
    OWENSBORO HEALTH, INC. (15-6109); Jackson Purchase Medical Center and Lake Cumberland Regional Hospital (15-6110), Plaintiffs-Appellants, v. UNITED STATES DEPARTMENT OF HEALTH AND HUMAN SERVICES; Sylvia Mathews Burwell, Secretary, United States Department of Health and Human Services; Centers for Medicare and Medicaid Services, Defendants-Appellees.
    Nos. 15-6109
    15-6110
    United States Court of Appeals, Sixth Circuit.
    Argued: June 9, 2016
    Decided and Filed: August 10, 2016
    
      COUNSEL ARGUED: Stephen R. Price, Sr., Wyatt, Tarrant & Combs, LLP, Louisville, Kentucky, for Appellants. Car-leen M. Zubrzycki, United States Department of Justice, Washington, D.C., for Ap-pellees. ON BRIEF: Stephen R. Price, Sr., Virginia H. Snell, Wyatt, Tarrant & Combs, LLP, Louisville, Kentucky, for Appellants. Carleen M. Zubrzycki, Alisa B. Klein, United States Department of Justice, Washington, D.C., for Appellees.
    Before: BOGGS, ROGERS, and STRANCH, Circuit Judges.
   OPINION

ROGERS, Circuit Judge.

This consolidated appeal concerns the amount of additional Medicare reimbursements that the plaintiff hospitals should receive for serving a disproportionate share of low-income patients and whether the calculation of those additional Medicare reimbursements is affected by how a state chooses to allocate its Medicaid funds. The amount of additional Medicare reimbursements that a hospital is entitled to receive for serving a disproportionate share of low-income patients depends, in part, on the number of days that the hospital served patients who were “eligible for medical assistance under a State plan approved under [the Medicaid statute].” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). The hospitals contend that because Kentucky has chosen in its Medicaid plan to award additional Medicaid funds to hospitals based on how many days they treat patients who are eligible for the Kentucky Hospital Care Program (“KHCP”), a state program that provides medical coverage to low-income individuals who do not qualify for Medicaid, KHCP patient days should be counted in the calculation of the additional Medicare reimbursements. However, because the statutory term “eligible for medical assistance under a State plan approved under [the Medicaid statute]” is synonymous with “eligible for Medicaid” and because KHCP patients are, by definition, not eligible for Medicaid, the district courts correctly concluded that the statute unambiguously excludes KHCP patient days from the calculation for awarding additional Medicare reimbursements to hospitals that serve a disproportionate share of low-income patients.

I.

Under Medicare, a federally funded program that provides health insurance for the elderly and disabled, see 42 U.S.C. § 1395c, hospitals are not reimbursed for the actual cost of treating Medicare beneficiaries. Instead, the federal government reimburses hospitals for treating Medicare patients through a “prospective payment system” based on predetermined rates for a given diagnosis, regardless of the actual cost of treatment. 42 U.S.C. § 1395ww(d). Those predetermined rates may be adjusted for specific hospitals. 42 U.S.C. § 1395ww(d)(5). This case involves one of those hospital-specific adjustments: the Medicare Disproportionate Share Hospital (“DSH”) adjustment. Under the Medicare DSH adjustment, the government pays a hospital more for treating Medicare patients if the hospital serves a “significantly disproportionate number of low-income patients.” 42 U.S.C. § 1395ww(d)(5)(F)(i)(I). The reason for this adjustment is Congress’s judgment that low-income Medicare patients generally are in poorer health and therefore generally are costlier to treat. See H.R. Rep. No. 98-861, at 1356 (1984) (Conf. Rep.), reprinted in 1984 U.S.C.C.A.N. 1445, 2044; S. Rep. No. 98-23, at 54 (1983), reprinted in 1983 U.S.C.C.A.N. 143,194.

