As this is not a dental professional blog, I would like to define Orthodontics.
Orthodontics is the art and science concerned with the treatment of malocclusion. I can confidently say that the real start for Orthodontics sciences was based on a simple form of data analytics. Angle (a dentist) declared his six keys for normal occlusion after analyzing records for the relation between upper and lower jaws for many patients.
Although we can not consider this number of records as “big data” especially if we applied the 4V‘s concept here, but still it is a sort of data analytics. The analysis Angle performed resulted in concluding the standard keys for normal occlusion.
Orthodontics and Epidemiology
It is a start similar to that of Epidemiology, when John Snow analyzed the data of many deceased persons during London Cholera epidemic. It was the time to discover Cholera and at the same time to establish the basis for Epidemiology and Public Health sciences.
There are different types and categories of malocclusion and accordingly different techniques for treatment (removable, fixed, different types of wires, different types of braces, clear aligners, functional appliances and headgears). The most important question that big data analytics can help with is “what is the best line of treatment for this case of malocclusion?”
The role of the Big Data Revolution
The Clinical Orthodontics Practice Study Journal performs hundreds of surveys and analyses in order to improve the quality of care and to establish best practices guidelines for every clinical case.
The great evolution in using the Electronic Health Records (EHRs) and the synchronous emergence of “cloud storage” as a mean for huge data storage played an important role in pushing orthodontics research forward.
The target of big data analysis in orthodontics is not limited only by choosing the proper line of treatment or establishing best practices guidelines. Big data analytics in Orthodontics can answer a lot of research questions like “is there a relation between orthodontic extraction and obstructive sleep apnea?”.
It can be used also to detect fraud in healthcare insurance claims or assessing the success rate for a specific governmental healthcare plan.
For example, NHS used big data analytics to analyze the results of their orthodontic treatment plans which started in 2010 and over a five year period in England and Wales. NHS were able to filter out fraud cases, how many cases started and did not complete the treatment and how many cases were misdiagnosed. They were able to analyze 150 thousand cases for ages 11-17 and with a known treatment outcome. 
Big data is also playing an important role in the academic life in the field of Orthodontics as an aid-tool for education.
Jacksonville University established an orthodontics data research registry and repository in order to offer the students, researchers and the academic staff a centralized orthodontics database for clinical information. The data is supposed to be used in research, academic presentations, and publications.
References: Berger C. Oracle Advanced Analytics for Anomaly Detection and Fraud Information Services and the Data Lab. 2015.