[{"clientId":1,"treatments":[{"clientId":1},{"clientId":1},{"clientId":3}]},{"clientId":3,"treatments":[{"clientId":1},{"clientId":2},{"clientId":3}]}]

db.collection.aggregate([{"$match":{"clientId":1}},{"$project":{"_id":0,"treatments":{"$filter":{"input":"$treatments","cond":{"$eq":["$$this.clientId",1]}}}}}])