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REVIEW ARTICLE
Year : 2021  |  Volume : 11  |  Issue : 4  |  Page : 262-266

Statistical Models for Estimating Linear Growth Velocity: A Systematic Review


1 African Centre of Excellence in Data Science (ACE-DS), University of , Kigali; Centre for Infectious Disease Research in , Lusaka, Zambia, Rwanda
2 Centre for Infectious Disease Research in Zambia, Lusaka, Zambia
3 5College of Science and Technology, University of Rwanda, Kigali, Rwanda
4 Aga Khan University Hospital, Karachi, Pakistan
5 Centre for Infectious Disease Research in Zambia, Lusaka; Department of Biostatistics, School of Public Health, University of Ghana, Legon Accra, Ghana, Zambia

Date of Submission01-Mar-2021
Date of Decision07-Mar-2021
Date of Acceptance12-Jun-2021
Date of Web Publication26-Oct-2021

Correspondence Address:
Obvious N Chilyabanyama
Centre for Infectious Disease Research in Zambia (CIDRZ), PO Box 34681, Lusaka
Rwanda
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Source of Support: None, Conflict of Interest: None


DOI: 10.4103/ijnpnd.ijnpnd_6_21

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   Abstract 


Poor linear growth among infants is still a global public health issue. Linear growth velocity has been variously suggested as a more robust measure for growth over the classical measure of attained height for age. In this study, we systematically reviewed available literature for models used in estimating linear growth velocity. We searched Medline, Embase, Cochrane methodology register, Joanna Briggs Institute EBP, through the Ovid interface, and PubMed database to identify relevant articles that used statistical models to estimate linear growth velocity among infants. Longitudinal studies published in English were included. Two reviewers independently screened the titles and abstracts to identify potentially eligible studies. Any disagreements were discussed and resolved. Full-text articles were downloaded for all the studies that met the eligibility criteria. We synthesized literature using the preferred reporting items for systematic review and meta-analyses guidelines for the most used statistical methods for modelling infant growth trajectories. A total of 301 articles were retrieved from the initial search. Fifty-six full-text articles were assessed for eligibility and 16 of which were included in the final review with a total of 303,940 infants, median sample size of 732 (interquartile range: 241–1683). Polynomial function models were the most used growth model. Three (18.8%) of the articles modelled the linear growth. Two (12.5%) articles used mixed-effects models and another two (12.5%) used the Jenss-Bayley growth models to model linear growth. Other models included residual growth model, two-stage multilevel linear spline model, joint multilevel linear spline model, and generalized least squares with random effects. We have identified linear mixed-effects models, polynomial growth models, and the Jenss-Bayley model as the used models for characterizing linear growth among infants. Linear mixed-effects model is appealing for its robustness even under violation of largely robust even to quite severe violations of model assumptions.

Keywords: Growth velocity, infants, jenss-bayley models, linear mixed-effects models, polynomial models


How to cite this article:
Chilyabanyama ON, Chilengi R, Ngaruye I, Iqbal NT, Bosomprah S. Statistical Models for Estimating Linear Growth Velocity: A Systematic Review. Int J Nutr Pharmacol Neurol Dis 2021;11:262-6

How to cite this URL:
Chilyabanyama ON, Chilengi R, Ngaruye I, Iqbal NT, Bosomprah S. Statistical Models for Estimating Linear Growth Velocity: A Systematic Review. Int J Nutr Pharmacol Neurol Dis [serial online] 2021 [cited 2021 Dec 6];11:262-6. Available from: https://www.ijnpnd.com/text.asp?2021/11/4/262/329206




