
622 F.3d 1219 (2010)
PHOENIX MEMORIAL HOSPITAL; Casa Grande Regional Medical Center; University Medical Center; John C. Lincoln Hospital-North Mountain; St. Joseph's Hospital & Medical Center; Maricopa County Medical Center; Chandler Regional Hospital; Phoenix Baptist Hospital, Plaintiffs-Appellants,
v.
Kathleen SEBELIUS, in her official capacity as Secretary, U.S. Department of Health and Human Services, Defendant-Appellee.
No. 09-15506.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted March 9, 2010.
Filed September 21, 2010.
*1220 Roger N. Morris, Melody Ann Emmert, Lisa E. Davis, Quarles & Brady LLP, Phoenix, AZ, for the plaintiffs-appellants.
Tony West, John J. Tuchi, Anthony J. Steinmeyer, August E. Flentje, Department of Justice, Washington, D.C., for the defendant-appellee.
*1221 Before: BETTY B. FLETCHER, RICHARD R. CLIFTON, and CARLOS T. BEA, Circuit Judges.

OPINION
B. FLETCHER, Circuit Judge:
Eight Arizona hospitals that all receive federal reimbursement for treating Medicare patients appeal the district court's grant of summary judgment in favor of the Secretary of Health and Human Services. The hospitals argue that the adjustment they receive for serving disproportionately high numbers of low-income patients should be increased because the reimbursement does not account for all low-income patients included under the Arizona Health Care Cost Containment System. We have jurisdiction under 28 U.S.C. § 1291 and we affirm.

BACKGROUND

A. Statutory Framework
Under Part A of the Medicare program, the federal government reimburses providers for covered medical services for elderly and disabled individuals. 42 U.S.C. § 1395 et seq. Since 1983, hospitals have received Medicare reimbursement for inpatient hospital services through the Prospective Payment System (PPS). 42 U.S.C. § 1395ww(d); Legacy Emanuel Hosp. & Health Ctr. v. Shalala, 97 F.3d 1261, 1262 (9th Cir.1996). Under PPS, individual hospitals receive reimbursement "based on a predetermined amount that an efficiently run hospital should incur for inpatient services depending on the patient's diagnosis at time of discharge." Legacy Emanuel Hosp. & Health Ctr., 97 F.3d at 1262. The PPS then can be adjusted in several ways to account for hospital-specific factors. 42 U.S.C. § 1395ww(d)(5). The adjustment at issue in this case gives additional reimbursement to hospitals that serve a "significantly disproportionate number of low-income patients." 42 U.S.C. § 1395ww(d)(5)(F)(i)(I). This adjustment, known as the Medicare disproportionate share hospital (DSH) adjustment, seeks to compensate hospitals for the additional expense per patient associated with serving high numbers of low-income patients. See, e.g., H.R.Rep. No. 99-241 at 16 (1986), reprinted in 1986 U.S.C.C.A.N. 579, 594.
Whether a hospital qualifies for the DSH adjustment, and how much that adjustment will be, depends on the hospital's "disproportionate patient percentage." See 42 U.S.C. § 1395ww(d)(5)(F)(v). The disproportionate patient percentage is a mathematical calculation that "serves as a `proxy' for all low-income patients." Legacy Emanuel Hosp. & Health Ctr., 97 F.3d at 1263 (quotation omitted). One part of this calculation, known as the "Medicare Low Income Proxy," accounts for low-income Medicare patients and relates to the number of Medicare patients who qualify for Supplemental Security Income. 42 U.S.C. § 1395ww(d)(5)(F)(vi)(I). The second part of this calculation relates to the number of non-Medicare low-income patients served by a hospital, expressed as a percentage of the hospital's entire patient population. It is commonly referred to as the "Medicaid Fraction" or "Medicaid Low Income Proxy." Congress has defined the formula for calculating the Medicaid Low Income Proxy as:
the fraction (expressed as a percentage), the numerator of which is the number of the hospital's patient days for such period which consist of patients who (for such days) were eligible for medical assistance under a State plan approved under subchapter XIX of this chapter, but who were not entitled to benefits under part A of this subchapter, and the denominator of which is the total number *1222 of the hospital's patient days for such period.
