Estimating Craniofacial Growth Cessation: Comparison of Asymptote- and Rate-Based Methods

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

Research output: Contribution to journalArticlepeer-review


Objective: To identify differences between asymptote- and rate-based methods for estimating age and size at growth cessation in linear craniofacial measurements. Design: This is a retrospective, longitudinal study. Five linear measurements were collected from lateral cephalograms as part of the Craniofacial Growth Consortium Study (CGCS). Four estimates of growth cessation, including 2 asymptote- (GCasym, GCerr) and 2 rate-based (GCabs, GC10%) methods, from double logistic models of craniofacial growth were compared. Participants: Cephalometric data from participants in 6 historic longitudinal growth studies were included in the CGCS. At least 1749 individuals (870 females, 879 males), unaffected by craniofacial anomalies, were included in all analyses. Individuals were represented by a median of 11 images between 2.5 and 31.3 years of age. Results: GCasym consistently occurred before GCerr and GCabs consistently occurred before GC10% within the rate-based approaches. The ordering of the asymptote-based methods compared to the rate-based methods was not consistent across measurements or between males and females. Across the 5 measurements, age at growth cessation ranged from 13.56 (females, nasion-basion, GCasym) to 24.39 (males, sella-gonion, GCerr). Conclusions: Adolescent growth cessation is an important milestone for treatment planning. Based on our findings, we recommend careful consideration of specific definitions of growth cessation in both clinical and research settings since the most appropriate estimation method may differ according to patients’ needs. The different methods presented here provide useful estimates of growth cessation that can be applied to raw data and to a variety of statistical models of craniofacial growth.

Original languageEnglish (US)
JournalCleft Palate-Craniofacial Journal
StateAccepted/In press - 2021

Bibliographical note

Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported financially by the NIH award numbers provided.

Publisher Copyright:
© 2021, American Cleft Palate-Craniofacial Association.


  • cephalometry
  • craniofacial growth
  • craniofacial morphology
  • facial growth

PubMed: MeSH publication types

  • Journal Article


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