Phase 2, open-label, randomized, multi-center studies in infants and premature infants are necessary to determine treatment and preventative strategies for ROP. This study was designed to: a) target infants at the highest risk of ROP in a large number of centers with variable rates of ROP (all stages and severe ROP or stage 3+); and b) assess whether caffeine plus systemic or ophthalmic NSAID will decrease ROP among infants most at risk for ROP. The study is designed to determine whether the novel treatment regimens are safe and potentially effective for ROP prevention and to obtain requisite data for the development of a Phase III efficacy/safety randomized blinded trial. Since caffeine is used extensively in NICUs as standard of care for ELGANs, no placebo group is included.