Self controlled case series method is used to compare the outcome in a single group esp in vaccine research, the comparison group being the outcomes in risk period and control period, if I understood correctly. Is it a methodologically sound method and can it be applied in other scenarios?
It depends on the situation. I cannot speak about the vaccine setting you are refering to.
The worst scenario for applying this that I can think of is something like this: We want to test some intervention in patients with some chronic disease that tends to fluctuate over time. We include those with a minimum of X events of some type (e.g. hospitalization, relapses or something like that) in the previous year in our study. We look at whether in the next year the number of events is lower. That kind of study is often pretty meaningless, because regression to the mean happens and patients were bound to have fewer events even without intervention. You can try do better by trying to establish what would have happened when selecting patients like that (e.g. by looking at external/historical controls - still much harder to get sound comparisons than in a randomized study), but that’s not what people that run many of these “self-controlled” studies do.
Okay, maybe I can do worse than the above: I recruit patients who have bad symptoms from the common cold, assess their symptoms with a questionnaire that asseses cold symptoms, give than some intervention, and then apply the same questionnaire again 14 days later. I would assume nobody would believe that my intervention “cures” you of the common cold just because for nearly all patients the symtpoms after the intervention have more or less disappeared.
Best case scenario when this is very compelling: huge effect of intervention and we know patients should not (or are at least extremely unlikely to change state on their own). Example: First use of insulin (see e.g. https://www.diabetes.org.uk/about_us/news_landing_page/first-use-of-insulin-in-treatment-of-diabetes-88-years-ago-today) - there the effect was so clear (see also the Bradford-Hill criteria) that a formal analysis using historical/external controls was not really needed.
In short, the key question is whether you know what would have happened without the intervention and whether what happens with the intervention is so different that you can be pretty sure it was due to the intervention. Sometimes you may be able to credibly argue that what you observed in a time period without intervention would more or less be what you should see in other time periods (some variation over time periods is presumably to be expected, but if what you see with treatment by far exceeds the possible chance variation, then that can be convincing).