42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). Thus, the amount of additional reimbursement a hospital receives for each Medicare patient it serves depends in part on the number of patients "eligible for medical assistance under a State plan approved under [Title] XIX." Id.
Although this case concerns reimbursement for Medicare patients, the heart of the dispute centers on which patients are included in the Medicaid Low Income Proxy. The more patients included, the greater the amount of the additional reimbursement. Medicaid, Title XIX of the Social Security Act, 42 U.S.C. § 1396 et seq., is a cooperative federal-state program that provides health care to indigent individuals who are elderly, blind, or disabled, or members of families with dependent children. Under the Medicaid program, the federal government provides funds to states to offset some of the expense of furnishing medical services to low-income persons. Id.; 42 C.F.R. § 430.0. The program is jointly financed by the federal and state governments, and states administer the program according to federal guidelines. 42 U.S.C. § 1396 et seq.; 42 C.F.R. § 430.0. To participate in Medicaid, a state must submit a plan that the Secretary approves. 42 U.S.C. § 1396a(a). A plan specifies certain categories of individuals and types of medical services that will be covered. See 42 U.S.C. § 1396a. State plans must cover the "categorically needy," those individuals who qualify because they are eligible for assistance under either the Aid to Families with Dependent Children program or the Supplemental Security Income program. See Spry v. Thompson, 487 F.3d 1272, 1274 (9th Cir.2007). Participating states also can provide coverage to the "medically needy," those individuals who have incomes above the poverty line, but who lack the means to pay for medical care. See id. "Within those broad requirements, however, states are given discretion to determine the type and range of services covered, the rules for eligibility, and the payment levels for services." Legacy Emanuel Hosp. & Health Ctr., 97 F.3d at 1262 (citing 42 C.F.R. § 430.0.). If the Secretary approves a states's plan, the state will be eligible for federal payments. 42 U.S.C. §§ 1315, 1396, 1396c.
Section 1115 of the Social Security Act authorizes the Secretary to approve experimental or demonstration projects with the goal of encouraging states to adopt innovative programs that promote the objectives of Medicaid. Portland Adventist Medical Ctr. v. Thompson, 399 F.3d 1091, 1093 (9th Cir.2005); 42 U.S.C. § 1315(a). "For these experimental projects, the Secretary is authorized to waive compliance with the general federal requirements for Medicaid state plans set out in § 1396a." Portland Adventist Medical Ctr., 399 F.3d at 1093. Experimental projects may cover medical assistance costs for individuals who could be eligible for Medicaid even without a waiver as well as to individuals who would not be eligible. Id. (citing Interim Final Rule, Medicare Program; Medicare Inpatient Disproportionate Share Hospital (DSH) Adjustment Calculation, 65 Fed. Reg. 3136, 3136-37 (Jan. 20, 2000)). Patients who are eligible for services by way of the Secretary's waiver of particular requirements under section 1115 are known as "expansion populations" or "expanded eligibility populations." Id. Expansion and expanded eligibility populations are included in the calculation of the Medicaid Low Income Proxy. Id. at 1099.

B. The Arizona Hospitals' Challenge
The dispute here centers on the Secretary's attempt to clarify federal reimbursement policies for certain groups of patients. Arizona participates in Medicaid pursuant to a section 1115 demonstration *1223 project waiver. The state program, Arizona Health Care Cost Containment System ("AHCCCS"), provides acute care services to four eligibility categories relevant here: (1) the Title XIX Categorically Needy (Mandatory Medicaid); (2) the Medically Needy/Medically Indigent (MN/MI); (3) Eligible Low Income Children (ELIC); and (4) Eligible Assistance Children (EAC).
Up until 1990, plaintiffs received DSH adjustment payments that were calculated by including MN/MI, ELIC, and EAC (collectively "MN/MI") patient days in the DSH reimbursement formula. Although the Secretary administers DSH payments, it is a fiscal intermediary, typically a health insurance company authorized to act on the Secretary's behalf, who reviews the hospital's end-of-year cost reports.[1] 42 U.S.C. § 1395g; 42 C.F.R. §§ 405.1801(b)(1), 413.24(f), 413.64(f). In early 1992, the plaintiff hospitals were advised that the intermediary would not include these patient days in the DSH formula for fiscal years after 1990. From 1990 onward, therefore, Arizona's intermediary had a practice of excluding patient days attributable to these categories of recipients.
