Compact writing of "1, 3, 6, 9, 12, 24 and 36-month survival was analysed"

All are comprehensible, but they're not all equal.

First some to avoid:

• (d) is wrong because "between" is (usually) paired with "and" not "to".
• (c) can be read as the analysis taking place during that time, rather than being an analysis of data from that period.
• (e) "until" doesn't quite seem idiomatic here.

Beyond that, you're writing a compact abstract, so you want the tightest wording you can get get, that doesn't introduce unnecessary ambiguity. My field is different, but the upper limit of the timescale would seem to be a reasonable characteristic, much more so than the minimum step. That means you don't need to specify the lower bound, which rules out (a), as well as (c) and (d).

That leaves you with (b) "Patient survival up to 36 months was analysed" at 8 words.

But I think you can actually do better: "Patient 36-month survival was analysed." is 5 or 6 words depending on how you treat the hyphen and number. You could almost drop "Patient" (you're not going to be discussing the survival of anyone else) except you would then have trouble avoiding starting the sentence with the digits, and that's bad form. The relationship between this (now short) sentence and the next, which presumably gives a headline result, is also important. It needs to follow on, but you may be able to make your punctuation work hard.