One method of determining whether a hospital qualifies for a Medicare DSH adjustment and the amount of such adjustment is the hospital’s “disproportionate patient percentage,” which serves as a proxy for the number of low-income patients treated by the hospital. 42 U.S.C. § 1395ww(d)(5)(F)(v). A hospital’s “disproportionate patient percentage” is determined, in part, by the so-called “Medicaid fraction” or “Medicaid proxy,” which is defined as: “the number of the hospital’s patient days for such period which consists 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 benefits under part A of [Medicare],” divided by “the total number of the hospital’s patient days for such period.” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II). The key dispute in this case is how to interpret the phrase “eligible for medical assistance under a State plan approved under subchap-ter XIX of this chapter.”

“[S]ubehapter XIX of this chapter” refers to Medicaid. See 42 U.S.C. §§ 1396-1396w-5. In Medicaid, each state creates a unique plan to provide medical coverage for low-income individuals. The state plan establishes eligibility criteria for coverage under the plan as well as the nature and scope of medical care provided under the plan. 42 C.F.R. § 430.10. If the Secretary of Health and Human Services approves the state’s plan, the federal government makes matching payments to the state for the “medical assistance” that is provided to individuals who qualify under the state’s plan. 42 U.S.C. § 1396b(a)(l). Unlike Medicare, in which the federal government does not reimburse providers for the actual cost of treating patients, in Medicaid, the federal government provides matching payments to the state for “the total amount expended [by the state] ... as medical assistance under the State plan.” Id. The state then distributes the federal funds to the medical providers as described in its Medicaid plan. 42 C.F.R. § 430.0.

Like Medicare, Medicaid requires an upward rate adjustment for providers serving a disproportionate share of low-income patients. 42 U.S.C. § 1396a(a)(13)(A)(iv). However, the Medicaid DSH adjustment operates differently than the Medicare DSH adjustment. While the Medicare DSH adjustment is defined uniformly for all states by the Medicare statute, 42 U.S.C. § 1395ww(d)(5)(F)(I), in Medicaid, each state “specifically defines the hospitals” that qualify for its Medicaid DSH adjustment in its state Medicaid plan, 42 U.S.C. § 1396r~4(a). Further, while the Medicaid proxy in the Medicare DSH adjustment counts only days on which hospitals treated patients who “were eligible for médical assistance under a State plan approved under [the Medicaid statute],” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II), a state’s Medicaid DSH adjustment may be based on “the costs, volume, or proportion of services provided to patients eligible for medical assistance under a State plan approved under [the Medicaid statute] or to low-income patients,” 42 U.S.C. § 1396r-4(c)(3)(B) (emphasis added).

Additionally, the purpose of the Medicaid DSH adjustment is different from the purpose of the Medicare DSH adjustment. As explained above, the purpose of the Medicare DSH adjustment is to make the Medicare reimbursements closer to the actual cost of treating Medicare patients who are in poorer health and therefore are more expensive to treat; however, it is not necessary to account for this purpose through the Medicaid DSH adjustment, because the federal government already pays the states based on the actual amount they spend on Medicaid patients. See 42 U.S.C. § 1396b(a)(l). Instead, the purpose of the Medicaid DSH adjustment is to assist facilities in providing care to “the uninsured patients that they serve, since these facilities [that qualify for the Medicaid DSH adjustment] are unlikely to have large numbers of privately insured patients through which to offset their operating losses on the uninsured.” H.R. Rep. No. 103-111, at 211 (1993), reprinted in 1993 U.S.C.C.A.N. 378, 538.

Kentucky’s Medicaid DSH definition includes patients who qualify for a state program known as the Kentucky Hospital Care Program (“KHCP”). Kentucky’s Medicaid DSH definition is based on the number of days a hospital incurs costs for “indigent patients.” Indigent patients— meaning patients who qualify for KHCP— are defined as patients “without health insurance or other source of third party payment with incomes below 100% of the federal poverty level.” Kentucky law further provides that individuals must be ineligible for Medicaid in order to qualify for coverage under KHCP. See Ky. Rev. Stat. § 205.640(5).

