"Studies of one" are also known as case studies, N-of-1 studies or case reports. I will refer to them below as case reports, for simplicity. They vary in quality just like any other type of studies. Case reports have a place in biomedical research and can often be very valuable, widely cited and/or otherwise influential. Double-blind randomized controlled clinical trials (RCTs), or, better, meta-analysis of multiple such trials, are the current gold standard. But they are obviously not always feasible for a variety of reasons.
There are specific guidelines for writing case reports, for example:
Riley D.S., et al (2017) J Clin Epidemiol. 89:218-235. doi: 10.1016/j.jclinepi.2017.04.026. CARE guidelines for case reports: explanation and elaboration document. https://www.sciencedirect.com/science/article/pii/S0895435617300379
This above article also lists a number of peer-reviewed journals that explicitly accept case reports (Table 1), important historical examples of case reports (section 1.1), and different types of case reports with specific examples (section 2).
Types of case reports:
Research where the number of patients is limited for any reason. For example, research conducted the beginning of a potential disease outbreak, research on uniquely informative patients, reports of rare drug side effects, drug-drug and food-drug interactions. Others in this thread have also listed rare condition treatment and emerging phenomena.
Research that carries high cost. For example, whole genome or whole exome sequencing when those studies were still very expensive.
Research that cannot be applied in RCT for any reason, such as limitations of input, treatment scarcity, ethical considerations, etc.
Specific examples and references:
- Chen H., et al (2014) Lancet. 383(9918):714-21. doi: 10.1016/S0140-6736(14)60111-2. Clinical and epidemiological characteristics of a fatal case of avian influenza A H10N8 virus infection: a descriptive study. https://www.sciencedirect.com/science/article/pii/S0140673614601112
We report the first human infection with a novel reassortant avian
influenza A H10N8 virus.
- Byun M., et al. (2010) J Exp Med. 207(11):2307-12. doi: 10.1084/jem.20101597. Whole-exome sequencing-based discovery of STIM1 deficiency in a child with fatal classic Kaposi sarcoma. http://jem.rupress.org/content/207/11/2307.long
Whole-exome sequencing-based discovery of STIM1 deficiency in a child
with fatal classic Kaposi sarcoma.
- Garrett-Bakelman F.E., et al. (2019) Science. 364(6436). pii: eaau8650. doi: 10.1126/science.aau8650. The NASA Twins Study: A multidimensional analysis of a year-long human spaceflight. https://science.sciencemag.org/content/364/6436/eaau8650.long
[...] significant changes in multiple data types were observed in
association with the spaceflight period; the majority of these
eventually returned to a preflight state within the time period of the
study. These included changes in telomere length, gene regulation
measured in both epigenetic and transcriptional data, gut microbiome
composition, body weight, carotid artery dimensions, subfoveal
choroidal thickness and peripapillary total retinal thickness, and
Addressing your specific questions about "studies of one", N=1 studies, case studies, or case reports:
What does the academic medical field think of this type of paper?
It depends on the field, and the quality of the specific study, and can vary a lot between respected, influential, etc, and irrelevant, not even acceptable for publication in high quality journal.
Can such a paper be a good paper?
Yes, again, depending on the field, and the quality of the specific study.
Is it usually considered a "bad paper", when compared to a paper that
has e.g. many patients that received the same treatments, where
variations and complications are discussed?
All other things being equal, obviously a case study with N=1 would be inferior to a study with multiple independent patients. In cases like this, N=1 papers would have a hard time getting through peer review in high quality journals, because the reviewers are likely to be aware of the current standards in that specific field, such as RCTs, epidemiological or association studies. I doubt N=1 study on the effects of a well-known statin on cholesterol would be published, if multiple double-blind RCTs are already available on orders of magnitude more patients.
Is this sort of paper simply part of the cutting edge of medical
science, that all results are useful?
In the context of this question, one can assume that a high quality case study is indeed "cutting edge", and there is a reason why N=1 was the best one could get at the time.