Short‐term dynamics of linear growth among Peruvian infants in the first year of life in a population with linear growth faltering

Infant growth is recognized to vary over the short term, with periods of greater and lesser linear growth velocity. Our objectives were to (1) examine the potential differences in overall growth profiles between children who experienced cumulative growth faltering in the first year of life consistent with that seen by many children living in poverty in low‐ and middle‐income countries, versus children without growth faltering and (2) test whether biological factors were associated with the timing of magnitude of growth saltations.


| INTRODUCTION
Linear growth is a key measure of infant health and development (de Onis & Branca, 2016).Among infants living in poverty in low and middle-income countries, slower than expected growth compared to the global reference population can cumulate in stunting, defined as the child's length-for-age falling below two standard deviations below the median (World Health Organization, 2006).Because stunting affects 22% of children under five globally (UNICEF/WHO/World Bank Group, 2021), leading to an estimated excess of 164 000 thousand deaths and 3% of all disability adjusted life years per year (Institute for Health Metrics and Evaluation, 2019), reducing the prevalence of childhood stunting remains a major global health priority (Vaivada et al., 2020).
Risk factors for stunting such as low birth weight, inadequate dietary intakes, and pathogen exposures are well recognized (MAL-ED Network Investigators, 2017aInvestigators, , 2017b)).However, the individual and cumulative impact of these factors on stunting remains imperfectly understood.This is because long-term growth faltering is a cumulative process, driven by interactions between transient insults and systematic growth-limiting conditions that result in chronic growth suppression (Silverberg et al., 2021); and because human growth is adaptive, with processes of catch-up that allow for recovery if conditions improve.Questions remain about how short-term growth dynamics cumulatively produce long-term growth deficits (Moore et al., 2020).For instance, there is evidence that ponderal growth, associated with energy reserves, may be necessary for linear growth (Cliffer et al., 2021), and that transient infections temporarily slow growth, with catchup possible over longer periods (Richard et al., 2014).However, characterizing short-term growth is challenging because short-term growth velocity is highly variable and can be difficult to measure (Greco et al., 1990;Greco et al., 1994;Liivak et al., 2009;Tillmann & Clayton, 2001).When examined on the order of days or hours, infant and child growth appears noncontinuous, with periods during which rapid "growth saltations" occurring-possibly overnight- (Lampl & Johnson, 2011), as well as periods of almost no growth ("stasis") (Lampl et al., 1992(Lampl et al., , 1993)).This variation has led to growth being described as "saltatory" (Lampl et al., 1992).
Data from children with growth-limiting genetic and hormonal disorders may offer some insight into the biological signals that underlie short-term nonlinear growth dynamics.For instance, growth in children with congenital adrenal hyperplasia is characterized by long-duration, low magnitude growth saltations with reduced periods of growth stasis: this patterning is hypothesized to result from steady, low-level growth hormone secretion, which contrasts to a healthy pattern of spontaneous bursts in growth hormone (Gill et al., 2001;Hermida et al., 1996).In contrast, children with growth hormone deficiency and Turner syndrome appear to have growth spurts of low magnitude, with increased time spent in stasis (Tillmann et al., 2002).Among children with growth-affecting disorders, short-term changes in height also predict longer-term growth, and there is interest in using short-term growth dynamics to chart treatment efficacy (Liivak et al., 2009;Suki & Frey, 2017).
Less evidence is available about how these nonlinear dynamics may be altered among children at risk of stunting in resource-constrained environments where inadequate dietary intakes and frequent early childhood infections underly growth faltering.Understanding the interplay between the environmental exposures and biological regulators that drive these nonlinear dynamics may inform systems biology modeling of growth dynamics (Suki & Frey, 2017), and similarly aid in the identification of shorter-term pattens that might indicate risk of future stunting.The ability to positively identify a change in the pattern of growth that indicates a response to treatment might also be a useful proxy endpoint for intervention studies.
Here, we examine high-resolution growth dynamics through three-time weekly measurements of infant length collected from a Peruvian cohort that experienced significant growth faltering in the first year of life.Because stunted children are heterogeneous, comprising both children born small, who remain on a consistent trajectory as they grow and children born larger, whose length-for-age Z-score falls as they grow, we conducted separate analyses of both growth profiles.Our objectives were to (1) examine potential differences in overall growth profiles between children who experienced cumulative growth faltering in the first year of life consistent with that seen by many children living in poverty in lowand middle-income countries, versus children without growth faltering and (2) test whether biological factors were associated with the timing or magnitude of growth saltations.