In this case, hospitals submitted cost reports to their fiscal intermediaries (the entities that distribute Medicare funds) that included both Medicaid and KHCP patient days in their Medicare DSH adjustment calculations. The Eastern District of Kentucky hospitals’ cost reports were for the years 2005-2007, while the Western District of Kentucky hospital’s cost reports were for the years 2003-2005. The fiscal intermediaries disagreed with the hospitals and excluded KHCP patient days from the hospitals’ Medicare DSH adjustments. The hospitals appealed to the Provider Reimbursement Review Board (“PRRB”), which affirmed the fiscal intermediaries’ decisions. The hospitals then appealed the PRRB’s decisions to the Administrator of the Centers for Medicare & Medicaid Services, whose decisions constitute the final administrative decisions of the Secretary. The Administrator affirmed the PRRB’s decisions. The hospitals timely sought judicial review of the Administrator’s decisions.

The hospitals and the Secretary both filed motions for summary judgment in the district courts. Both the Eastern, and Western Districts of Kentucky affirmed the Administrator’s decisions. Applying the framework set forth in Chevron, U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984), the Eastern District held that “eligible for medical assistance under a State plan approved under sub-chapter XIX” unambiguously excludes patients receiving KHCP benefits under Chevron Step One. First, the Eastern District reasoned that KHCP patients do not receive “medical assistance” as defined by the Social Security Act. The court explained that the Medicaid statute defines “medical assistance” as “payment of part or all of the cost of [certain enumerated categories of] care and services.” Because Medicaid DSH payments are distributed prospectively and not as compensation for any specific medical service, the Eastern District reasoned that KHCP patients do not receive “medical assistance” as it is statutorily defined and therefore may not be counted in the Medicaid proxy of the Medicare DSH formula. Second, the Eastern District reasoned that the Secretary’s approving of the definition of Kentucky’s Medicaid DSH adjustment did not constitute approving the KHCP plan, because the Secretary did not approve the qualifications, nature, or scope of KHCP.

The Western District similarly held that “eligible for medical assistance under a State plan approved under subchapter XIX” unambiguously means “eligible for Medicaid” under Chevron Step One. Because KHCP patients are not eligible for Medicaid, the Western District held that the days associated with their treatment cannot be included in a provider’s Medicare DSH formula. Like the Eastern District, the Western District reasoned that the Secretary did not approve the KHCP plan, because the Secretary approved only the definition of Kentucky’s Medicaid DSH adjustment and did not approve the details of KHCP. However, in a footnote, the Western District rejected the Eastern District’s reliance on the fact that Medicaid DSH funds do not constitute “medical assistance.”

The Western District also addressed the hospital’s arguments that the Secretary’s exclusion of KHCP patient days violates the Equal Protection Clause and was arbitrary and capricious. The hospital argued that the Secretary’s exclusion of KHCP patient days was without a rational basis, because the Secretary includes in the Medicaid proxy the days on which hospitals treat patients who have been provided with Medicaid coverage under a § 1115 waiver. The hospital argued that these patients, who would not be eligible for Medicaid but for the § 1115 waiver, are functionally identical to KHCP patients. The Western District rejected the hospital’s arguments, reasoning that KHCP patient days can be rationally distinguished from § 1115 patient days based on the fact that statutes treat the two groups differently and on the fact that the federal government has control over § 1115 projects but not over KHCP.

The hospitals appeal, arguing that the Medicaid proxy unambiguously includes KHCP patient days. In the alternative, they argue that, if the statute is ambiguous, the Secretary’s interpretation of the statute as excluding KHCP patient days violates the Equal Protection Clause and is arbitrary and capricious under the Administrative Procedure Act.

II.

A. The Numerator of the Medicaid Proxy Unambiguously Excludes KHCP Patient Days

We review the meaning of the Medicare statute under the deferential two-step process set forth in Chevron. Under Chevron Step One, if “the intent of Congress is clear,” then we must “give effect to the unambiguously expressed intent of Congress” using traditional tools of statutory construction. 467 U.S. at 842-43, 104 S.Ct. 2778. If the statute is silent or ambiguous, then under Chevron Step Two we defer to the agency’s interpretation if that interpretation constitutes a “permissible” construction of the statute. Id. at 843, 104 S.Ct. 2778.

