Am I introducing bias by assuming birthdate is middle of month? I have a dataset containing dichotomous disease measures as well as some continuous anthropometric measures on a cohort of patients, and includes their month and year of birth as well as the exact date of data collection.
In an effort to reduce noise in my statistical analyses, I want to replace the default age variable with a more accurate one, as the provided age variable is rounded down to the nearest year. As we only have the date of birth to the nearest month (owing to data sensitivity), I made the assumption that patients were born in the middle of the month (16th for 31 day months, 15.5th for 30 days months, etc...) then calculated the difference between their assumed D.O.B. and their "data collection" date, giving me an approximate age in days, accurate to the closest half month.
A colleague informs me that I'm introducing bias into my derived age variable and they have attempted to explain to me why, but I'm simply unable to understand their explanation. They also tell me that what I am doing is no more accurate than simply counting in months (i.e. rounding the data collection date to the nearest month then finding the difference in number of months), but surely by using the exact date of collection, I am incorporating more information?
My questions are:


*

*Is my derived age variable biased? If so, why?

*Is my derived age in days more accurate than calculating age in whole months?


I apologise if this seems incredibly obvious to you and I appreciate any help you can give! Thank you.
 A: 
Is my derived age in days more accurate than calculating age in whole
  months?

Obviously not. You cannot make measurement more precise then it was actually measured. Imagine that besides assuming middle of month, you assumed also that the patients were born at 12:30, 30 seconds, 30 milliseconds, etc. - would it make your measurement super precise? It is impossible to de-aggregate aggregated data. Notice that in long run your procedure would yield the same results as picking uniformly random day for each patient - would such procedure make measurement any more accurate?
A: I'm just going to state the obvious and say that I agree with you and I can't evaluate your colleague's explanation without seeing it. For (1), I can't even tell what direction the bias should be expected to be in. Are people substantially more likely to be born near the beginning or end of a month? Not that I know of. For (2), it's obvious that using your method will give you slightly more accurate estimates than computing in whole months. The increase in accuracy may be so slight as to make no difference, but certainly your method won't hurt.
