@TimHarford points to Slate on the risks and benefits of amniocentesis. In short, the standard recommendation is all wrong: it should be more recommended for younger than for older women. Why? Even though risk of genetic defects among older women is higher, the costs of a miscarriage are also higher because it gets harder to have a new pregnancy if the amnio fails.
I'd put together some expected value tables for amnio in case it were needed our last time round. The obstetrician seemed a bit surprised, but it wasn't the first or the last time I'd do something shockingly economistic.
I'm not going to here reproduce the expected value tables lest I attract pitchforks and torches. The Slate article covers most of it and helpfully links to an economics working paper that uses a rather fancier model than I worked up: they use a dynamic model that incorporates the chances of amnio on a replacement pregnancy where I simplified by just assuming an average expected value replacement. It's nice that this working paper's out there though - it'll save others from having to hack out their own simpler versions and might help improve doctors' recommendations.