   Background Top


Poor linear growth among infants is still a global public health issue. In 2018, the global prevalence of stunting was estimated to be 22.2%, corresponding to approximately 150.8 million in children under five, and in Africa, it is estimated to be about 30.3% accounting for about 58.7 million children under five.[1] The prevalence of stunting varies by world region with the highest prevalence in Africa. The global and regional prevalences of stunting are classified as high and very high, respectively, by the World Health Organization classification.[2],[3] Poor linear growth has short- and long-term effects on children’s cognitive impairments, delayed motor skill development, impaired brain function, poor school performance, morbidity, and mortality.[1],[4] Studies have shown that children who are stunted are more likely to die compared to those who are not.[5],[6]

The accurate monitoring of linear growth in infants is essential for assessment of health status, identifying deviations from normal growth and determining the effectiveness of interventions. The classical measure of linear growth has been “attained height or length for age” z-score (HAZ). Infant growth has a complex trajectory and under adequate nutrition, it decelerates initially until first year and tapers off gradually until the second year of life. When there is growth problem due to inadequate nutrition, the HAZ may be missed out in picking this problem. Linear growth velocity has been variously suggested as a robust measure.[7],[8],[9] Examining linear growth velocity leads to early detection of growth-related problems compared to HAZ.[10]

Growth velocity models provide a useful tool for monitoring growth, assessing infant’s nutritional problems, and may signal optimal time for interventions to prevent malnutrition.[11] Several statistical models exist and they differ in complexities.[12] In this study, we aimed to systematically review available literature for models, which are used for estimating linear growth velocity.


   Methods Top


Search strategy and selection criteria

The review was based on the preferred reporting items for systematic review and meta-analyses guidelines.[13] We searched Medline, Embase, Cochrane methodology register, Joanna Briggs Institute EBP, through the Ovid interface, and PubMed database to identify research articles that used statistical and mathematical models to estimate linear growth velocity. The search terms were medical subject heading terms, including linear growth velocity terms (“growth velocity,” “linear growth velocity,” “linear growth retardation,” “weight/height changes,” “z-scores”) and terms for statistical models (“statistical model,” “statistical method,” “mathematical model,” “mathematical method,” “growth model”). The full search strategy for Ovid platform is provided in Supplementary Table S1. The Ovid search strategy was adapted for PubMed. The date of publication of the articles was not limited to any time boundary.

We screened the titles and abstracts of identified articles for duplicates and eligibility. We included articles if they were original research articles in peer-reviewed journal published in English and longitudinal studies (cohort studies; randomized controlled trials) that modeled growth velocity as the outcome regardless of the intervention. Only studies on children under 24 months were included. We excluded studies that focused on plants and animals. We also excluded case series reports, reviews, and short latter publications. Two reviewers (ONC and SB) independently screened the titles and abstracts to identify potentially eligible studies. Any disagreements were discussed and resolved accordingly. Full text was downloaded for all the articles that met the eligibility criteria for citing.

Data synthesis

Two reviewers (ONC and SB) independently extracted relevant data using standardized data extraction form. Any discrepancies were discussed and resolved. For each study, we extracted the statistical methods used, the sample size, and the country in which the study was conducted. We reported the frequency of use of each statistical method used to describe linear growth in the articles.


   Results Top


Characteristics of included studies

A total of 301 articles were retrieved from the initial search. After removing duplicates, 271 unique articles were considered for possible inclusion in the review [Figure 1]. The duplicates were same articles but identified in multiple search databases. A total of 215 articles, which were not related to the topic, were screened out. The remaining 56 full-text articles were assessed for eligibility and 16 of which were included in the final review [Table 1].
Figure 1 Flow chart of study selection for the systematic review

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Table 1 Characteristics of articles reviewed

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Ten (62.5%) of the studies included in this review were conducted in developed countries, whereas six (37.5%) were in lower-middle-income countries. Only one (6.3%) study was conducted in the sub-Saharan region. The 16 articles reviewed included a total of 303,940 infants with a median sample size of 732 (interquartile range: 241–1683).

