Characterizing early child growth patterns of height-for-age in an urban slum cohort of Bangladesh with functional principal component analysis

This was a prospective cohort study conducted between January 1, 2008 and December 31, 2012 in Dhaka, Bangladesh, consisting of 330 boys and 296 girls who lived in an urban slum of the Mirpur Thana area. Potential study subjects were identified from a local census for pregnant women, and healthy newborns were enrolled within 72 h of birth after written informed consent from the parents or guardians. Infants were followed until 2 years old. Information about socioeconomic status, maternal health, and hygienic practice was collected at enrollment. Maternal height (m) and weight (kg) were also measured at enrollment. Follow-up and surveillance were performed by trained research staff members who visited each study house twice a week and recorded information about child morbidity using a structured questionnaire. When a child had an acute illness, he or she was referred to the study clinic for further evaluation and treatment. Information on exclusive breast-feeding was obtained from monthly reports about the child’s consumption of human milk without supplementation (including water but excluding medications), and breast-feeding practices were monitored by field observation throughout infancy. Details about the study population and surveillance were described previously [9, 23‐25]. The study was approved by the Institutional Review Board of the University of Virginia and the Ethical Review Committee of the International Centre for Diarrhoeal Disease Research, Bangladesh (icddr,b).

Anthropometric measurements in this observational cohort study were collected by field research assistants upon enrollment and every 3 months during follow-up. All research staff were trained in appropriate techniques for anthropometry measurement and nutritional status assessment in a community setting. Weight and length of the children were measured with electronic scales and length boards that were precise to 0.01 kg and 0.1 cm (SECA Gmbh & Co, Hamburg, Germany). All anthropometry measurement instruments were well maintained and calibrated. The mean of two consecutive measurements at each visit was recorded. Nutritional status was assessed by comparing height and weight in the study cohort with the WHO growth reference for the same age and sex (WHO Anthro software, version 3.0.1, WHO, Geneva, Switzerland) [9]. Specifically, height-for-age z-score (HAZ) is an age- and sex-normalized measure of child height given in units of standard deviations and relative to the median age- and sex-conditional height distribution of the WHO reference population [26, 27]. A positive (+) or negative (−) sign depends on whether the child’s actual height is more or less than the median height of the WHO reference population at that age for that sex. When the actual height of a child is exactly equal to the median, the resultant HAZ is 0 (zero). The HAZ is of particular interest because it captures the long-term cumulative effects of health throughout childhood and is known to be correlated with later life outcomes [3, 28]. In this study, longitudinal HAZs in the first 2 years of age were the response measurements. For reliable estimation of individual growth curves, only those children who had ≥ 5 anthropometric measurements (i.e., who had growth observations approximately for the first year) were included.

Considering a continuous underlying growth curve of HAZs for each child, the directional change in growth and variation among growth curves of the cohort were identified and captured with the functional principal component analysis (FPCA) [11]. Separate FPCA was performed for boys and girls because of the effect of sex on growth and development. The FPCA estimated dominant modes of temporal variation among the individual growth, and extracted leading functional principal components (FPCs) that represented the temporal patterns associated with the largest proportions of variation. Each individual growth curve of HAZ was then approximated by summation of the estimated mean curve and a linear combination of the leading FPCs. The coefficients of these FPCs were referred to as the FPCA scores, characterizing the deviation of the individual curve from the mean curve.

There were several challenges in the growth modeling of HAZ in this study with traditional FPCA [11]. The HAZ growth data were relatively sparse, and measured at different times. Some data were incomplete for the entire 2 years because of early dropout. In addition, observations from the growth curves were subject to measurement error. To overcome those challenges, we performed the FPCA method using “funeigen” in the “funreg” package (version 1.1) in R 3.1 (http://​cran.​r-project.​org/​web/​packages/​funreg/​index.​html), which is able to accommodate sparse unbalanced data and account for measurement error [29]. This method was similar to the principal analysis through conditional expectation (PACE) method [12].

