Cenyu Shen and Bo-Christer Björk have published "'Predatory' Open Access: A Longitudinal Study of Article Volumes and Market Characteristics" in BMC Medicine.
Here's an excerpt:
Despite a total number of journals and publishing volumes comparable to respectable (indexed by the Directory of Open Access Journals) open access journals, the problem of predatory open access seems highly contained to just a few countries, where the academic evaluation practices strongly favor international publication, but without further quality checks.