Bayesian approach to longitudinal craniofacial growth: The Craniofacial Growth Consortium Study

Richard J. Sherwood, Hee Soo Oh, Manish Valiathan, Kieran P. McNulty, Dana L. Duren, Ryan P. Knigge, Anna M. Hardin, Christina L. Holzhauser, Kevin M. Middleton

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Early in the 20th century, a series of studies were initiated across North America to investigate and characterize childhood growth. The Craniofacial Growth Consortium Study (CGCS) combines craniofacial records from six of those growth studies (15,407 lateral cephalograms from 1,913 individuals; 956 females, 957 males, primarily European descent). Standard cephalometric points collected from the six studies in the CGCS allows direct comparison of craniofacial growth patterns across six North American locations. Three assessors collected all cephalometric points and the coordinates were averaged for each point. Twelve measures were calculated from the averaged coordinates. We implemented a multilevel double logistic equation to estimate growth trajectories fitting each trait separately by sex. Using Bayesian inference, we fit three models for each trait with different random effects structures to compare differences in growth patterns among studies. The models successfully identified important growth milestones (e.g., age at peak growth velocity, age at cessation of growth) for most traits. In a small number of cases, these milestones could not be determined due to truncated age ranges for some studies and slow, steady growth in some measurements. Results demonstrate great similarity among the six growth studies regarding craniofacial growth milestone estimates and the overall shape of the growth curve. These similarities suggest minor variation among studies resulting from differences in protocol, sample, or possible geographic variation. The analyses presented support combining the studies into the CGCS without substantial concerns of bias. The CGCS, therefore, provides an unparalleled opportunity to examine craniofacial growth from childhood into adulthood.

Original languageEnglish (US)
Pages (from-to)991-1019
Number of pages29
JournalAnatomical Record
Issue number5
StatePublished - Oct 12 2020

Bibliographical note

Funding Information:
American Association of Orthodontists Foundation, Grant/Award Number: Legacy Collection; National Institute of Dental and Craniofacial Research, Grant/Award Numbers: R01 DE024732, R01 DE024732‐06W1, R03 DE021435 Funding information

Funding Information:
The craniodental research programs of the studies that make up the CGCS have a long and storied history. We are grateful for the long‐term efforts of all the directors, investigators, and research staff for these studies and growth studies in general. These studies were supported by funding from a wide variety of sources over the years including private donations, institutional support, and the support of foundations and associations. Support for the Craniofacial Growth Consortium Study was provided by the National Institute of Dental and Craniofacial Research (NIH). Finally, we humbly acknowledge the dedication of the participants from each study. The participants and their families have rightfully earned a place of honor in the history of human growth and development.

Publisher Copyright:
© 2021 American Association for Anatomy


  • Bayesian inference
  • cephalometrics
  • craniofacial growth
  • double logistic
  • growth modeling


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