Intermediaries in other states, however, historically had allowed hospitals to include days for patients who qualified for general assistance and other state-only funded programs in their DSH calculation. In the mid-1990s, several of the intermediaries who previously had included state-only program days in the DSH calculation notified hospitals that they no longer would include these days and would seek to recoup erroneously paid funds. In December 1999, the Secretary issued Program Memorandum 99-62 ("Program Memorandum"), a "clarification of allowable Medicaid days in the Medicare [DSH] adjustment calculation." This Program Memorandum explained that states with both state-only and federal-state eligibility groups in one program would not be allowed to include state-funded beneficiaries who were not eligible for Medicaid under a Title XIX federal-state cooperative program. The Program Memorandum also provided guidance on the "hold harmless" policy that the Secretary had announced on October 15, 1999. It instructed intermediaries that hospitals that had received erroneous payments and hospitals that had not received such payments, but had appealed that determination before October 15, 1999, would be allowed to include state-funded general-assistance days in the Medicaid Low Income Proxy calculation.[2] In all other circumstances, such days would not be included in the calculation:
If a hospital did not receive any payment based on the erroneous inclusion of general assistance or other State-only health program, charity care, Medicaid DSH, and/or waiver or demonstration population days for cost reports that were settled before October 15, 1999, and the hospital never filed a jurisdictionally proper appeal to the Provider Reimbursement Review Board on this issue, you are not to pay the hospital based on the inclusion of these types of days for any open cost reports for cost *1224 reporting periods beginning before January 1, 2000.
Four of the hospitals that are parties here filed an appeal with the Provider Reimbursement Review Board (PRRB) on December 12, 2001. In a May 4, 2007 decision, the PRRB allowed the inclusion of the MN/MI population in the Medicaid Low Income Proxy, reversing the intermediary and finding that the intermediary had, in fact, included MN/MI days in the DSH Medicare calculation. The PRRB also found that the MN/MI population fell under the state's plan, as approved in the 1982 waiver "irrespective of how the programs and sub-programs were funded." The PRRB did not consider the effect of the Program Memorandum.
On July 6, 2007, the Centers for Medicare and Medicaid Services administrator reversed the decision of the PRRB on its own motion.[3] The CMS administrator found that "the days involved in this case are related to individuals that are not eligible for medical assistance as that term is used under Title XIX and thus, are not properly included in the Medicaid patient percentage of Medicare DSH calculation." The administrator also found that the hospitals were not entitled to protection under the "hold harmless" provision.
The hospitals here filed a complaint in federal district court on September 7, 2007, alleging the Secretary's decision was arbitrary, capricious, an abuse of discretion, and otherwise not in accordance with law for three reasons: (1) the Ninth Circuit had determined that section 1115 waiver populations must be included in the DSH calculation, (2) the Secretary's "action ignores and is inconsistent with the reasoned decision issued by the PRRB," and (3) the Secretary's "action is inconsistent with decisions of the PRRB reached in many other similar cases." The district court decided dual motions for summary judgment on January 12, 2009, granting the Secretary's motion for summary judgment and denying the hospitals' motion. The district court found that "AHCCCS has two separate and distinct components, one of which is Arizona's section 1115 demonstration project and one of which is the state-funded health care program for indigent persons." The MN/MI populations were part of the state-funded program. Thus, MN/MI patients were not eligible for medical assistance under Arizona's Medicaid plan. Not only did Arizona describe AHCCCS as composed of two distinct plans, but the district court found persuasive on this point evidence that Arizona applied to include the MN/MI patients in its Medicaid plan in 1997.
With regard to the hold-harmless provision, the district court found that "[t]he evidence in the record shows that the practice for plaintiffs from 1990 onward was to not include MN/MI days in their DSH adjustments." The district court further found that even those plaintiff hospitals that had filed appeals by October 15, 1999 had not raised the specific issue, as required for hold-harmless relief. Therefore, the hospitals did not qualify for such relief.
The plaintiff hospitals timely appealed.