Under Chevron Step One, the numerator of the Medicaid proxy in the Medicare DSH provision unambiguously excludes patients who are ineligible for Medicaid. Patient days for patients such as KHCP patients, who are not eligible for Medicaid and whose treatment is funded through Medicaid DSH adjustments, may not be included in the Medicaid proxy numerator. The hospitals focus on the phrase “State plan approved under subchapter XIX” in isolation from the rest of the Medicaid proxy’s text. However, when the entire statutory phrase is considered, it is clear that “eligible for medical assistance under a State plan approved under subchapter XIX” is an unambiguous term of art synonymous with “eligible for Medicaid” and that KHCP patients are not eligible for “medical assistance” as that term is statutorily defined. Additionally, neither our precedent nor a comparison to the “Pickle method” of calculating the Medicare DSH adjustment compels a contrary result.

i.

First, it is clear that Congress uses “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” as a synonym for “eligible for Medicaid.” Congress uses phrases identical to, or nearly identical to, “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” throughout the Social Security Act, rather than phrases such as “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid.” While Congress’s repeated use of the phrase “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” alone indicates that Congress used the phrase to identify individuals who are eligible for Medicaid, even more illuminating are the few times that Congress did use “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid.”

When Congress has used the terms “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid,” the terms have predominantly been used as a shorthand for a longer phrase identical to or nearly identical to the one used in the Medicaid proxy numerator. For example, in one instance, Congress explicitly defined “Medicaid eligible” to mean “entitled to medical assistance under a state plan approved under this subchapter.” 42 U.S.C. § 1396s(b)(2)(B)(I). Likewise, Congress specified that, for the purposes of a sub-paragraph on nursing facility services, “ ‘certain medicaid-eligible individual’ means an individual who is entitled to medical assistance for nursing facility services in the facility under this subchapter.” 42 U.S.C. § 1396r(c)(7)(B). Other times Congress has equated “Medicaid eligibility,” “eligible for Medicaid,” or “eligible for Medicaid benefits” with phrases nearly identical to that used in the Medicaid proxy. See 29 U.S.C. § 1169(b)(2) (“medicaid eligibility” with “eligible for or is provided medical assistance under a State plan for medical assistance approved under title XIX of the Social Security Act”); 42 U.S.C. § 1320b-22(b)(3)(B)(ii)(I) (“medicaid eligibility” with “provide medical assistance under subchapter XIX of this chapter”); 42 U.S.C. § 1395w-4(g)(3)(A) (“eligible for medicaid benefits” with “eligible for any medical assistance ... with respect to such services under a State plan approved under subchapter XIX of this chapter”); 42 U.S.C. § 1396a(e)(13)(C)(ii)(III) (using the phrase “not eligible for Medicaid” to describe 42 U.S.C. § 1397jj(b)(l)(C), which refers to children who are not “eligible for medical assistance under subchapter XIX”); 42 U.S.C. § 1397ee(d)(l) (“Medicaid eligibility” with “eligibility for medical assistance under the State plan under subchapter XIX of this chapter”).

The hospitals argue that the infrequent use of the terms “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid” demonstrates that “Congress clearly knows how to say ‘Medicaid eligible’ when it means ‘Medicaid eligible.’ ” However, the hospitals do not identify any instances where Congress has used such phrases and has not meant them to be equated with a longer phrase similar to the one used in the numerator of the Medicaid proxy. Instead, the fact that Congress has several times used the terms “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid” as shorthand for phrases like “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” indicates that the phrase “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” is likewise intended to mean the same as “Medicaid eligible,” “Medicaid eligibility,” or “eligible for Medicaid” when it appears in isolation.

