NCI SBIR/STTR applications can be contract solicitations for specific problems, as you point out. The majority are (as I understand it) funded however through

NCI SBIR/STTR applications can be contract solicitations for specific problems, as you point out. The majority are (as I understand it) funded however through the omnibus solicitation, which can be directed to high-priority research areas or to general problems within the scope of the NCI. I assume the same is true for other NIH agencies.