DISCUSSION
We review de novo both the district court's grant of summary judgment and its holdings on questions of statutory interpretation. Portland Adventist Medical Ctr., 399 F.3d at 1095. We "construe the DSH statute and assess the Secretary's interpretation of it following the standards set forth in Chevron U.S.A., Inc. *1225 v. Natural Resources Defense Council, Inc., 467 U.S. 837, 842-43, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984)." Id. We first determine "whether Congress has directly spoken to the precise question at issue." Chevron, 467 U.S. at 842, 104 S.Ct. 2778. If the answer is yes, then we "must give effect to the unambiguously expressed intent of Congress" and the agency's interpretation receives no deference. Id. at 842-43, 104 S.Ct. 2778. If the statute is either silent or ambiguous, we determine "whether the agency's answer is based on a permissible construction of the statute." Id. at 843, 104 S.Ct. 2778.
The Medicare statute authorizes judicial review of a factual finding by the Secretary, 42 U.S.C. § 1395oo(f)(1), in accordance with the Administrative Procedure Act ("APA"), 5 U.S.C. § 706. See Alaska Dep't of Health and Social Servs. v. Ctrs. for Medicare and Medicaid, 424 F.3d 931, 937 (9th Cir.2005). Under the APA, we review an agency's final decision for substantial evidence based on the administrative record. See 5 U.S.C. § 706(2)(E).

A. Arizona's MN/MI Populations Are Not "Eligible for Medical Assistance Under an Approved Plan" As Contemplated in the Statute
We first address the Secretary's determination that, under the DSH statute, the hospitals were not entitled to include MN/MI, EAC, and ELIC (collectively "MN/MI") patient days in the numerator of the Medicaid Low Income Proxy. In essence, the challenge the hospitals raise here goes back to the intermediary's 1990 decision not to include MN/MI days in the DSH calculation. The hospitals argue that the MN/MI populations should be included in the DSH calculation because, under the section 1115 waiver, such individuals are "eligible for medical assistance under a State plan approved under [Title XIX]." 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II).
To analyze the validity of the hospitals' claim, we turn to the phrase describing the Medicaid Low Income Proxy: "the number of the hospital's patient days for such period which consist of patients who (for such days) were eligible for medical assistance under a State plan approved under [Title XIX], but who were not entitled to benefits under [Medicare] Part A." 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). We previously have held that populations eligible for Medicaid should be included in the calculation, regardless of whether the hospital actually received payment for every day that particular patient received care. Legacy Emanuel Hospital & Health Ctr., 97 F.3d at 1266. We also have held that low-income patients eligible for medical services under a demonstration project approved in a waiver were part of the calculation, and that the Secretary must include expansion populations receiving medical assistance under a state plan approved under Medicaid in the Medicaid Low Income Proxy calculation. Portland Adventist Medical Ctr., 399 F.3d at 1099. We now face the task of determining whether the MN/MI populations, included in the Arizona plan as a whole, are part of the populations receiving "medical assistance under a State plan approved under [Title XIX]."
The Secretary argues that AHCCCS has two components, one of which is Arizona's Medicaid plan and one of which is the state's program for providing health care to low-income persons who are not eligible for Medicaid. If the term "eligible for medical assistance" means "eligible for Medicaid," then the populations covered under the state's program would not be included in the calculation. The hospitals contend that "eligible for medical assistance" includes all patients eligible for any type of medical assistance under a state plan. The hospitals argue that the Secretary's finding that "[t]he State's operation *1226 of [a] separate State-only funded program for certain indigent persons that did not meet the Medicaid program was not referenced in the approval of the waiver" is not supported by the evidence and insist that the Secretary "approved" the entire AHCCCS program when granting Arizona's request for a section 1115 waiver.[4]
Arizona first sought approval from the Secretary for a section 1115 demonstration project in 1982. Arizona submitted an application for its demonstration project called "AHCCCSA Statewide Approach to Cost-Effective Health Care Financing." Various parts of the record reflect the fact that Arizona treated AHCCCS as having two parts.
