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Developmental trajectories of height, weight and BMI across childhood: Bayesian hierarchical modeling of longitudinal data

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Title: Developmental trajectories of height, weight and BMI across childhood: Bayesian hierarchical modeling of longitudinal data
Author(s): Kauppala, Tuuli
Contributor: University of Helsinki, Faculty of Science
Degree program: Master 's Programme in Mathematics and Statistics
Specialisation: Statistics
Language: English
Acceptance year: 2021
Children’s height and weight development remains a subject of interest especially due to increasing prevalence of overweight and obesity in the children. With statistical modeling, height and weight development can be examined as separate or connected outcomes, aiding with understanding of the phenomenon of growth. As biological connection between height and weight development can be assumed, their joint modeling is expected to be beneficial. One more advantage of joint modeling is its convenience of the Body Mass Index (BMI) prediction. In the thesis, we modeled longitudinal data of children’s heights and weights of the dataset obtained from Finlapset register of the Institute of Health and Welfare (THL). The research aims were to predict the modeled quantities together with the BMI, interpret the obtained parameters with relation to the phenomenon of growth, as well as to investigate the impact of municipalities on to the growth of children. The dataset’s irregular, register-based nature together with positively skewed, heteroschedastic weight distributions and within- and between-subject variability suggested Hierarchical Linear Models (HLMs) as the modeling method of choice. We used HLMs in Bayesian setting with the benefits of incorporating existing knowledge, and obtaining full posterior predictive distribution for the outcome variables. HLMs were compared with the less suitable classical linear regression model, and bivariate and univariate HLMs with or without area as a covariate were compared in terms of their posterior predictive precision and accuracy. One of the main research questions was the model’s ability to predict the BMI of the child, which we assessed with various posterior predictive checks (PPC). The most suitable model was used to estimate growth parameters of 2-6 year old males and females in Vihti, Kirkkonummi and Tuusula. With the parameter estimates, we could compare growth of males and females, assess the differences of within-subject and between-subject variability on growth and examine correlation between height and weight development. Based on the work, we could conclude that the bivariate HLM constructed provided the most accurate and precise predictions especially for the BMI. The area covariates did not provide additional advantage to the models. Overall, Bayesian HLMs are a suitable tool for the register-based dataset of the work, and together with log-transformation of height and weight they can be used to model skewed and heteroschedastic longitudinal data. However, the modeling would ideally require more observations per individual than we had, and proper out-of-sample predictive evaluation would ensure that current models are not over-fitted with regards to the data. Nevertheless, the built models can already provide insight into contemporary Finnish childhood growth and to simulate and create predictions for the future BMI population distributions.
Keyword(s): longitudinal modeling hierarchical linear models bayesian inference bivariate outcome growth modeling

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