This is a classic case of spelling difference between American English and British English.
Etiology or aetiology is most commonly used as a medical term for the cause of a certain disease. It is also the name of the field of medicine focused on finding the cause of conditions or diseases.
Outside the United States we find aetiology, aetiologies, aetiologic, aetiological, and aetiologically.
Using as a case study Robert Burton’s 1621 book, The Anatomy of Melancholy, Kendler observed that before the middle of the 19th century, mental disorders were not thought to have a single, clear aetiology; on the contrary, Burton provides a mind-boggling list of possible causes for melancholy. [Practical Ethics]
In their paper, published in BMC Veterinary Research, they explain that C. pseudotuberculosis is the aetiological agent of caseous lymphadenitis, a common disease in small ruminant populations throughout the world and responsible for a significant economic impact for producers. [The Pig Site]
And inside the United States we have etiology, etiologies, etiologic, etiological, and etiologically.
About Gelclair® (Bioadherent oral rinse gel)Gelclair® is an easy-to-use bioadherent oral rinse gel indicated for the management and relief of pain of various etiologies, including oral mucositis/stomatitis, irritation due to oral surgery, ulcers caused by braces or ill-fitting dentures, certain systemic diseases, and for diffuse aphthous ulcers. [CNN Money]
“An improved understanding of the etiologic underpinnings of SUD and ADHD is crucial and will have important clinical and public health implications,” the investigators write. [Medscape]
The researchers concluded, “Because bone turnover has been implicated as a significant etiological factor for bone loss, these findings raise the interesting possibility that oral magnesium supplementation may have beneficial effects associated with high bone turnover, such as age-related osteoporosis.” [Prohealth]
It is unclear why NT-proBNP should be predictive of the primary endpoint components, especially those not clearly etiologically related to this physiology, such as hemorrhagic stroke,” they wrote in a related editorial. [Healio]