For example, let's say there is a test that checks for a birth defect that must be treated or it will result in infant mortality. Let's also say that the test causes infant mortality one time in 10,000. Whether you perform the test has to do with the statistical likelihood that the fetus will have the birth defect - if the likelihood is less than the probability of the test killing the baby then you shouldn't do it.
On this topic, I recently realized the dangers in trying to propagate "evidence-based" throughout all sectors of healthcare. A nurse was complaining about a doctor questioning if a certain drug was safe for breast-feeding women (well for the child, actually). Indignantly, the nurse said "but this manual right here says it's safe! How much more evidence-based can it get!". To her, "the book says so" was "evidence". 'Evidence-based medicine' is no panacea - the principles maybe, but the hard part is in the implementation.