The FDA's efforts to regulate laboratory tests and their supplies or kits actually dates back to 1990 or so (here, see section, "History Before Analyte Specific Reagents"). In particular, the FDA made efforts to regulate all "in vitro diagnostic multi-index assays" around 2006-2007 (here). As these tests became more established and required CPT codes, the AMA CPT made a code section "MAAA - Multi Analyte Assays with Algorithms" which allowed the AMA to avoid using the term "IVD" as part of the definition.
For at least several years, the College of American Pathologists has commented on FDA regulatory efforts toward laboratory molecular procedures, and favored regulation of "black box" tests with proprietary algorithms (e.g. here and here). On February 23, 2015, the AMA submitted comments to the House Energy & Commerce workgroup, favoring FDA regulation of MAAA tests. AMA writes,
"The AMA agrees that a small subset of complex genetic/genomic tests, e.g., those that use proprietary and non-transparent algorithms that do not lend themselves to review and refinement by laboratory physicians and professionals, should be subject to oversight, potentially by the FDA."
AMA comments are available online here. A cloud copy of the public AMA document is here. Note that the AMA comments to the Hill on a whole range of healthcare reforms, not just lab tests.
The AMA's page for precision medicine is here. (May require email registration, but not AMA membership).