We don't have synonyms for close study yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are case study.
(n) :
(uncountable) Research performed in detail on a single individual, group, incident or community, as opposed to, for instance, a sample of the whole population.
(n) :
(uncountable) Research performed in detail on a single individual, group, incident or community, as opposed to, for instance, a sample of the whole population.