Analysis of longitudinal jaw growth data to study sex differences in timing and intensity of the adolescent growth spurt for normal growth and skeletal discrepancies

  • Satpal S Sandhu

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The upper jaw (maxilla) and the lower jaw (mandible) grow in a downward and forward direction resulting in normal skeletal jaw relationship (Class I) with normal anteroposterior (upper and lower jaw length) and vertical (total face height) growth changes. An excessive or deficient growth in either jaw or both jaws result in skeletal malocclusions (Class II and Class III) characterized by anteroposterior and vertical skeletal discrepancies. Studying timing and intensity of the adolescent growth spurt is essential for the successful correction of skeletal malocclusions. A natural approach to estimation of timing (age at peak growth velocity, APGV) and intensity (peak growth velocity, PGV) involves fitting growth curve models (GCMs) and estimating derivatives.

Different linear mixed effects (LME) and nonlinear mixed effects (NLME) GCMs have been successfully applied to height data for estimating timing and intensity of the adolescent growth spurt. However, a systematic review of the literature (database searched until December 31, 2016) showed that studies applying GCMs to longitudinal jaw growth data focused exclusively on conventional polynomial based linear GCM. Furthermore, none of the previous studies simultaneously compared anteroposterior and vertical growth changes between normal skeletal jaw relationship and skeletal malocclusions.

In this thesis, I explored the potential of three LME and two NLME GCMs for studying jaw growth data available from the American Association of Orthodontists Foundation (AAOF) Craniofacial Growth Legacy Collection. Data comprised of repeated growth measurements of upper and lower jaw length and total face height on 128 males (mean age 11.67 years, standard deviation 2.92) and 139 females (mean age 11.60 years, standard deviation 2.88) between seven and 18 years of age. The LME models included were the conventional polynomial (CP), fractional polynomial (FP), and restricted cubic spline (RCS). The NLME models studied were the super imposition by translation and rotation (SITAR) and Preece-Baines (PB). The research goal was to first evaluate and compare the fit of LME and NLME GCMs and then apply the best fitting linear or nonlinear GCM to the jaw growth data for studying class differences in the timing and the intensity of adolescent growth spurt between normal skeletal jaw relationship and skeletal malocclusions (i.e., Class I vs Class II, Class I vs Class III, and Class II vs Class III) for males and females.

In the first of the three research studies which make up this thesis, a simulation study was conducted to evaluate and compare the performance of popular information criteria (Akaike information criterion, AIC; Bayesian information criterion, BIC) and prediction criteria (measure of variance explained, R2; concordance correlation coefficient, CCC) for selecting the optimal functional form for GCMs. I restricted attention to CP GCM in this study. Balanced and unbalanced data were simulated and analysed for different sample sizes and varying model complexity. Different versions of the restricted maximum likelihood (REML) based AIC and BIC were calculated to study the effect of different penalty adjustments on their performance. The AIC and BIC which included the total number of model parameters in their penalty terms performed at least as well and often better than their counterparts which included only the number of variance-covariance parameters. Both AIC and BIC performed consistently better than the prediction criteria in selecting the true model. Amongst the two information criteria, AIC performed better than BIC especially when sample size was small, and the model involved a complex variance covariance structure.

In the second research study, the AIC was then used to compare the fit of covariate adjusted CP, FP, RCS, SITAR and PB GCMs fitted to the upper jaw length, lower jaw length and total face height measurements (hereafter referred as outcomes). Data were analysed separately for males and females. Each GCM was fitted by including all possible individual-specific random effects. In addition to fit to the data, I also compared GCMs in terms of their ability to estimate covariate adjusted growth trajectories (distance, velocity and acceleration) and adolescent growth spurt parameters (APGV and PGV). The PB model failed to converge for any of the three outcomes for both sexes. Results showed that unlike RCS and the SITAR GCMs, both CP and FP GCMs estimate biologically implausible growth trajectories (negative growth velocity). The RCS GCM fitted best to the data (as measured by the AIC) and therefore was selected for answering the clinical research questions in the final research study.

In the final research study, the RCS GCM was then used to estimate class differences in growth trajectories and the adolescent growth spurt parameters for males and females. Results showed sex differences in the timing and the intensity of adolescent growth spurt for normal growth and skeletal malocclusions. Females, on average, experience a less intense adolescent growth spurt which occurs almost one and half year earlier than males. Results indicated that an early but less intense growth spurt in the upper jaw length and the lower jaw length is mainly responsible for the development of anteroposterior (upper and lower jaw length) and vertical (total face height) skeletal discrepancies for Class II and Class III skeletal malocclusions. The clinical implications of the research findings are discussed.
Date of Award23 Jan 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SponsorsEconomic and Social Research Council
SupervisorGeorge B Leckie (Supervisor), Kate M Tilling (Supervisor) & Rach Hughes (Supervisor)


  • Growth Curve Model
  • Longitudinal data
  • Jaw growth

Cite this