Approximate date of birth, based on survey date and age

[FLuca]

I would like to generate a variable that approximates the day of birth based on the available survey data.
I have a continuous variable for age at the moment when the survey has been conducted, I have year and month of birth, I have the year of the survey, and I have three exact dates referring to three moments of the survey (i.e. when the survey started, when the survey ended, and the middle of the survey).
Below you can see a subsample of the dataset.

* Example generated by -dataex-. To install: ssc install dataex
clear
input float age double(yearbirth monthbirth Survey_Year Survey_Start Survey_End Survey_Middle)
15.660274 1995  9 2011 18724 18763 18743
15.928767 1991  4 2007 17198 17256 17227
16.019178 1991  4 2007 17258 17262 17260
16.019178 1991  4 2007 17258 17262 17260
16.279451 1995  1 2011 18721 18732 18726
 15.59726 1995  5 2011 18567 18627 18597
15.517808 1991 11 2007 17252 17331 17291
15.838356 1995  5 2011 18672 18699 18685
 15.59452 1991  8 2007 17198 17256 17227
15.635616 1995  8 2011 18659 18747 18703
15.750685 1991  8 2007 17272 17297 17284
 15.69315 1995  8 2011 18714 18735 18724
15.673972 1991  9 2007 17257 17317 17287
 15.91233 1995  6 2011 18724 18763 18743
15.671233 1995  7 2011 18672 18699 18685
15.517808 1991 10 2007 17258 17262 17260
 15.50685 1991 11 2007 17257 17317 17287
15.630137 1992  9 2007 17592 17683 17637
15.421918 1995 12 2011 18721 18773 18747
 15.48767 1995 12 2011 18764 18778 18771
end
format %td Survey_Start
format %td survey_End
format %td survey_Middle
label values yearbirth C02a
label values monthbirth OC02b
label def OC02b 1 "January", modify
label def OC02b 4 "April", modify
label def OC02b 5 "May", modify
label def OC02b 6 "June", modify
label def OC02b 7 "July", modify
label def OC02b 8 "August", modify
label def OC02b 9 "September", modify
label def OC02b 10 "October", modify
label def OC02b 11 "November", modify
label def OC02b 12 "December", modify

How would you proceed to estimate the day of birth?

[Please, note that everything else in the dataset is anonymized, so an estimate of the day of birth would not allow the identification of a person; plus, without the exact day of birth, identification would not be possible anyway]

[Andrew Musau]

gen dob= floor(Survey_Middle- age*365.25)

You can use the age() function recently introduced to confirm the above:

gen age2= age_frac( dob , Survey_Middle)
assert age==age2

[FLuca]

Many thanks Andrew, I am going to try your suggested solution!