The fitted growth curves from PFCA in actual height (cm) and HAZ for boys and girls were plotted with the WHO growth standards that described the sex-specific percentiles of childhood growth from birth to age 24 months (Fig. 1). The fitted curves for most children in the cohort were below the 50th percentile of the WHO growth standards and deviated further down from the standards with increasing age, i.e., most subjects had downward growth patterns in HAZ with respect to the WHO growth standards [1] (http://​www.​who.​int/​childgrowth/​mgrs/​en/​) [27]. With FPCA, these fitted individual growth trajectories can be characterized by the leading FPCs and the corresponding FPC scores measure the deviation of individual curves from the mean curve. However, these FPC scores are only relative within the study cohort. To measure the downward growth comprehensively from the expected with respect to the WHO growth standards, we derived an index based on the FPC1 and FPC2 scores along with the WHO standards as described below.

For each subject in the study cohort, we defined a reference curve from the WHO growth standards and quantified downward growth trajectories of HAZ based on the deviation of the subject’s growth curve from the corresponding WHO reference curve. We first estimated the FPC1 and FPC2 scores for those “pseudo children” who had exact growth along the available WHO percentiles and defined them as the reference FPC scores. These reference FPC scores were estimated by regressing the difference between the reference and estimated mean curves on the two FPCs evaluated over 18 equally spaced times from birth to age 24 months. These reference FPC1 scores were used to classify subjects into 5 FPC1 strata that were defined by two consecutive reference FPC1 scores in the order of percentiles of those “pseudo children”. A similar classification method for functional data using FPC scores was developed previously [30]. Each stratum consisted of children who had similar growth patterns, and the WHO standard curve that corresponded to the upper limit of the stratum served as the reference curve for all subjects in that stratum. Then, within a given FPC1 stratum, an adjusted FPC2 score (adj-FPC2) for a child was calculated as the difference between the subject’s FPC2 score and the FPC2 score of the reference curve; i.e., adj-FPC2 = child’s FPC2 score - FPC2 score of the corresponding WHO reference curve. Because the adj-FPC2 score accounted for the FPC1 score indirectly through stratification and for the FPC2 score directly in the calculation, it measured deviation of individual growth trajectory from the expected with respect to the WHO standards, and thus quantified the growth faltering from the WHO reference. A positive adj-FPC2 indicated that the child had downward growth in HAZ relative to the corresponding WHO reference curve. The larger a positive adj-FPC2, the greater the change in growth or the more severe the growth faltering.

After the adj-FPC2 score was calculated to quantify growth faltering, we considered it as the response and evaluated its associated risk factors in a linear regression model. Similar idea of using FPC scores as predictors or responses in the subsequent analysis has been proposed in the literature [31]. For interpretation purposes, the continuous risk factors were centered at the mean in the regression analysis. Risk factors of interest included HAZ at birth, maternal height and weight, mother with any formal education, family size, monthly family income, duration of exclusive breast-feeding, number of diarrheal episodes from birth to age 6 months, source of drinking water, food coverage practice, and strata of FPC1 score. We also calculated the false discovery rate (FDR) adjusted p-values for these risk factors using the Benjamini and Hochberg method [32].

The essential modes of temporal variation among the fitted curves were extracted by FPCs. The two leading FPCs (FPC1 and FPC2) accounted for > 98% of the temporal variation in the HAZ growth trajectories: with 93% in FPC1 and 6% in FPC2 for boys and 96% in FPC1 and 3% in FPC2 for girls (Fig. 2). The FPC1 and FPC2 captured the directions of the departure of individual curves from the mean curve. The FPC1 decreased with increasing age in boys and girls, consistent with progressively decreased HAZ. The FPC2 also decreased with age but was positive at a younger age and negative at an older age, implying a directional change in the growth trajectory with respect to the mean curve.

