  In clinical research, the effect of a treatment or intervention is widely
assessed through clinical importance, instead of statistical significance. In
this paper, we propose a principled statistical inference framework to learning
the minimal clinically important difference (MCID), a vital concept in
assessing clinical importance. We formulate the scientific question into a
novel statistical learning problem, develop an efficient algorithm for
parameter estimation, and establish the asymptotic theory for the proposed
estimator. We conduct comprehensive simulation studies to examine the finite
sample performance of the proposed method. We also re-analyze the ChAMP
(Chondral Lesions And Meniscus Procedures) trial, where the primary outcome is
the patient-reported pain score and the ultimate goal is to determine whether
there exists a significant difference in post-operative knee pain between
patients undergoing debridement versus observation of chondral lesions during
the surgery. Some previous analysis of this trial exhibited that the effect of
debriding the chondral lesions does not reach a statistical significance. Our
analysis reinforces this conclusion that the effect of debriding the chondral
lesions is not only statistically non-significant, but also clinically
un-important.
