"complaint by" is correct and usable in written English.
You would use it when introducing the name of a person who has made a complaint. For example, "The police are investigating a complaint by John Smith."
A doctor dismissed another's complaint by simply saying, "I'm important".
The complaint by Mr. Goodman's character is based in fact.
That inspired a formal complaint by Tulsa's athletic director.
"Stern," published in 1962, predates "Portnoy's Complaint" by five years.
The Penn complaint contains details not included in the initial complaint by the Abramson research institute.
The investigation came about as a result of a complaint by Reprieve first made last July.
The court order was in response to a complaint by three residents near the site.
After the complaint by Swedish Match, the commission asked the antifraud office to investigate.
BEHIND THE NEWS The case stemmed from a complaint by a former quality manager.
The headmistress dismissed the complaint by saying that it was homemade oil, Mr. Shahi said.
Both of the plaintiffs were held for about 30 hours, the complaint by Mr. Kuby said.
