Interpretation of: Patients received treatment within the first 2 days of hospitalisation

I believe there is no certain answer to this question. The meaning resides with the author (or speaker). The main confusion arises from the two relevant meanings of day: a calendar day; and a period of 24 hours. This ambiguity may only be resolved by definition.

The patient was admitted at time X.

1. Day as a (complete) calendar day. Two complete days following the day of admission (Jan 1). Hence treatment was before the end of Jan 3.

2. Day as exactly 24 hours. Treatment within 48 hours of the time of admission. Hence treatment was before time X on Jan 3.

I note that option 2 has a minor difficulty similar to the main question. To what precision are hour and the time X related? Is hour to be understood as an hour, or 60 minutes, or 3600 seconds? There is scope for legal quibble here but it adds little to this present discussion.

I discount a third option where 2 days = a period of time that may be reasonably rounded to 2 days rather than 3 days. Hence treatment was before time X + O.5 days on January 3. If the patient was admitted after noon on Jan 1, this would mean treatment before a time in the morning of Jan 4. Most people would see this argument as misleading sophistry.