Knee adduction moment (KAM) is correlated with the progression of medial knee osteoarthritis (OA). Although a generic gait modification can reduce the KAM in some patients, it may have a reverse effect on other patients. We proposed the "decomposed ground reaction vector " (dGRV) model to 1) distinguish between the components of the KAM and their contribution to the first and second peaks and KAM impulse and 2) examine how medial knee OA, gait speed, and a brace influence these components. Using inverse dynamics as the reference, we calculated the KAM of 12 healthy participants and 12 patients with varus deformity and medial knee OA walking with/without a brace and at three speeds. The dGRV model divided the KAM into four components defined by the ground reaction force (GRF) and associated lever arms described with biomechanical factors related to gait modifications. The dGRV model predicted the KAM profile with a coefficient of multiple correlations of 0.98 +/- 0.01. The main cause of increased KAM in the medial knee OA group, the second component (generated by the vertical GRF and mediolateral distance between the knee and ankle joint centers), was decreased by the brace in the healthy group. The first peak increased, and KAM impulse decreased with increasing velocity in both groups, while no significant change was observed in the second peak. The four-component dGRV model successfully estimated the KAM in all tested conditions. It explains why similar gait modifications produce different KAM reductions in subjects. Thus, more personalized gait rehabilitation, targeting elevated components, can be considered.