Additional evidence for the conclusion that the numerator of the Medicaid proxy in the Medicare DSH provision is synonymous with “eligible for Medicaid” comes from the fact that the Medicaid DSH provision is broader than the Medicare DSH provision. While the Medicaid proxy in the Medicare DSH formula is limited to patients who “were eligible for medical assistance under a State plan approved under [the Medicaid statute],” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II), a state’s Medicaid DSH adjustment may be based on “the costs, volume, or proportion of services provided to patients eligible for medical assistance under a State plan approved under [the Medicaid statute] or to low-income patients,” 42 U.S.C. § 1396r-4(c)(3)(B) (emphasis added). By including the identical phrase “eligible for medical assistance under a State plan approved under [the Medicaid statute]” in both DSH provisions but then adding the phrase “or to low-income patients” in only one provision, Congress has indicated that it views patients who are “eligible for medical assistance under a State plan” as not inclusive of all “low-income patients.” Including non-Medicaid low-income patients in the Medicaid proxy of the Medicare DSH formula would render the distinction between the two DSH provisions meaningless. Instead, as the Third, Ninth, and D.C. Circuits have held, the difference in scope between the Medicaid and Medicare DSH provisions leads to the conclusion that the phrase “eligible for medical assistance under a State plan” refers only to Medicaid patients. See Univ. of Wash. Med. Ctr. v. Sebelius, 634 F.3d 1029, 1036 (9th Cir. 2011); Cooper Univ. Hosp. v. Sebelius, 686 F.Supp.2d 483, 495 (D.N.J. 2009), aff'd, 636 F.3d 44 (3d Cir. 2010); Adena Reg’l Med. Ctr. v. Leavitt, 527 F.3d 176, 180 (D.C. Cir. 2008).

Finally, the hospitals’ own interpretation of the Kentucky law governing KHCP indicates that “eligible for medical assistance” is a term of art synonymous with “eligible for Medicaid.” The hospitals, citing Ky. Rev. Stat. § 205.640(5), accept that Kentucky law provides that individuals must be ineligible for Medicaid in order to qualify for KHCP. However, Ky. Rev. Stat. § 205.640 — the statute governing KHCP — does not refer to Medicaid by name when it provides that KHCP patients must be ineligible for Medicaid. Instead, the KHCP statute communicates that KHCP patients must be ineligible for Medicaid by stating that “[h]ospitals receiving reimbursement under this section ... shall not bill patients for services provided to patients not eligible for medical assistance with family income levels up to one hundred percent (100%) of the federal poverty level.” Ky. Rev. Stat. § 205.640(5) (emphasis added). Thus, the hospitals implicitly acknowledge that “eligible for medical assistance” is a synonym for “eligible for Medicaid” under the KHCP statute, but then insist that the same term does not mean “eligible for Medicaid” under the Medicare DSH provision — and they do not explain why the term “eligible for medical assistance” might carry a different meaning in the Kentucky KHCP statute as compared to the federal Medicaid and Medicare statutes. The hospitals cannot have it both ways. Their interpretation of the Kentucky KHCP statute therefore supports the conclusion that the numerator of the Medicaid proxy in the Medicare DSH provision is unambiguously synonymous with “eligible for Medicaid.”

ii.

Second, the numerator of the Medicaid proxy in the Medicare DSH pro-vision unambiguously excludes KHCP patients because KHCP patients are not eligible for “medical assistance” as that term is statutorily defined. The term “medical assistance” contained within the Medicaid proxy is a technical term of art. “Medical assistance” is not defined in Subchapter XVIII (the Medicare statute), but is instead defined in Subchapter XIX (the Medicaid statute). Because there is a natural presumption that “identical words used in different parts of the same act are intended to have the same meaning,” Atlantic Cleaners & Dyers, Inc. v. United States, 286 U.S. 427, 433, 52 S.Ct. 607, 76 L.Ed. 1204 (1932), and because the Medicare DSH provision specifically refers to the subchapter where the definition of “medical assistance” is found, “medical assistance” as used in the Medicare DSH provision has the same meaning as when it is used in the Medicaid statute.

“Medical assistance” is defined as “payment of part or all of the cost of the following care and services ... for individuals ... who are” members of statutorily defined categories of persons. 42 U.S.C. § 1396d(a). Thus, the only individuals who are capable of being “eligible for medical assistance” are those who are members of the categories of persons listed in § 1396d(a). As the hospitals admitted at oral argument, KHCP patients do not fall within any of the categories of persons listed in § 1396d(a). Because they do not belong to any of the § 1396d(a) categories, KHCP patients are not individuals for whom the state’s payment of the cost of medical services constitutes “medical assistance.” This is in accord with the Ninth Circuit’s holding that patients are not “eligible for medical assistance” if they “[do] not fit within the statutory classes of people” listed in § 1396d(a), University of Washington Medical Center, 634 F.3d at 1035, and the Third Circuit’s approval of the conclusion that “patients ‘eligible for medical assistance’ under Section 1396d(a) must be eligible for Medicaid,” Cooper University Hospital, 686 F.Supp.2d at 491, aff'd, 636 F.3d 44 (3d Cir. 2010).

