The phrase "based on the case of" is correct and usable in written English.
You might use this phrase in a variety of contexts, including when discussing a legal decision, a historical event, a scientific study, etc. Here is an example: Based on the case of Brown v. Board of Education, the Supreme Court ruled that segregated schools were unconstitutional.
However, the results are based on the case of one course at a single Japanese university, and the number of participants was not large.
"Tinker, Tailor" is partly based on the case of Kim Philby, one of a handful of British spies and Cambridge University alumni who were recruited by the Soviets in the 1930s.
He found out that both were based on the case of a treacherous wife, Ruth Snyder, and a hapless corset salesman, Judd Gray.
Nora Ephron's first screenwriting effort never saw the light of day: a polish on the script for All the President's Men, based on the case of her then-husband, Carl Bernstein.
It is based on the case of Lizzie Borden of Fall River, Mass., who was charged with killing her miserly father and sniping stepmother with an ax in 1892.
Officials say that Ukraine is being unfairly maligned in the West, largely based on the case of Ms. Tymoshenko, who they insist was legitimately convicted on charges related to the alleged rigging of natural gas contracts with Russia.
Its findings, based on the cases of 214,000 cancer patients aged 20 to 89, will prompt further work by health authorities on how to better engage Indigenous patients with services and treatment.
Based on the cases of our clinical practice, we describe the tips to facilitate the diagnosis of SIGBIC.
Thirdly, recent studies pointed at the "return of the port into the city" (El Hosni 2015), based on the cases of London, Taipei, Tokyo, and Osaka, where several factors1 combined to re-shift modern container terminals in the urban space.
The agreement between the assessments done with OCRA and ULRA was also analysed based on the cases of OCRA zones against ULRA's three-zone and six-zone systems (Kee and Karwowski 2007).
The Conjuring, for one, a movie based on the case files of well-known paranormal investigators Ed and Lorraine Warren, parallels the Warren's best-known cases.