All the studies included in this review were followed-up studies that collected anthropometric data over time prospectively or retrospectively. We considered studies that had a short follow-up period of collected data in shorter intervals. The minimum follow-up period was 4 months and the maximum follow-up period was 24 months. Height, weight, and head circumference were the most common parameters collected. These measurements were either modeled as they were or they were standardized and modeled as z-scores.

Linear growth velocity models

Polynomial function models were the most used growth models: three (18.8%) of the articles modeled linear growth; two (12.5%) articles used mixed-effects models; and another two (12.5%) used the Jenss-Bayley growth models to model linear growth. Other models used to describe linear growth were super imposition by translation (SITAR), growth mixture models, count and Guo functions, and conditional random slope. The rest were lowess curves, exponential methods, two points methods, residual growth model, two-stage multilevel linear spline model, joint multilevel linear spline model, generalized least squares with random effect, and Rohrer ponderal index.


   Discussion Top


Our review identified the nth order polynomial functions, mixed-effects models, and the Jenss-Bayley growth models as commonly used methods for modeling growth velocities. The choice of these models is largely guided by the objective of the study and the data available. For instance some studies maybe carried out to provide surveillance, and understanding linear growth etiology, whereas others maybe conducted to predict growth velocities.[30] Often, the postulated relationship between height and time also informs the decision for which method to use.

Mixed-effects models are appealing for modeling child growth because in addition to population level estimation, they also provide insight on child-specific growth trajectories through the random components. They also allow for sparse sampling because the structural equations are based on data from participants. Mixed-effects models have a variant of models that make them robust to model the nonlinear trajectories of growth.[31],[32] They do not require balanced data, which makes it suitable for longitudinal data that usually have missing values at some observation time points. In addition, mixed-effects models support several variance–covariance structures of the residuals, thus allowing flexibility for different types of data structures such as clustering and time-varying covariates. The assumption of normality and randomness in the missing values are the major shortcomings of this model. Once these assumptions are violated, the model becomes less robust.[33],[34]

Polynomial growth functions of nth order are highly suitable to model nonlinear relationships that exist between age and child’s height. Overtime the relationship between a child’s growth and age may change shape,[35] but these models would still be robust because of their flexibility, simple form, and low computational cost. Polynomial models work well on any size of data, and this makes them a good model in lower-middle income country (LMIC) where longitudinal data maybe scanty.

Applying the three commonly used models to empirical anthropometric data of infants would enable comparison of model robustness. This would enable researchers pick the best performing model based on the Bayesian information criteria, Akaike information criteria, and mean square error; all these are not reported in the studies included in this review. Further we note that none of the included studies used machine learning techniques to characterize linear growth among infants.

Despite the importance of characterizing linear growth, there is no standardized method that can be used to characterize linear growth. There is no agreement among researchers on which methods are most robust for modeling linear velocity among infants. Although some researchers argue that the Jenss-Bayley model and polynomial growth models are inadequate for modeling linear growth in infants, others argue for its robustness and adequacy.[36],[37],[38] The robustness of the models also depends on the population being studied. For example, some models may be robust to infant population and yet perform poorly in older children or adult population because growth trajectories may vary with age. In the early days of life, growth maybe exponential and in older ages, it maybe linear.

Although several literature exist for child growth modeling, we need to recognize that predicting child-specific growth trajectory remains a methodological problem. Estimating population level parameters is straightforward in large studies. However, child-specific estimation problems are more complicated as it requires high level of technical details. Addressing child-specific growth retardation would require having to pay attention to the various choices for the variety of applications. Our review adds to the literature by pooling together existing statistical models for characterizing child growth trajectory.


   Conclusion Top


In our review, we have identified linear mixed-effects models, polynomial growth models, and the Jenss-Bayley model as the most commonly used models for characterizing linear growth among infants. Linear mixed-effects model is appealing for its methodological properties.

Financial support and sponsorship

I wish to Acknowledge the world bank centre of excellence in Data Science for sponsoring my studies.

Conflicts of interest

There are no conflicts of interest.



 
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