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The phrase "age at time of" is correct and usable in written English.
It can be used when referring to someone's age during a specific event or moment in time.
Example: "The study analyzed the participants' health outcomes based on their age at time of diagnosis."
Alternatives: "age during" or "age when".
Exact(58)
The median age at time of excision was 6.0 years.
Students must be 15 years of age at time of registration.
Students must be 18 years of age at time of registration.
Average age at time of surgery was 13.3 months (range, 6 to 180 months).
Median age at time of HBO2 was 52 years (range 22-77).
The youngest age at time of first vaccination was 14 years.
The average gestational age at time of the interview was 9.23 weeks (SD = 3.46).
Average age at time of surgery was 47 years (range 44 50 years).
The mean age at time of diagnosis was 28.61 years (17 58 years).
Similar(2)
A striking feature of atypical BSE cases is their advanced age at time of detection.
Mean age at time of referral to BCHD was 36 years (SD 16 years).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com