For the 1982 application, the Secretary granted fourteen specific waivers that would allow Arizona to implement its demonstration project, none of which related to providing medical assistance to MN/MI patients. Subsequently, in 1997, Arizona requested a specific waiver for approval to include MN/MI populations in the Medicaid plan. AHCCCS noted in the 1997 waiver application that the MN/MI program is "100% state-funded" and that "[m]any of the individuals in the state-funded programs could be eligible for Medicaid if they applied for the current AHCCCS Medicaid program or could be eligible to receive Medicaid services through a federal medically needy option." Moreover, Arizona law has classified the MN/MI populations as ineligible for Medicaid. See Ariz.Rev.Stat. §§ 11-297, 36-2905, 36-2905.03 (expressly defining "medically indigent," "medically needy," and "eligible child" as not eligible for Medicaid) (1999).
The other compelling evidence that MN/MI patients were not part of Arizona's Medicaid plan is the fact that Arizona, during the relevant time period, received federal reimbursement only for patients in the Title XIX Categorically Needy (Mandatory Medicaid) category and that the funding source for the MN/MI populations came from the state and counties. In addition, it is undisputed that Arizona did not receive such reimbursement for the MN/MI populations. The Medicaid Act specifically defines "medical assistance" as "payment of part or all of the cost of" enumerated services. 42 U.S.C. § 1396d(a). Because "medical assistance" means the payment of federal funds toward certain services, Arizona should have been receiving reimbursement for these populations if they were "eligible for medical assistance" as contemplated in the DSH calculation. See Adena Regional Medical Ctr. v. Leavitt, 527 F.3d 176, 179-80 (D.C.Cir.2008).
For these reasons, we agree with the district court that AHCCCS has two separate and distinct components, one of which is Arizona's section 1115 demonstration project and one of which is the state-funded health care program. During the relevant time period, the MN/MI populations were part of the state-funded program and thus were not eligible for medical assistance under Arizona's Medicaid plan, even though they were eligible for medical assistance under AHCCCS. Thus, we affirm the district court's holding that *1227 the Secretary's decision that MN/MI patient days were properly excluded from the Medicaid Low Income Proxy was not contrary to law, arbitrary or capricious, or unsupported by substantial evidence.

B. The Hospitals Are Not Eligible for "Hold Harmless" Treatment
The hospitals argue that, in the event that we find the days for MN/MI patients should not be included in the calculation of the Medicaid Low Income Proxy, several hospitals specifically appealed the exclusion of these patient days and thus should be eligible for "hold harmless" treatment. We agree with the district court that these hospitals are not entitled to "hold harmless" treatment.
On this issue, we find helpful the Seventh Circuit's analysis of the "hold harmless" provision in Rush University Medical Center v. Leavitt, 535 F.3d 735 (7th Cir.2008). As the Seventh Circuit explains, and as we explained earlier, "[a]t the outset of this `disproportionate share' program, it was unclear how persons covered by states' general-assistance programs would be classified. Some hospitals (and some of the Medicare program's fiscal intermediaries) equated general-assistance patients to Medicaid patients; others did not." Rush Univ. Med. Ctr., 535 F.3d at 738-39 (7th Cir.2008). The Program Memorandum clarified the rules, explicitly excluding general-assistance patients from among the low-income patients calculation, but explaining that if a hospital's intermediary had allowed reimbursement that included non-eligible patients in the number of low-income patient days, a grandfather clause prevented the Secretary from seeking to recoup those dollars. Id. at 739. To qualify for this "hold harmless" treatment, hospitals must have either included general-assistance patients with Medicaid patients in cost reports filed before October 15, 1999, or have appealed the non-inclusion of these patients by that date. Id. Hospitals that did not include such patients and did not specifically appeal the issue before October 15, 1999 could not seek to add an appeal of the determination to an appeal filed before that date. Id. In essence, "[t]he idea is that any hospital that added a claim based on general-assistance patients must have been trying to take advantage of the grandfather treatment, which was first announced on October 15, 1999. Only claims that predate the announcement of grandfather-clause treatment are allowed." Id.