Plots of the fitted mean curves of HAZ vs age and the curves that were 2 standard deviations of the FPC scores above (+++) and below (---) the mean curves showed a broad range of HAZ growth curves along with FPC scores (Fig. 3). For FPC1, the curves that were 2 standard deviations of the FPC1 scores above and below the mean curves had similar patterns as the mean curve (Fig. 3a and b), which captured the decreasing growth and were interpreted as overall growth pattern; a larger positive FPC1 score indicated an accelerated decreasing curve, and a negative FPC1 score indicated a slower decreasing curve of HAZ in relation to mean curve. In contrast, for FPC2, the curves that were 2 standard deviations of the FPC2 scores above and below the mean curve crossed over the mean curve at approximately 12 months of age for both boys and girls (Fig. 3c and d) and thus captured the change in growth trajectory; a larger positive FPC2 score indicated a greater change in growth trajectory relative to the mean curve. However, the FPC2 alone was not very informative to quantify the degree of downward growth or growth faltering relative to the WHO standards, as the FPC2 score was centered at a mean zero for the cohort in the FPCA method, which would imply roughly 50% of children in the cohort had positive/negative FPC2 scores. In other words, the FPC2 scores measured the relative growth faltering by comparing the subjects within the cohort, not to the WHO growth standards. Comparatively, the unadjusted FPC2 scores for most subjects were larger than the reference FPC2 scores of the WHO standard curves, and the adjustment for the WHO standards and stratification on FPC1 scores resulted in that adj-FPC2 scores were positive for all children except 29 boys (Fig. 4). The results were consistent with the growth patterns observed in Fig. 1, where most children in the cohort had downward growth in HAZ. Therefore, using the WHO standards as the benchmark, the adj-FPC2 was a meaningful index to quantify the degree or severity of growth faltering as it accounted for the magnitude and direction of deviation in growth trajectory from the WHO standards.

As described in the Methods Section, children were classified into five strata on the basis of their FPC1 scores. Children in each stratum had similar overall growth patterns. The mean adj-FPC2 score was the highest in Stratum 1 and the lowest in Stratum 5 (Table 2), indicating an ordered degree of growth faltering, with the most severe faltering seen in Stratum 1. The linear regression analysis of the adj-FPC2 score on the risk factors and the FPC1 strata showed that overall model fitting was adequate (R ² = 0.64 for boys and 0.63 for girls) (Table 3). Significance of FPC1 strata suggested that the overall growth was important for growth faltering. Children with poorer overall growth (lower FPC1 strata) were more likely to have growth faltering (Table 3). HAZ at birth was significant for boys and girls without and with FDR adjustment, but because of the high correlation between HAZ at birth and FPC1 score this needed to be interpreted with FPC1 stratum. Larger babies at birth were more likely to experience poorer growth, especially for those in lower strata, and the effect was attenuated for those in higher strata. Such an observation could be in part due to the regression to the mean.

In addition, without FDR adjustment, significant factors associated with the poor growth (p-value < 0.05) were family income, family size, having an animal in the house and exclusive breastfeeding over 6 months for boys, and maternal weight and access to municipal water supplies for girls. Specifically, boys from higher-income families or having an animal in the house were less likely to have growth faltering, whereas those from larger families and exclusively breastfed for longer than 6 months were more likely to have poor growth. Girls were less likely to have faltering if their mothers had normal weight or their households had access to the municipal water supply. Without adjustment, food coverage practice had a marginally significant effect against faltering in girls (p-value = 0.056). After FDR adjustment, these identified risk factors remained significant or marginally significant, except for the food coverage practice in girls.

Table 4 shows the Pearson correlations of FPC scores from FPCA with HAZs and the changes in HAZ percentiles over time. Note that HAZs represented overall growth trajectory and the change in HAZ percentiles reflected relative change in growth trajectory. The FPC1 score was significantly correlated with HAZ at birth, ages 6, 12, 18, and 24 months (Pearson correlation coefficient: boys, −0.996 to −0.849; girls, −1.00 to −0.971). However, the FPC1 score was only weakly or not correlated with the changes of HAZ percentiles from birth to age 24 months or from 6 to 18 months (Table 4). These results agreed with the interpretation that FPC1 captured the overall growth pattern but not the change of the pattern. In contrast, the adj-FPC2 score was highly correlated with the changes of HAZ percentiles over time, but only weakly with individual HAZ measurements (Table 4). These results agreed well with the notion that adj-FPC2 captured the downward change in the growth trajectory, i.e., growth faltering. Moreover, FPC1 and adj-FPC2 scores would be better summary indices than individual HAZ measurements at discrete times because they together characterized the entire growth process continuously from birth to age 2 years.