PERSONALIZED TREATMENTS: SOUNDS HEAVENLY, BUT WHERE ON EARTH DID THEY FIND MY GUINEA PIGS?

XIAO-LI MENG – HARVARD UNIVERSITY

ABSTRACT

Are you kidding me? Surely no one should take personalized literally. Fair enough, but then how un-personalized is personalized? That is, how fuzzy should “me” become before there are enough qualified “me”s to serve as my guinea pigs? Wavelet-inspired Multi-resolution (MR) inference (Meng, 2014, COPSS 50^th Anniversary Volume) allows us to theoretically frame such a question, where the primary resolution level defines the appropriate fuzziness — very much like identifying the best viewing resolution when taking a photo. Statistically, the search for the appropriate primary resolution level is a quest for a sensible bias-variance trade-off:  estimating more precisely a less relevant treatment effect verses estimating less precisely but a more relevant treatment effect for “me.” Theoretically, the MR framework provides a statistical foundation for transitional inference, an empiricism concept, rooted and practiced in clinical medicine since ancient Greece. Unexpectedly, the MR framework also reveals a world without the bias-variance trade-off, where the personal outcome is governed deterministically by potentially infinitely many personal attributes. This world without variance apparently prefers overfitting in the lens of statistical prediction and estimation, a discovery that might provide a clue to some of the puzzling success of deep learning and the like (Li and Meng, 2021, JASA).