| METHODS
A total of 68 children were enrolled into this sub-study of the Peru cohort of the Etiology, Risk Factors and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development (MAL-ED) study.The MAL-ED study was an observational cohort study that has been described extensively (Network Investigators et al., 2014;Yori et al., 2014).The geographic location of the cohort is the Peruvian Amazon, a low-altitude part of the country with a distinct rainy and dry season (Colston et al., 2020) The prevalence of food insecurity was greater than 50% (Psaki et al., 2012) while macronutrient intakes were generally sufficient, with the probability of dietary adequacy for specific micronutrients and minerals varying by nutrient (Antiporta et al., 2021).Almost all infants were breastfed, and, although exclusive breastfeeding was interrupted very early for most infants, partial breastfeeding continued, for the majority, through 1 year of age (Ambikapathi et al., 2016;Richard et al., 2018).Infants were enrolled within 17 days of birth, and their growth, diet and illness experiences were documented until 24 months of age.Eligible infants were considered healthy at birth, weighed at least 1.5 kg at birth, and were born to a mother who was at least 16 years of age.
For the substudy, the length (cm), weight (kg), midupper arm circumference, and subscapular skinfold thickness were assessed three-times weekly from birth to 1 year of age.A team of two study workers were assigned to collect the data.Length was measured by a team of two trained study technicians using a commercial recumbent length measuring board with a 106 cm capacity, measured to the nearest 0.1 cm, with the baby in supine position with the crown of the head touching the headboard.Each technician held the head or the feet of the infant during the first measurement and then changed places to measure the child a second time.Prior to starting, the technicians underwent standardized training on length measurement (Lohman et al., 1988) until their technical error of measurement was <0.29 cm (WHO Multicentre Growth Reference Study Group, 2006).The weight was measured once, to the nearest 10.0 g, while the baby was naked using a digital baby scale; and subscapular skinfold thickness was measured to the nearest 0.2 mm and repeated three times, using a Holtain skinfold caliper which was calibrated monthly using a standardization block.The time of day for all measurements was noted.Data collection was conducted between December 2010 and March 2012.
As part of the MAL-ED study, households were also visited twice weekly to query caregivers regarding signs of illness.This work was conducted by a study worker independent of the specialized anthropometry team.From the morbidity data, the percentage of days ill was calculated over specific time periods.During these visits information on breastfeeding was also collected.Birth weight was abstracted from clinic records.
The study protocol was approved by the ethical review boards of A.B. Prisma and the Johns Hopkins Bloomberg School of Public Health.Written informed consent was obtained from caregivers participating in the study.
For analysis, weight and subscapular skinfold measures were converted to Z-scores using WHO reference standards (WHO Multicentre Growth Reference Study Group, 2007).Any children with fewer than 30 total measurements were excluded for the analysis (30 measurements was the 5th percentile of the distribution of the number of anthropometric measurements), which occurred when the family moved away from the study catchment area or withdrew from the study.This caused 4 children who left the study catchment area prior to 1 month of age (49 total anthropometric measurements) to be excluded.An additional three children were excluded from the study because more than 7 days separated all measurements, making it impossible to construct segments of continuous data for analysis.For the n = 61 children included, the growth of these children was analyzed as separate segments (i.e.analyzed separately) if separated by >7 days.This was done so that the denominator time in the calculation of periods of saltation or stasis excluded any unobserved period (≥7 days).
We then used a changepoint analysis approach (Pruned Exact Linear Tree [PELT]), implemented using the "cpt.mean"function in the "changepoint" package in R (Killick & Eckley, 2012), to identify growth saltations and periods of stasis.Changepoint detection was implemented using PELT algorithm, implemented using the "changepoint" package in R. PELT uses a dynamic programming approach to find an exact solution to the problem of identifying the optimal number and location of changepoints in a data series.PELT was selected because it does not require the user to pre-specify the number of changepoints, is relatively robust to dependence within the data (Gallagher et al., 2022) and produces more stable solutions compared to nonexact CP detection methods (Mersmann, 2021).We used the cpt.mean function after scaling the height by the technical error of measurement (Killick & Eckley, 2012).The penalty value was tuned by examining plots of the difference in test statistic by the number of changepoints for the elbow joint.The cpt. mean function was chosen over the cpt.meanvar function because, although changes in variance may occur as children grow (e.g., younger infants might be more difficult to measure than older ones), estimating both the mean and the variance of the function restricts the minimum segment length to be two, and we wished to allow sequential changepoints to be detected.After fitting the changepoint analysis estimated means, we examined the normality of the residuals using Shapiro-Wilks tests and Q-Q plots and examined the autocorrelation function of the residuals.
