Geriatric falls are driven mostly by the systems that keep a person upright: the balance apparatus, the strength of the legs, and the integrity of the joints used for gait. Impaired balance from vestibular, proprioceptive or central causes destroys postural control; muscle weakness from sarcopenia removes the ability to recover from a stumble; and rheumatoid arthritis produces painful, deformed, unstable joints with an antalgic gait. Each of these acts mechanically and directly to topple a patient. Hearing impairment, by contrast, contributes only indirectly $-$ chiefly by reducing awareness of the surroundings and as a shared marker of inner-ear ageing $-$ so among the four it is the option that is not a direct cause. Hence the odd-one-out is hearing.
\[\boxed{\text{Hearing impairment}}\]