In recent years, the minimal clinically important difference (MCID) has gained a lot of attention as a useful tool to support clinical relevance in fields such as orthopedics and rheumatology. Various methods have been developed to estimate MCID, but most of them lack theoretical justification. Besides, few studies focused on the estimation of the MCID at the individual level (iMCID), which facilitates the investigation of the population heterogeneity. In this paper, we propose a general surrogate loss family to estimate the iMCID and explore the asymptotic behavior of the estimated iMCID in a linear structure. Based on the asymptotic normality, we can construct an interval estimation for linear iMCID, making the estimation more informative. The outperformance of our proposed method and the asymptotic behavior of estimated iMCID are validated through the comprehensive simulation studies and the real data analysis of a randomized controlled trial.