To examine potential differences in the overall growth profiles between children (aim 1), the average duration of stasis periods (in days); and average saltation magnitude were calculated for each child.The mean values were compared between children who were stunted at 12 months, and those who were not stunted at 12 months of age using two-sided t-tests and the variance was compared using two-sided variance comparison tests.We also compared these characteristics between children who lost more than 0.25 in LAZ from 0 to 12 months and children who lost less than 0.25 LAZ from 0 to 12 months, using two-sided t-tests to compare means, and two-sample variance-comparison tests to compare variance.A change of À0.25 in LAZ from 0 to 12 months was selected as the cut-off because it approximated the median change for the cohort.
We then constructed hurdle regression models to enable us to examine the association between the odds of a saltation occurring on a given day, the magnitude of a saltation, and other factors with a theorized relationship to growth.Hurdle regression models were used for this purpose because they simultaneously model the odds of an event occurring, and given that the event does occur, its magnitude.Based on the comparison of model fits, we included age as a linear term when modeling the odds of a saltation occurring, and the natural log of age when modeling saltation magnitude.All hurdle regression models also adjusted for potential within-child correlation by estimating the variance with a clustered sandwich estimator (Hardin, 2003;Rogers, 1993).To examine whether there were overall differences in growth between children who were stunted at 12 months versus not, we first constructed hurdle regression models that adjusted only for age and the presence of stunting at 12 months.Similar models were constructed to test for evidence that infants who lost more than 0.25 in LAZ versus less than 0.25 LAZ from 0 to 12 months.No other covariates were included, as the intention of these models was to test for evidence of overall differences in saltatory patterns of growth between infants with or without growth faltering, rather than to investigate potential factors that might mediate or explain the differences observed.
To better understand the biological factors that might help to explain the timing of magnitude of growth saltations (aim 2), we again used hurdle regression models to consider specific biological factors that are known to affect risk of for growth faltering.We considered the (1) birth weight, (2) breastfeeding (days of maternally reported breastfeeding) and (3) recent morbidity (days of maternally reported diarrhea) (3 or more liquid or semiliquid stools in the past 24 h or maternally reported fever) in the 21 days prior to the growth spurt.( 4) Breastfeeding (days of breastfeeding in the 21 days prior to the growth spurt) was included because there is evidence that breastfed children vary in body composition, and in the pattern of growth, compared to formula-fed infant (Lind et al., 2018).Almost all infants in our study began life breastfeeding but experienced variability in the age of weaning, while formula feeding was rare.To examine potential associations between the weight gain and linear growth, we also examined the (5) weight-for-age Z-score (WAZ), ( 6) subscapular-skinfold-for-age Z-score (SSZ), and ( 7) arm circumference-for-age Z-score (ACZ), measured 21 days prior to the saltation.Given prior reports that increases in weight precede increases in length (Dewey et al., 2005;Iannotti et al., 2012;Lampl et al., 2005;Richard et al., 2012), we also examined (7) the change in WAZ, (8) the change in SSFZ, and (9) the change in ACZ in the 21 days prior to the growth spurt (ΔWAZ, ΔSSFZ, ΔACZ, a positive value implying a recent increase in WAZ, SSQ, or ACZ).We chose to lag breastfeeding, illness, WAZ, SSFZ, and ACZ by 21 days based on the evidence of high-resolution studies of time to observable catch-up and catch-down growth following the initiation of growth-limiting medications in animal studies (Chagin et al., 2010) or among children initiating growth-supporting therapies (Greco et al., 1994).The models were also adjusted for child age and for time since the prior saltation.
For each variable of interest 1-9, first, a univariate hurdle model was constructed where a single exposure was considered as the variable of interest and the outcomes were both the odds of a saltation occurring, and, if it did, the magnitude of the saltation.In a second step, a multivariate model adjust for the variable of interest and child age, but no other covariates.In the final step, a full multivariable model based on inclusion of all remaining theoretically justifiable variables was constructed and then reduced to a final multivariable model with nonsignificant factors excluded.Given that ΔWAZ, ΔSSFZ, ΔACZ were correlated with one another, we compared model fit statistics (Akaike's information criteria) to choose to retain ΔACZ over ΔSSFZ or ΔWAZ in the tier 1 model (odds of a saltation occurring), and ΔWAZ over ΔSSFZ and ΔACZ in the tier 2 model (given that a saltation occurred, what was its magnitude).Hurdle regression models were implemented in Stata version 18.0 using the "craggit" command.

