BackgroundLate-life depression (LLD) and mild cognitive impairment (MCI) are risk factors for Alzheimer disease (AD). However, the interactive effect between LLD and MCI in the progression to AD remains unknown. The purpose of this research is to clarify whether this interaction exists and determined the characteristics of the structural change patterns in LLD and MCI. MethodTo address this question, a total 225 participants (91 with intact cognitive function (IC), 34 with MCI, 35 with LLD-IC, 47 with LLD-MCI and 18 with AD) were recruited for the current study and their T1 scanning were acquired. Machine learning was applied to estimate the brain's age gap according to grey matter information (thickness and volume was calculated based on the Human Connectome Project Multi-Modal Parcellation version 1.0 and the Desikan atlas). A structural covariance network (SCN) was constructed based on grey matter volume. Rich-club analysis, global network properties and the Jaccard distance were utilized to describe the topological features in each cohort. Their cognitive functions (executive function, processing speed and memory) were evaluated by a full-scale battery of neuropsychological tests. ResultThe interactive effect between LLD and MCI was detected through the brain age gap. The estimated age was positively correlated with processing speed and memory in LLD and non-LLD subjects. In the SCN analysis, the rich-club coefficient and global network properties were disrupted in the MCI group, but remained normal in the LLD-IC, LLD-MCI and AD groups. There was a significant discrepancy in brain structural change patterns between the AD and other cohorts by the Jaccard distance. ConclusionThe application of machine learning reflects that synergies between LLD and MCI could increase the risk of developing AD. According to the SCN, the structural coordination was disrupted in MCI and was kept normal in the other cohorts, while the discrepancies in brain structural change patterns appeared in AD. Overall, the brain age gap could be a potential predictor of AD, and the Jaccard distance has the potential to be a new type of SCN analysis indicator.