"All the text in this article relates to medicine, but the concept of ""sufficient cause"" has been well-known in philosophy and in science for centuries.

I suggest:
Broaden the definition
Point out the term's long history.
Contrast with ""necessary cause"" (A won't happen unless B happens, but als has other prequisites).
Examples of the concept's use in various fields.
Possibly create a separate page ""Sufficient cause (medicine)"" and re-link other medical pages to it."