| RESULTS
A total of 61 children contributed between 35 and 135 measurements to the analysis (Table 1).The typical measurement was made in the late morning (around 11:00 a.m.) and the study technical error of measurement between the two technicians on any given day was 0.16 cm.The total number of measurements used in the analysis was 6040: 655 and 964 from 0 to 3 month old boys and girls respectively; 788 and 826 from 3 to 6 month old boys and girls respectively, 903 and 738 measures from 6 to 9-month-old boys and girls, and 534 and 632 measures from 9 to 12-month old boys and girls, respectively.The smaller number of measurements from 0 to 3 months reflect less data from the first weeks of life: the median age of enrollment was 4 days old, but 12 infants were enrolled after the were 10 days old, and four were enrolled after 30 days (three boys and one girl).The decreasing number of measurements at older ages reflected the fact that families were more likely to travel with older infants.
Approximately 1% (0.8%) of measures were made 1 day apart, 61.4% of measures were made 2 days apart, 30.7% were made 3 days apart, and 7.06% were made four or more days apart.The mean birthweight was 3.08 kg (SD 0.93), and the mean length for age Z score at birth À1.05 (SD 0.94); by 12 months of age the mean LAZ was À1.43 (SD 0.97), and 29.5% of the percent of children studied were stunted (LAZ <À2).
The mean birth weight of the sample was 3.08 kg (SD = 0.43), slightly below the Peruvian national average of 3.2 kg (Carrillo-Larco et al., 2021).Mean anthropometric measurements at 0, 6, and 12 months old are provided in Table 2. Children who were stunted at 12 months of age also had lower LAZ scores at birth (Table 3).Our first aim was to examine potential differences in overall growth profiles between children.
There was no difference in the timing or the magnitude of saltations when comparing children who were stunted at 12 months old to those who were not compared to children who were not.However, stunted children tended to have greater variability in the duration of stasis, and magnitude of growth salutations, compared to children who were not stunted at 12 months old (Table 3).There was also no difference in the magnitude of saltations when comparing children who experienced greater growth faltering (larger decline in LAZ) versus those who did not, however, the time between saltations was greater in children with a larger cumulative decline in LAZ (Table 4 and Table S1).
Our second aim was to test whether biological factors were associated with the timing of magnitude of growth saltations (aim 2).There were no statistically significance differences in the timing or magnitude of saltations between boys and girls (Table 5 and Table S2) Breastfeeding was associated with saltation likelihood and magnitude in unadjusted models, but this was attenuated after adjusting for age-associated decreases in the frequency and magnitude of saltation (Table 5).After adjusting for age, a greater positive ΔACZ in the 21 days prior, remained significantly associated with a greater odd of saltation (OR = 1.35, p < .001),while a larger ΔACZ was associated with a greater saltation magnitude (0.13 cm, p = 0 < .001).For reference, ΔACZ ranged from À0.32 (at the 5th percentile) to 1.27 (at the 95th percentile).
Comparing a child with a ΔACZ of 0.21 (one standard deviation above the mean) in the 21 days prior to a child with a ΔACZ of 0.21 (the mean) the odds of a saltation on a given day would increase by 16%, and the estimated magnitude of the saltation of would increase by 0.064 cm.Children with recent illness had a lower odds of saltation (OR = 0.98, p-value = .024),and this was attenuated after adjusting for ΔACZ in the 21 days prior.

| DISCUSSION
Understanding how short-term growth dynamics are altered among growth-faltering infants in resourcelimited setting may inform interventions to reduce the burden of stunting.We used a changepoint analysis approach to examine the short-term growth dynamics of Peruvian infants at risk of stunting.Our results (saltations of mean magnitude 0.97 cm, separated by periods of stasis of mean 13.7 days) are similar to those previously  T A B L E 3 Intervals between saltation events and the magnitude thereof from 0 to 12 months: comparsion of changpoint analysis results for stunted versus nonstunted children.published on similarly time-intensive data of infants of a similar age (Lampl et al., 1992;Lampl & Johnson, 1993).However, our estimate of stasis length, and saltation magnitude, are likely to be influenced both by greater measurement error than the data described in these prior publications, as well as differences in the changepoint detection method to identify saltations, so they should not be regarded as directly comparable.This analysis was enabled by high-resolution data, with no more than 7 days separating any two measurements.This enabled us to identify saltations while reducing the risk that multiple growth events might be conflated.
Although alterations in short-term growth among children with disorders affecting growth hormone production have been reported, less is known about the short-term growth of developmentally normal, healthy infants who experience growth faltering due to conditions of poverty.Our goal was to examine the extent to which growth faltering in this context is explained by (i) the changes in the duration of stasis periods, (ii) changes to the magnitude of saltations, or (iii) both.Regarding the former, we note that, as expected, children born smaller stayed smaller.However, we did not identify differences in their pattern of growth.We did observe that children with greater cumulative losses in LAZ in the first year of life had, on average, longer periods of stasis, compared to those whose LAZ was maintained.One study of weight and length dynamics comparing smalland appropriate for gestational age found shorter stasis periods, and lower magnitude, in the small for gestational age group (Gladstone et al., 1998).
