[s] or [z]

A phonological rule changes /s/ (single "s")to/z/ following a "voiced" consonant or a vowel (which is "voiced" by definition). Phonetically the "er" of Alzheimer's is a vowel, even though /r/ is a voiced consonant anyway.

An exception to that rule seems to occur mid-word where the "s" precedes a voiceless consonant such as "t" as in the name "Johnstone". Here the /n/ is voiced but the "s" remains /s/ in order that the "t" stays as /t/ and does not become /d/.