Dangling present participle

Question

The following sentence sounds normal, but I would like to ask if it has a correct structure or is it dangling participle because the subject of the main clause is "the doctor" whereas that of participle phrase is "the number of surgeries."

The doctor says the number of surgeries he performs on people with cancer is now low, approaching the level before the incident.

Answer 1

This is fine. All syntactic and semantic cues point to the number of surgeries &c as the subject/predicand^† of the participle clause

1. The clause to which the participle clause is attached is not the headed by says but the clause headed by is, whose subject is the number of surgeries &c.

2. We ordinarily 'track' not to the subject of the head clause but to the nearest semantically plausible NP to find the subject of a participle clause; in this case the nearest NP is the number of surgeries &c. (Moreover, the doctor as the subject/predicand of approaching &c is semantically implausible.)

3. The participle clause is juxtaposed to low and semantically is obviously a supplement enlarging on the meaning of that adjective—which is, again, the predicate complement of the clause headed by is and is ascribed by that clause to its subject, the number of surgeries &c.

---

^† _{In this case, where the clause acts as an adjective and the verb is a bare copula, subject and predicand are the same entity.}