Hello. This is more a theoretical question.I've just start studying biostatistics and I'm having some doubts. I'm focusing in case-control studies.

First, the classical result from Anderson (1972) and Prentice and Pike (1979) says that the case-control study when a logistic model is being used can be viewed as a prospect study, the case-control character can be ignored.

After reading that I thought everything was done, there was nothing more to study. According to that result you can estimate your coefficients (apart from the intercept) and they are likelihood estimates. But no... There are many other ways of dealing with case-control studies, such as Weighted Likelihood, Pseudo Likelihood, Semi-parametric Likelihood... but why?

Is there a limitation on that result obtained by Anderson? Are this new methodologies broader? Or they are "just" trying to estimate the coefficients more efficiently?

One last question: when I use softwares (such as R, or others) what methodology do they use to make a logistic regression of a case-control study?