Changes on brain imaging may precede clinical manifestations or disclose disease progression opaque to conventional clinical measures. Where, as in multiple sclerosis, the pathological process has a complex anatomical distribution, such changes are not easily detected by low-dimensional models in common use. This hinders our ability to detect treatment effects, both in the management of individual patients and in interventional trials. Here we compared the ability of conventional models to detect an imaging response to treatment against high-dimensional models incorporating a wide multiplicity of imaging factors. We used fully-automated image analysis to extract 144 regional, longitudinal trajectories of pre- and post- treatment changes in brain volume and disconnection in a cohort of 124 natalizumab-treated patients. Low- and high-dimensional models of the relationship between treatment and the trajectories of change were built and evaluated with machine learning, quantifying performance with receiver operating characteristic curves. Simulations of randomised controlled trials enrolling varying numbers of patients were used to quantify the impact of dimensionality on statistical efficiency. Compared to existing methods, high-dimensional models were superior in treatment response detection (area under the receiver operating characteristic curve = 0.890 [95% CI = 0.885–0.895] vs. 0.686 [95% CI = 0.679–0.693], P < 0.01]) and in statistical efficiency (achieved statistical power = 0.806 [95% CI = 0.698–0.872] vs. 0.508 [95% CI = 0.403–0.593] with number of patients enrolled = 50, at α = 0.01). High-dimensional models based on routine, clinical imaging can substantially enhance the detection of the imaging response to treatment in multiple sclerosis, potentially enabling more accurate individual prediction and greater statistical efficiency of randomised controlled trials.