Estimation of data adaptive minimal clinically important difference with a nonconvex optimization procedure

Understanding the limitation of solely relying on statistical significance, researchers have proposed methods to draw biomedical conclusions based on clinical significance. The minimal clinically important significance is one of the most fundamental concepts to study clinical significance. Based on an anchor question usually available in the patients' reported outcome, Hedayat et al. presented a method to estimate minimal clinically important significance using the classification technique. However, their method implicitly requires that the binary outcome of the anchor question is equally likely, i.e. the balanced outcome assumption. This assumption cannot be guaranteed a priori when one designs the study; hence, it cannot be satisfied in general. In this paper, we propose a data adaptive method, which can overcome this limitation. Compared to Hedayat et al., our method uses a faster gradient based algorithm and adopts a more flexible structure of the minimal clinically important significance at the individual level. We conduct comprehensive simulation studies and apply our method to the chondral lesions and meniscus procedure study to demonstrate its usefulness and also its outperformance.