can I compare failure rates of two appliances in case I do not have an equal number of each? I am a student working on an original article about oral appliances that are place after the extraction of primary teeth in children. there are two variants of these appliances, fixed and removable.
I collected the data retrospectively (from 2019-2021), so I have no control of how many was placed and ended up with 345 fixed and 118 removables. I am to assess and compare the failure and survival rates of both groups. I cannot tell if it is a problem that I do not have an equal number of both appliances, if I can carry out a Kaplan-Meier survival rate analysis? and what would you recommend to do in this case?
If anyone could guide me or give me useful material to read, I would be very grateful.

There is no need to have equal numbers in both groups. Real-world survival data almost never ends up that way. Even in randomized trials that are designed to have equal numbers in each of two treatment groups, problems can lead to different numbers being analyzed between the groups.
If you just want to compare the two types of appliances without accounting for other variables, then Kaplan-Meier analysis is a good choice. If you want to account for other variables that might be associated with failure rates, then an extension to a survival regression model like Cox proportional hazards analysis would be called for.
The vignette provided by the R survival package is a pretty good place to start, illustrating concepts with the freely available software of the package. This page has some suggestions for other references on survival analysis, and there are nearly 3000 pages on this site with the survival tag.
