.

Keywords: Child growth; Cohort; Functional principal component analysis; Longitudinal; Urban slums.

Fig. 1

Flow chart of study participants

Fig. 2

Functional boxplots of height and weight functions with a black curve representing the median curve, aqua green and pink area denoting the 50% central region, the two inside blue curves indicating the envelops of 50% central region, the two outside blue curves indicating for two non-outlying extreme curves, and the red dashed curve representing the outlier candidates. A Functional boxplots of Height function. B Functional boxplots of Weight function

Fig. 3

The outliergram plot for height functions. Right: Modified band depth versus modified epigraph index of the 290 functions. The solid parabola and the dashed one represents the boundary between outlying and non-outlying observations. Left: Height functions of 290 children during ages between 0 and 36 months

Fig. 4

The outliergram plot for weight functions. Right: Modified band depth versus modified epigraph index of the 290 functions. The solid parabola and the dashed one represents the boundary between outlying and non-outlying observations. Circle stand for outlier (subject id). Left: Weight functions of 290 children during ages between 0 and 36 months

Fig. 5

A principal component analysis of aligned 290 height trajectories. The first four important harmonics, each plot shows the mean function (solid black) +/− small amount of harmonics or functions obtained by adding or subtracting from mean function. The x-axis denotes the age in months

Fig. 6

A principal component analysis of aligned 289 weight trajectories. The first three important harmonics, each plot shows the mean function (solid black) +/− small amount of harmonics or functions obtained by adding or subtracting from mean function. The x-axis denotes the age in months

Fig. 7

A Eigen plots for height functions (B) Eigen plots for weight functions