Assessing which person is the one with the next birthday - date

Question

In Stata I am trying to assess which of the given birthdays is the next one compared with a given date. My data looks like this:
All dates are in daily format (%dD_m_Y), e.g. 18mar1926
Variable date which is the reference date with which all other dates should be compared
Variables birth1, birth2, birth3, birth4, birth5, birth6 contain the birthday of all possible household members.
For example: A household with two adults A and B. The birthday of A is 20th Nov 1977 and the birthday of person B is 30th March 1978. The reference date is 29.11.2020. I want to know who is the person who has the next birthday, in the example above it is person B, because person A has had its birthday one week before the reference date, so the next birthday in this household will be celebrated on the 30 March 2021.
Example data:
date
birth1
birth2
birth3
birth4
birth5
birth6
02feb2021
15jan1974
27nov1985
30nov2020
31aug1945
27jun1999
07apr1997
19nov2020
27sep1993
30dec1996
29jan2021
29mar1973
05dec2020
21jan1976
02oct1976
21jan1976
25may1995
15feb1997
25nov2020
25nov1943
29nov1946
02feb2021
28apr1979

Answer 1

EDITED to account for Feb 29
*The edit will treat people who have a February 29 birthday as if it were March 1 in cases when the year of date is not a leap year. If that doesn't make sense for your particular use case, it should be easy to alter the code below as you see fit.
Since you want the next birthday in the year rather than the closest birthday, you can use the year of date and the month and day from birth{i} to create a date for each person's next birthday. Then you can sinmply take the earliest value from each household. I reshape long, and generate a person and household id in order to do this.
Make example data
clear
set obs 6
set seed 1996
generate date = floor((mdy(12,31,2020)-mdy(12,1,2015)+1)*runiform() + mdy(12,1,2015))
format date %td
forvalue i = 1/6 {
gen birth`i' = floor((mdy(12,31,1996)-mdy(12,1,1980)+1)*runiform() + mdy(12,1,1980)) if _n < `i' == 0
format birth`i' %td
}
replace birth6 = birth4 in 6 // want a tie
replace birth2 = date("29feb1996","DMY") in 3 // Feb 29
Find Next Birthday
gen household_id = _n
reshape long birth, i(date household_id) j(person)
drop if mi(birth)
gen person_next_birthday = mdy( month(birth), day(birth), year(date))
* TREAT FEB 29 as if they have a march 1 birthday in non-leap years
replace person_next_birthday = mdy(3,1,year(date)) if month(birth) == 2 ///
& day(birth) == 29 & mod(year(date),4)!=0
replace person_next_birthday = mdy( month(birth), day(birth), year(date) + 1) if person_next_birthday < date
replace person_next_birthday = mdy(3,1,year(date)+1) if month(birth) == 2 ///
& day(birth) == 29 & mod(year(date) + 1,4)!=0 & person_next_birthday < date
format person_next_birthday %td
bysort household_id (person_next_birthday): gen next_bday = person_next_birthday[1]
format next_bday %td
drop person_next_birthday
reshape wide birth, i(date household_id next_bday) j(person)
gen next_bday_persons = ""
* Make a string to present household persons who have next bday
foreach v of varlist birth* {
local person = subinstr("`v'","birth","",.)
local condition = "month(`v') == month(next_bday) & day(`v') == day(next_bday)"
local condition_feb29 = "month(next_bday) == 3 & day(next_bday) == 1 & month(`v') == 2 & day(`v') == 29"
replace next_bday_persons = next_bday_persons + "|`person'" if `condition' | `condition_feb29'
}
replace next_bday_persons = regexr(next_bday_persons,"^\|","")
order next_bday_persons, after(next_bday)
The last loop is unnecessary, but illustrates that this is robust to ties.