In a very general sense, what are the different ways in which a retrospective observational study can be made to be robust?
Cross-validation? Well-defined exposures? etc.
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The weakness of observational studies is the lack of randomization. The best way to make these studies valid (not biased), is to do them by matching cases to controls through methods such as propensity scoring. This makes each experimental case very similar to its control case in terms of the various covariates that are expected to affect the response (e.g. age, gender, status etc). My assumption is that you are using the term robust to mean close to unbiased which a randomized control study would be.