There is growing evidence that variation in linear growth can largely be explained by energetic trade-offs involving routine immune activity (Urlacher et al., 2019) and that body fat plays a critical role in buffering linear growth against completing immune-related energetic demands (Urlacher et al., 2018).The associations we observe are consistent with these findings, as greater changes in body fat and body weight as measured by ΔACZ, ΔSSFZ, and by ΔWAZ in the 21 days preceding was associated with a higher odd of a growth saltation occurring, and a larger magnitude of growth.However, these associations may not necessarily be causal, and may, for instance, result from inadequate adjustment for age, socioeconomic status, or other factors that influence gains in weight and length independently of one another.Absolute ACZ was also associated with growth, but not as strongly as ΔACZ.Unexpectedly, sex was not associated with either the duration of stasis or the magnitude of saltations, as others have demonstrated with higher-resolution (daily) measurement data (Lampl et al., 2005).The relatively small number of infants in our sample may have caused us to be underpowered to identify these differences, or specific characteristics of our study population, such as higher mean LAZ scores among girls relative to boys (Table S2), may have obscured these differences.Our population also had a very low prevalence of underweight or wasting: the mean WAZ over the entire study period was À0.28 (SD = 1.14) and the mean WLZ was 0.59 (SD = 1.01).Therefore, our results may not be consistent with findings from other contexts, for example, populations with a higher burden of acute malnutrition.
Finally, it has been reported that children who ultimately become stunted may experience more variability in their length velocity over periods of $3 months (Cliffer et al., 2021), which suggests that periods of limited growth resulting from episodic insults, and periods of accentuated growth resulting from the need for catchup, may figure more prominently in the growth of these children.We also found evidence greater variability in the duration of stasis periods or magnitude of growth saltations between infants with or without stunting, although not for infants with or without cumulative growth faltering.
The major limitation of this analysis, not unique to us, is measurement error.Other limitations of our study include a relatively young population of infants 0 to 1 year of age, which limits our ability to investigate growth from 1 to 2 years of age-an age where substantial growth faltering occurs and where dynamics may differ compared to infancy-or during catch-up.An additional limitation is that our choice of a 21-day lag interval between potential exposure variables and saltation outcomes.We selected a three-week lag based on available literature (Chagin et al., 2010;Greco et al., 1994).Alternative approaches, such as selection of the lag period based on comparison of model fit, also have limitations in that they lack a biological basis and may increase the risk of false positives due to overfitting.However, given that the lag period we selected was based on studies of aberrant growth, it may be inappropriate to healthy children or cause relationships that are more dynamic than 3 weeks, or evolve over longer periods, to be obscured.
Characterizing short-term growth dynamics may help to describe the linkages between linear growth and biological factors such as intermittent hormone secretion, energy balance, and transient and chronic growthlimiting conditions, thus informing systems modeling of growth dynamics (Suki & Frey, 2017).This work informs our understanding of how oscillations in growth are altered among growth-constrained infants in resourcelimited setting.Longer-term longitudinal analyses will clarify these findings and illuminate the lasting impact of short-term growth dynamics on attained height.
Z-scores (LAZ) calculated from the World Health Organization reference standard (World Health Organization, 2006).T A B L E 2 Anthropometric status of study children at three ages.0 months a (N = 61) 6 months (N = 60) 12 months (N = 52) WAZ b ;

F
I G U R E 1 Growth curve of a sample child.Length data (in blue), estimated length based on changepoint analysis (in blue) for a single study child.Gaps in the smoothed data around $150 days old are a result of the missing data.For intervals with no missing data, saltations are indicated with red arrows.
Weight-for age Z-scores (WAZ), length for age Z-scores (LAZ), subscapular skinfold for age Z-scores (SSFZ), and MUAC-for-age Z-scores calculated from the World Health Organization reference standards(WHO Multicentre Growth Reference Study Group, 2007; World Health Organization, 2006).
a Anthropometry at 0 months was measured at enrollement into the MAL-ED study, which occurred on average 5 days after birth (range: 1 to 17).The birthweight, which is reported in the text, was based on the health facility record.Decreasing numbers are the result of cohort attrition.b Hurdle model for odds of saltation and magnitude of growth saltation.Hurdle models of saltation timing and magnitude.
T A B L E 4 T A B L E 5