In sum, the hospitals read the numerator of the Medicaid proxy as if it includes patients who were “eligible [to receive medical care] under a State plan approved under subchapter XIX.” If that were the case, the hospitals’ arguments would be more persuasive — KHCP patients do receive medical care in the colloquial sense pursuant to Kentucky’s Medicaid plan. However, KHCP patients are not eligible to receive “medical assistance” as it is statutorily defined pursuant to a state plan approved under subchapter XIX.

iii.

Third, the hospitals’ arguments to the contrary are without merit. The hospitals argue that our holdiiigs in Jewish Hospital, Inc. v. Secretary of Health & Human Services, 19 F.3d 270 (6th Cir. 1994), and Metropolitan Hospital v. U.S. Department of Health & Human Services, 712 F.3d 248 (6th Cir. 2013), indicate that the Medicaid proxy includes KHCP patient days. In Jewish Hospital, we considered the Secretary’s interpretation of “eligible for medical assistance under a State plan approved under subchapter XIX” as meaning that only those days actually paid by Medicaid can be used in the calculation of the Medicaid proxy in the Medicare DSH provision. 19 F.3d at 272. We rejected the Secretary’s interpretation under Chevron Step One, reasoning that “Congress defined the Medicaid proxy with respect to eligibility for and not actual payment of benefits.” Id. at 275. We explained that “[a] Medicaid eligible individual is no less ‘eligible for medical assistance’ on some days simply because his or her state Medicaid program only pays for a fixed number of days.” Id. Given Congress’s intent to supplement the resources of hospitals serving a disproportionate share of low-income individuals, we stated that “the Secretary’s promulgated regulation runs counter to this clear intent by unnecessarily restricting the available subsidy, without foundation in the statute.” Id.

The hospitals argue that Jewish Hospital stands for the propositions that “the Medicaid Proxy unambiguously requires the Secretary to count all days on which hospitals provide medical treatment to low income patients under an approved state plan,” and that interpretations of the Medicaid proxy that “uniformly restrict[ ] DSH adjustments” are invalid. However, Jewish Hospital hurts the hospitals’ arguments more than it helps them. First, Jewish Hospital does not provide that any interpretation of the Medicaid proxy that restricts DSH adjustments is invalid; rather, we held that interpretations that are “without foundation in the statute” are invalid. Id. at 275. As explained above, there is ample support in the statute for the contention that the Medicaid proxy does not include days on which hospitals treated non-Medicaid patients whose care is funded through Medicaid DSH payments. Thus, because the interpretation has a foundation in the statute, the fact that it restricts DSH adjustments is not disposi-tive. Second, dicta in Jewish Hospital suggest that “eligible for medical assistance under a State plan approved under sub-chapter XIX” is synonymous with “eligible for Medicaid.” For example, in Jewish Hospital, we stated that the Medicaid proxy “is based upon Medicaid-eligible patients.” Id. at 272. The Jewish Hospital court also explained that Congress did not want the Medicare DSH adjustment to be “readily altered by state legislative fiat,” id. at 274, indicating that the Jewish Hospital court would not have agreed with the hospitals that how Kentucky chooses to distribute its Medicaid DSH funds could affect hospitals’ Medicare DSH adjustments.

