Imagine the sentence "Alice tinkers with her health care system. Bob revamped his." It's the same concept, but with "its" as the pronoun.
Can you expand on what the mistake is?
Taiwan, in contrast, revamped its [own|healthcare|something] top to bottom.
Otherwise it looks like "Taiwan, in contrast, revamped its [top] [to [the] bottom]."
It's not missing the antecedent, it's near the end of the previous sentence, just like the other person you replied to said.
Singapore, which we wrote about in October, tinkers with its health care system all the time. Taiwan, in contrast, revamped its top to bottom.
The its clearly refers to health care system from the previous sentence.
In other words it's typically used as a possessive determiner in this construction.
It's somewhat similar to the following:
-Have you eaten?
-Yes, I've.
What they didn't mention, is that often med students get their studies paid by one of the hospitals and then are tied to that hospital up to 7-ish years at depressed salaries --which is likely contributing to the shortage.
>Taiwan, in contrast, revamped its top to bottom.
Sorry, "its" what? Copy editors, please.