An asymptotically normal representation for the minimal clinically important difference under a nonconvex surrogate loss

In clinical research, the effect of a treatment or intervention is widely assessed through clinical importance, instead of statistical significance. In this paper, we study an asymptotically normal representation for the minimal clinically important difference (MCID), a vital concept in assessing clinical importance. We formulate the scientific question into a 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 with the patient-reported pain score change as the primary outcome. The ultimate goal of this trial 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 in that the effect of debriding the chondral lesions is not only statistically nonsignificant, but also clinically un-important.