Early cognitive response after repetitive transcranial magnetic stimulation (rTMS) may predict later cognitive change in Alzheimer disease, but the incremental value of domain-specific response is unclear. We analyzed data from 112 randomized participants; 101 entered a Week-5 landmark cohort and 91 had complete predictors and outcomes at 8, 16, and 24 weeks post-treatment. Nested predictor-set comparisons used ridge regression to evaluate baseline information, trial variables, early total-score response, and domain-specific response. Model-class comparisons included ridge, multi-task elastic net, restricted random forest, and longitudinal mixed effects. Validation used repeated treatment-site-stratified 5-fold cross-validation with five repetitions, nested hyperparameter tuning, and paired participant-level bootstrap comparisons with 10,000 resamples. Adding Week-3 and Week-5 ADAS-Cog total-score response improved prediction. The early total-response ridge achieved overall MAE 3.067, RMSE 3.885, and $R^2=0.384$. Replacing two total-response variables with 22 component-level changes worsened performance (MAE 3.363, RMSE 4.269, $R^2=0.257$). The paired MAE difference was -0.297 points (95% CI -0.485 to -0.115). Mixed effects was competitive (MAE 3.162), with an uncertain overall difference from total-response ridge. Sensitivity analyses using absolute future scores and excluding Week-3 response supported the main findings. In this sample, early aggregate ADAS-Cog response was more informative than a higher-dimensional domain-specific representation. The model is an internally validated early-response updating tool, not a pretreatment selection model or evidence of causal rTMS efficacy.

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