Metropolitan Hospital likewise does not support the hospitals’ arguments. In Metropolitan Hospital, we deferred to the Secretary’s interpretation of a different part of the Medicare DSH formula— “entitled to benefits under [Medicare] part A” — which involved the Secretary’s treatment of “dual-eligible days,” or days on which a hospital treats a patient who is eligible for both Medicare and Medicaid and who has exhausted his or her Medicare coverage during a given spell of illness. 712 F.3d at 252-53, 265-70. We reasoned, in part, that the Secretary’s interpretation was not contrary to Congress’s intent under Chevron Step One, because the Secretary’s regulation did not uniformly restrict DSH adjustments, and because the hospital’s alternative interpretation of the statute would have had the same exclusionary effect on a different set of low-income patient days. Id. at 264-65. The hospitals argue that Metropolitan Hospital supports their contention that an interpretation of the Medicare DSH provision that restricts the availability of DSH adjustments is invalid. However, we recognized in Metropolitan Hospital that there is “no support for a clear statutory mandate to account for all low-income patients” in the Medicare DSH provision. Id. at 263. Thus, the fact that the Secretary’s interpretation of the statute here would award a lower Medicare DSH adjustment than the hospitals requested is not dispositive.

Additionally, as in Jewish Hospital, dicta in Metropolitan Hospital suggest that “eligible for medical assistance under a State plan approved under subchapter XIX” means “eligible for Medicaid.” When explaining the Medicare DSH formula, we paraphrased the numerator of the Medicaid proxy in the Medicare DSH provision — i.e., the phrase “eligible for medical assistance under a State plan approved under subchapter XIX”' — as “eligible for [Medicaid].” Metro. Hosp., 712 F.3d at 251 (brackets in original). Later, we summarized the Jewish Hospital court’s examination of the phrase “eligible for medical assistance under a State plan approved under subchapter XIX” as being a discussion of the Secretary’s “interpretation of ‘eligible for [Medicaid].’ ” Id. at 264 (brackets in original). Thus, the fact that we equated the phrase “eligible for medical assistance under a State plan approved under subchapter XIX” with “eligible for Medicaid” in both Jewish Hospital and Metropolitan Hospital (albeit in dicta) further demonstrates that the Medicaid proxy unambiguously excludes KHCP patient days.

The hospitals also argue that the “Pickle method,” an alternative method by which hospitals may calculate eligibility for a Medicare DSH adjustment, demonstrates that Medicaid DSH patient days are properly included in the numerator of the Medicaid proxy. Hospitals can qualify for a Medicare DSH adjustment in one of two ways: (1) the “proxy method,” which is the focus of this case and which involves counting the number of days on which the hospital treated patients who “were eligible for medical assistance under a State plan approved under subchapter XIX of this chapter,” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II), and (2) the “Pickle method,” named for its sponsor Congressman J.J. Pickle, which involves counting the revenue that hospitals receive from state and local sources, 42 U.S.C. § 1395ww(d)(5)(F)(i)(II). The Pickle method provides that a hospital qualifies for a Medicare DSH adjustment if it:

is located in an urban area, has 100 or more beds, and can demonstrate that its net inpatient care revenues (excluding any of such revenues attributable to this subchapter or State plans approved under subchapter XIX of this chapter), during the cost reporting period in which the discharges occur, for indigent care from-State and local government sources exceed 30 percent of its total of such net inpatient care revenues during the period.

Id.

According to the Administrator in the proceedings below, hospitals cannot include Medicaid DSH revenue in their Pickle-method formula. Put another way, according to the Administrator, Medicaid DSH revenue constitutes “revenues attributable to this subchapter or State plans approved under subchapter XIX of this chapter” and does not constitute “State and local government sources.” Because Medicaid DSH revenue cannot count for hospitals attempting to qualify for a Medicare DSH adjustment under the Pickle method, the hospitals reason that Medicaid DSH patient days must count for hospitals attempting to qualify for a Medicare DSH adjustment under the proxy method. If Medicaid DSH revenue constitutes “revenues attributable to ... state plans approved under subchapter XIX’ under the Pickle method, then, the hospitals argue, the patient days that created those revenues — i.e., Medicaid DSH patient days— must constitute days on which patients “were eligible for medical assistance under a State plan approved under subchapter XIX.”

