Grammatically, the sentence is **ambiguous**, meaning the word "he" could refer to either the doctor or the nurse.

However, based on standard English grammar and logic:

1.  **The Doctor:** This is the most likely interpretation. In English, a pronoun usually refers to the **subject** of the preceding clause ("The doctor").
2.  **The Nurse:** If the nurse is male, "he" could refer to him. However, the sentence does not provide enough context to confirm the nurse's gender.

Without more context, most readers would assume **the doctor** was late, but the sentence is technically unclearly written.
