Advanced Research Project Authority for Health Act or the ARPA-H Act This bill establishes within the National Institutes of Health (NIH) the Advanced Research Projects Authority for Health to accelerate innovation in health and medicine by investing in high-risk, high-reward research projects. The bill also establishes an interagency advisory committee to inform the authority's activities. The authority director shall be appointed by the President and report to the NIH director. The authority director must, among other duties, designate personnel to serve as program managers who select projects to support, make recommendations about terminating or continuing projects, and otherwise administer authority programs. The authority may use a variety of mechanisms to support the research projects, including grants, contracts, and prize competitions. To receive funding, an applicant must demonstrate sufficient, unsuccessful attempts to secure private funding for its project and other criteria. Furthermore, the authority's budget is separate from the NIH budget. In addition, the authority must (1) develop and periodically update a strategic plan, (2) annually report on its activities, and (3) seek to contract with the National Academies of Sciences, Engineering, and Medicine to evaluate the authority's performance. The Food and Drug Administration (FDA) may meet with the authority and other federal partners to discuss actions to facilitate the development of medical projects and products prioritized by the authority. The authority must reimburse the FDA for the costs associated with supporting authority activities. The bill also requires the Government Accountability Office to report on issues related to the authority's hiring and staffing.