@gojomo: Isn't it normally the case that an RCT follows an observational study? There's not much point in doing an observational study if someone's already done an RCT, but there is the other way round, since RCT's are more trusted.
Wrt publication bias; an underestimation of the false positive rate of observational studies wrt RCTs could occur if non-significant RCTs are being held back at a higher rate than observational ones, but it seems more likely to me that it's the other way around since RCTs are generally more expensive and time consuming than observational studies, and more trusted, so it's a bigger loss if the result isn't published.
I don’t have a sense of the ‘normal’; it might vary by field.
For example, for COVID vaccines, we’re being inundated with observational data - often informal, sometimes in reviewed studies - long after initial approval RCTs.
Wrt publication bias; an underestimation of the false positive rate of observational studies wrt RCTs could occur if non-significant RCTs are being held back at a higher rate than observational ones, but it seems more likely to me that it's the other way around since RCTs are generally more expensive and time consuming than observational studies, and more trusted, so it's a bigger loss if the result isn't published.