Three hospitals here appealed the DSH calculation for three separate years. Phoenix Memorial Hospital appealed its fiscal year 1995 Notice of Program Reimbursement on March 20, 1998, stating that "the Intermediary reduced Disproportionate Share payments based on Title XIX data obtained from [AHCCCS]." Phoenix Memorial's appeal stated that it "believe[d] this data to be incomplete, thus resulting in underpayment of Disproportionate Share payments." Casa Grande Regional Medical Center appealed its fiscal year 1996 Notice of Program Reimbursement on March 29, 1999, stating that the DSH "adjustment does not properly reflect the provider's Medicaid days applicable to both in-state and out-of-state patients." On June 30, 1999, the hospital stated that "[n]ot all Medicaid eligible days were included in the computation by the fiscal intermediary." St. Joseph's Hospital and Medical Center appealed its fiscal year 1994 Notice of Program Reimbursement on March 14, 1997, questioning "[w]hether the intermediary's adjustment of AHCCCS days to state data, and related adjustment of Disproportionate Share, was appropriate."
None of the timely filed appeals here indicate that the hospitals were appealing the exclusion of general-assistance patient days. Indeed, the intermediary had had a *1228 policy of excluding such days since 1990. And we agree with the Seventh Circuit and the district court here that a blanket appeal of the DSH calculation before October 15, 1999 is not sufficient to preserve appellate rights on this issue. Although the hospitals argue that this requirement imposes a higher pleading standard, "[t]he problem is not the omission of magic words but the fact that there were no synonyms for the right words, or even similes or metaphors." Id. at 740.
This result makes sense. The hospitals knew from 1990 onward that MN/MI patient days were not being included in the reimbursement calculation. The evidence in the record shows that the DSH Medicaid Low Income Proxy calculation excluded MN/MI days as a general rule. The hospitals stipulated to this practice before the PRRB, and testimony from the manager of Audit and Reimbursement for Blue Cross/Blue Shield in Arizona confirmed that the intermediary's practice was to exclude MN/MI days during the relevant time period.[5] These facts all support the Secretary's conclusion that these hospitals were not entitled to protection under the "prior practice" provision of the hold harmless policy. Therefore, we affirm the district court's holding that the hospitals were not eligible for hold-harmless relief.

CONCLUSION
In other cases and under other circumstances, we have concluded that the "Secretary has refused to implement the DSH provision in conformity with the intent behind the statute." Portland Adventist Medical Ctr., 399 F.3d at 1099. That is not the case here. Rather, the Secretary in this instance attempted to remedy disparate treatment among states and to prevent unfair consequences from flowing from this clarification. Hospitals like the hospitals that brought this action did not benefit from the initial confusion, but they were not injured by it either.
AFFIRMED.
NOTES
[1]  After the intermediary reviews the year-end cost reports, the intermediary issues a "Notice of Program Reimbursement" identifying the amount the hospital will be paid by Medicare for that hospital cost year. 42 C.F.R. § 405.1803.
[2]  A hospital that disagrees with the intermediary's determination can request an administrative hearing before the Provider Reimbursement Review Board. 42 U.S.C. § 1395oo(a). A hospital has the right under the statute to seek judicial review in federal court of a final determinationthat of the Board or of the Secretary, depending on whether the Secretary chose to conduct a review. Id. § 1395oo(f)(1).
[3]  In general, the Board's decision serves as the final agency decision unless the Secretary exercises her authority to review it. 42 U.S.C. § 1395oo(d), (f)(1).
[4]  In the stipulated facts before the PRRB, the parties agreed that "[t]he Secretary of Health and Human Services approved AHCCCS, and all of its programs and sub-programs, as part of Arizona's 1115 Waiver, irrespective of how the programs and sub-programs are funded." The Secretary was not a party to and did not participate in the hearing before the PRRB and thus cannot be bound by the stipulations entered into between plaintiffs and the intermediary. See Loma Linda Univ. Medical Ctr. v. Leavitt, 492 F.3d 1065, 1074 (9th Cir.2007) ("the Secretary is not necessarily bound by stipulations entered into at the PRRB hearing by an intermediary").
[5]  The hospitals point to testimony showing the intermediary included some MN/MI days in the DSH calculation for cost reports from 1994 to 2000. Other testimony, however, shows that the inclusion of these MN/MI days was probably the result of a clerical error. The hospitals do not allege that they have had to return the funds received as a result of these erroneously included days and the inclusion of a few erroneous days does negate the clear evidence that the intermediary's practice excluded these days.
