I mean, I am the Roman Emperor, and who is going to manage this field on Health, Defense, Treasury, Education, the Interior? Did the Romans have an institution similar to government ministries or the Cabinet today? When did the setting up of government ministries and departments start? I mean, the Roman Empire is very large, isn't it, so I wondered if there was an institution like this the Romans had?
Is there a specific time period you are interested in? While some aspects of administration remained consistent over the centuries, the actual structure of administration changed wildly. Knowing your period of interest can help potential respondents give you a more focused answer (and one you find more personally interesting!)
And to pig back of this question, which of these positions held the most status at various points?