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Modelação estatística aplicada a dados cefalométricos
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Authors
Abstract(s)
Introdução: Este trabalho teve por foco o estudo dos Modelos Lineares Hierárquicos
(HLM- Hierarchical Linear Model) Longitudinais, visando uma aplicação a dados reais de
especial interesse no âmbito da Saúde Pública. Estes modelos revelam-se de particular
importância em contextos que exigem flexibilidade no tempo, permitindo a modelação de
alterações não lineares e descontínuas no tempo, o tratamento de espaçamentos desiguais de
pontos de tempo, bem como situações desequilibradas quanto ao número de observações por
indivíduo. Os modelos longitudinais HLM são muitas vezes descritos como modelos de
curvas de crescimento e fornecem uma estrutura que incorpora variáveis em cada nível do
modelo.
No âmbito da etiologia dos problemas ortodônticos, o papel da via aérea no crescimento e
desenvolvimento das estruturas craniofaciais tem sido amplamente debatido na literatura
científica. Na aplicação a dados reais, foi explorada a modelação da inclinação mandibular
em indivíduos em crescimento, considerando como preditores outras características crâniofaciais, faríngeas e postura crânio-cervical.
Materiais e Métodos: Foram realizadas medições angulares, lineares e de área referentes à
maxila, mandíbula, postura crânio-cervical e via aérea superior, no pré-pico, pico e pós-pico
de crescimento em 157 teleradiografias de indivíduos sem historial de tratamento
ortodôntico. A inclinação mandibular (ML/NSL) foi ajustada em função de outras variáveis
craniofaciais através de um modelo linear hierárquico (MLH) longitudinal. Foram avaliados
os pressupostos de linearidade, homocedasticidade e normalidade dos resíduos nas diferentes
hierarquias dos modelos, seguindo-se a pesquisa de observações influentes.
Resultados: O ajustamento do modelo nulo indicou que 72,6% da variabilidade de ML/NSL
pode ser explicada pela variância between-person, sendo relativamente estável ao longo do
tempo. Foram obtidos dois ajustamentos relevantes com intercepts e declives aleatórios para
a variável tempo. O ajustamento com MLH permitiu estimar componentes fixas e aleatórias
ao nível do indivíduo, assim como ao nível do instante temporal para ML/NSL. Permitiu
ainda estimar a influência de determinados preditores na taxa de variação de ML/NSL ao
longo do crescimento. Conclusões: Não foi encontrada uma relação significativa entre as dimensões sagitais da via
aérea e a inclinação mandibular, considerando dois ajustamentos de regressão multinível
aplicados a três instantes relevantes do crescimento. Recomenda-se a aplicação de técnicas
de modelação multinível que permitam incorporar as alterações fisiológicas das dimensões
faríngeas ao longo do crescimento e, assim, esclarecer melhor o papel da via aérea no
desenvolvimento das estruturas craniofaciais.
Introduction: This work focused on the study of Longitudinal Hierarchical Linear Models (HLM- Hierarchical Linear Model), aiming at an application to real data of special interest in public health. These models are particularly important in contexts that require flexibility in time, allowing the modeling of non-linear and discontinuous changes in time, the treatment of unequal spacing of time points, as well as unbalanced situations regarding the number of observations per individual. Longitudinal HLM models are often described as growth curve models and provide a framework that incorporates variables at each level of the model. In the context of the etiology of orthodontic problems, the role of the airway in the growth and development of craniofacial structures has been widely debated in the scientific literature. In the application to real data, the modeling of mandibular inclination in growing individuals was explored, considering as predictors other craniofacial and pharyngeal characteristics and craniocervical posture. Materials and Methods: Angular, linear and area measurements were performed concerning the maxilla, mandible, craniocervical posture and upper airway at pre-peak, peak and post-peak cephalograms in 157 individuals with no history of orthodontic treatment. Mandibular inclination (ML/NSL) was adjusted as a function of other craniofacial variables using a longitudinal hierarchical linear model (MLH). The assumptions of linearity, homoscedasticity and normality of residuals from different levels were evaluated, followed by the appraisal of influential observations. Results: The null model adjustment indicated that 72.6% of ML/NSL variability can be explained by the between-person variance, which indicates it is relatively stable over time. Two relevant adjustments with random intercepts and slopes were obtained for the time variable. Modelling with MLH allowed for the estimation of fixed and random components at the individual level, as well as at the time level for ML/NSL. The influence of certain predictors on the rate of change of ML/NSL throughout growth was also estimated. Conclusions: No significant relationship was found between the sagittal dimensions of the airway and mandibular inclination, considering two multilevel regression adjustments applied to three relevant moments of growth. The application of multilevel modeling techniques is recommended to allow the incorporation of physiological changes in pharyngeal dimensions during growth and, thus, better clarify the role of the airway in the development of craniofacial structures.
Introduction: This work focused on the study of Longitudinal Hierarchical Linear Models (HLM- Hierarchical Linear Model), aiming at an application to real data of special interest in public health. These models are particularly important in contexts that require flexibility in time, allowing the modeling of non-linear and discontinuous changes in time, the treatment of unequal spacing of time points, as well as unbalanced situations regarding the number of observations per individual. Longitudinal HLM models are often described as growth curve models and provide a framework that incorporates variables at each level of the model. In the context of the etiology of orthodontic problems, the role of the airway in the growth and development of craniofacial structures has been widely debated in the scientific literature. In the application to real data, the modeling of mandibular inclination in growing individuals was explored, considering as predictors other craniofacial and pharyngeal characteristics and craniocervical posture. Materials and Methods: Angular, linear and area measurements were performed concerning the maxilla, mandible, craniocervical posture and upper airway at pre-peak, peak and post-peak cephalograms in 157 individuals with no history of orthodontic treatment. Mandibular inclination (ML/NSL) was adjusted as a function of other craniofacial variables using a longitudinal hierarchical linear model (MLH). The assumptions of linearity, homoscedasticity and normality of residuals from different levels were evaluated, followed by the appraisal of influential observations. Results: The null model adjustment indicated that 72.6% of ML/NSL variability can be explained by the between-person variance, which indicates it is relatively stable over time. Two relevant adjustments with random intercepts and slopes were obtained for the time variable. Modelling with MLH allowed for the estimation of fixed and random components at the individual level, as well as at the time level for ML/NSL. The influence of certain predictors on the rate of change of ML/NSL throughout growth was also estimated. Conclusions: No significant relationship was found between the sagittal dimensions of the airway and mandibular inclination, considering two multilevel regression adjustments applied to three relevant moments of growth. The application of multilevel modeling techniques is recommended to allow the incorporation of physiological changes in pharyngeal dimensions during growth and, thus, better clarify the role of the airway in the development of craniofacial structures.
Description
Keywords
Modelo Linear Hierárquico Dados longitudinais Cefalometria Crescimento Via aérea Linear Hierarchical Model Longitudinal data Cephalometry Growth Airway
Pedagogical Context
Citation
Amorim, Mónica Isabel Tavares - Modelação estatística aplicada a dados cefalométricos [Em linha]. [S.l.]: [s.n.], 2022. 120 p.