The question is about the methodology/biostatistics of clinical trials (I state this beforehand to avoid accusations of being an anti-vaxxer).
As multiple anti-COVID vaccines are offered on the market, the question naturally arises about their long-term efficacy and possible side effects. As SARS-CoV-2 virus has been known for a bit more than a year, neither of these could be tested directly, so one probably has to rely on indirect knowledge due to the experience in developing other vaccines. Given that multiple vaccines have been approved for a wide use, there should exist well-established procedures to assure their efficacy and safety.
The question is: how does one prove the long-term efficacy and absence of side effects during a short period of time (short in comparison to the expected duration of immunity and absence of side effects).
As @MattDMo have correctly pointed in their answer, the absence of long-term effects is established in the last phase of the clinical trials, while observing cohorts of vaccinated individuals during a long period of time. @MaximilianPress, in their comment, has also correctly brought up the fact that this is done within the framework of survival analysis. In particular, this means that it is sufficient to follow the vaccinated cohort during several years to evaluate the side effects that occur during their lifetime, as the survival analysis keeps track of the sensored data.
Here we are dealing with a situation where such a study could not be done - the best we can guarantee is the absence of the side effects in the next few months. We thus need to rely on a different method, which would account for the similarity between the established and the new vaccines.
I am less concerned about the vaccine efficacy, since the inefficacy of vaccines is usually against different strains of virus, as is in the case of influenza and Dengue.
Update 2 The accepted answer points out two important things:
- The long-term side effects of a vaccine/medication can be truly understood only in the Phase IV of the clinical trials, i.e., after the vaccine is in widespread use.
- The threshold for approving this specific vaccine is lower due to the emergency of the current health crisis.
This however still leaves open the question of the safeguards undertaken in the Phase III of the clinical trials, before the vaccine approval. I.e., the question is about ranking the candidate vaccines against the above-mentioned threshold.
- I understand why this question irritates, but I believe that it is not the asking, but rather refusing to seek the answer that plays in the hands of anti-vaxxers.
- I did follow the suggestions in the comments to pose this question in the medical and the statistics communities, but it seems to get there even less traction.
Recent suspensions of Astrazeneca vaccine in 9 European countries demonstrate the importance of this issue.