Une possibilité.
Ou tous simplement « avec un background d’immigration ».

Voir par exemple formulaire au Canada :

I feel pretty sure that the 'by' here has the sense of 'en focntion de' — it is used this way a lot in statistical fields.

As far as the bast translation of 'background' goes, I fear this is going to depend a great deal on your wider context; for example, just to start with, do we know that all the subjects are immigrants? If not, then by 'background' (an arguably poor choice of word), we might in fact be meaning 'whether or not they come from an immigrant background at all'. There may also be an issue here whether we are talking about children who have themselves immigrated, or children born in [the country] of immigrant parents?

All these points will need to be taken into account when choosing how to handle the 'background' part — but I suspect your main query was perhaps the use of 'by' here?

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Note added at 1 hr (2013-05-07 20:47:27 GMT)
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As I said, it all depends on what the writer meant by 'background' — I strongly suspect it was an attempt to be politically correct and avoid saying 'racial background' (which would explain the otherwise potentially puzzling use of 'background'); but as I have been at pains to explain, it very much depends whether or not it is already known that the subjects involved are all immigrants or not (what is the study group?) If not, then it would be nonsense to say in essence 'what country do they come from?' if they are in fact locals. In which case, the expression might conceivably mean 'whether or not the subject is from in immigrant background' — this should be immediately apparent from the wider context, but is NOT unequivocally clear from the limited context we have here.

I think the objectors are in fact really picking holes in an error in my non-native attempted formulation in FR — in the absence of adequate context to clarify the 'background' part, I was really only concentrating on the way to interpret the 'by' here; I wish now I had simply edited the question term to that effect.

"En réalité, garçons et filles, quelle que soit leur origine migratoire, sont confrontés à des rôles sociaux distincts qui peuvent influencer leurs performances scolaires et compromettre l’égalité des chances".

Les enfants de migrants: un véritable potentiel - Forum suisse pour l
www.migration-population.ch/.../les enfants de migrants.pdf‎

par antécédents migratoires ou antécédents d'immigration : voir par ex:

http://www.oecd-ilibrary.org/employment/perspectives-de-l-em...


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Note added at 12 hrs (2013-05-08 07:44:14 GMT)
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ventilé(e) est l'expression utilisée en statistiques