In St. Jude Medical Cardiology Division, Inc., v. Volcano Corp., 2014-1183 (April 24, 2014), an appeal of the denial of inter partes review in IPR2013-00258, the Federal Circuit held that a decision not to institute is not appealable:

We hold that we may not hear St. Jude’s appeal from the Director’s denial of the petition for inter partes review. We base that conclusion on the structure of the inter partes review provisions, on the language of section 314(d) within that structure, and on our jurisdictional statute read in light of those provisions.