Tensor-based morphometry (TBM) is a powerful method to map the 3D profile of brain degeneration in Alzheimer's disease (AD) and mild cognitive impairment (MCI). We optimized a TBM-based image analysis method to determine what methodological factors, and which image-derived measures, maximize statistical power to track brain change. 3D maps, tracking rates of structural atrophy over time, were created from 1030 longitudinal brain MRI scans (1-year follow-up) of 104 AD patients (age: 75.7+/-7.2 years; MMSE: 23.3+/-1.8, at baseline), 254 amnestic MCI subjects (75.0+/-7.2 years; 27.0+/-1.8), and 157 healthy elderly subjects (75.9+/-5.1 years; 29.1+/-1.0), as part of the Alzheimer's Disease Neuroimaging Initiative (ADNI). To determine which TBM designs gave greatest statistical power, we compared different linear and nonlinear registration parameters (including different regularization functions), and different numerical summary measures derived from the maps. Detection power was greatly enhanced by summarizing changes in a statistically-defined region-of-interest (ROI) derived from an independent training sample of 22 AD patients. Effect sizes were compared using cumulative distribution function (CDF) plots and false discovery rate methods. In power analyses, the best method required only 48 AD and 88 MCI subjects to give 80% power to detect a 25% reduction in the mean annual change using a two-sided test (at alpha=0.05). This is a drastic sample size reduction relative to using clinical scores as outcome measures (619 AD/6797 MCI for the ADAS-Cog, and 408 AD/796 MCI for the Clinical Dementia Rating sum-of-boxes scores). TBM offers high statistical power to track brain changes in large, multi-site neuroimaging studies and clinical trials of AD.