Or are birthdays seen as irrelevant? Is your world a tyrannical one where any kind of celebration is banned because the powers that be feel threatened if their subjects gather together for any reason? Could there be "underground birthdays" where people find a way of getting together regardless of any ban?
Is age something that is seen as a good thing in your society or something to be feared? Are certain birthdays (1, 18, 21, etc) particularly commemorated? If age is something to be feared why is that? For example, are people only allowed to live to a certain age, lying about your age is a criminal offence, and the day after reaching a certain birthday, you are killed by the state for having "outlived your usefulness"?
So you see it is possible to take a cheerful subject and write some quite bleak stuff around it!