The hospitals’ Pickle-method arguments are unpersuasive. The hospitals’ arguments ignore the fact that the proxy method includes the language “eligible for medical assistance” while the Pickle method does not. The Pickle method is not an exact reverse image of the proxy method, contrary to the hospitals’ characterizations. Instead, the proxy method’s inclusion of “eligible for medical assistance” — and its corresponding absence in the Pickle method — creates a meaningful difference between the two provisions. While the Pickle method excludes all subchapter XIX funds of any kind from its calculation, the proxy method is more restrictive and counts patient days during which only one specific type of subehapter XIX money — “medical assistance” — might have been spent. As explained above, subchapter XIX funds constitute “medical assistance” only if they are spent on certain statutorily defined categories of persons, to which KHCP patients do not belong.

The hospitals also err by assuming that Congress intended every low-income individual to be counted in one of the two methods available for calculating the Medicare DSH adjustment. The hospitals argue that “[i]t would have been irrational for Congress to include low-income patients funded exclusively by state governmental sources ... and ... simultaneously exclude vast numbers of low-income patient days funded under an approved state plan.” However, both methods of calculating the Medicare DSH adjustment provide only an estimate of the number of low-income individuals that a hospital treats, and neither is designed to account for every low-income patient. As we' explained in Metropolitan Hospital, there is “no support for a clear statutory mandate to account for all low-income patients” in the proxy method. 712 F.Bd at 263. Both the Medicaid proxy and the Pickle method are underinclusive of low-income patients in some way — the proxy method by excluding some non-Medicaid low-income patients, and the Pickle method by excluding Medicaid patients. That Medicaid DSH patients do not fit under either method merely reflects the fact that both methods for calculating the Medicare DSH adjustment are imperfect estimates of the number of low-income patients that a hospital treats.

Additionally, the legislative history behind the Pickle method weakens, rather than supports, the hospitals’ arguments. Congress included the Pickle method “[bjecause of concern that this proxy measure of low-income status might substantially understate the presence of low-income patients in some hospitals, most particularly public hospitals in states where the medicaid eligibility standards are stringent.” H.R. Rep. No. 99-241(1), at 18 (1985), reprinted in 1986 U.S.C.C.A.N. 579, 596. Congress’s concern for the effects of stringent Medicaid eligibility standards indicates that Congress viewed the proxy method as counting only patient days on which hospitals treat patients who are eligible for Medicaid and as not counting patient days on which hospitals treat other non-Medicaid low-income patients. Based on this legislative history, the Pickle method would not have been included if the proxy method had, in fact, accounted for non-Medicaid low-income patient days. Therefore, the very existence of the Pickle method indicates that Congress intended non-Medicaid low-income patients like KHCP patients to be excluded from the proxy method and for “eligible for medical assistance under a State plan approved under subchapter XIX of this chapter” to be synonymous with “eligible for Medicaid.”

Lastly, because the statute is unambiguous, the hospitals’ arguments that the Secretary supposedly changed her interpretation of the Medicaid proxy over time are unavailing. If Congress has “directly spoken to the precise question at issue,” then “that is the end of the matter.” Chevron, 467 U.S. at 842, 104 S.Ct. 2778. Moreover, the hospitals have not shown that the Secretary did, in fact, change her position. The hospitals cite PRRB decisions for the contention that the Secretary formerly adopted a position opposite to the one for which she now advocates. While a PRRB decision can become the final decision of the Secretary if the Secretary does not reverse, affirm, or modify the PRRB’s decision, see 42 U.S.C. § 1395oo(f)(l), all of the PRRB decisions cited by the hospitals were subsequently reversed or vacated by the Administrator. Therefore, none of the PRRB decisions cited by the hospitals constituted the final decision of the Secretary.

B. The Hospitals’ Remaining Arguments

The hospitals also argue that the Secretary’s interpretation and application of the numerator of the Medicaid proxy as excluding KHCP patient days violates the Equal Protection Clause and is arbitrary and capricious. The hospitals challenge only the Secretary’s application of the Medicaid proxy as violating the Equal Protection Clause and do not bring an Equal Protection Clause challenge to the statute itself. Because “the court, as well as the agency, must give effect to the unambiguously expressed intent of Congress,” Chevron, 467 U.S. at 842-43, 104 S.Ct. 2778, these arguments presuppose that the Medicaid proxy is ambiguous and are cognizable only if the Secretary had discretion in how to interpret and apply that ambiguous statute. In light of our holding that the Medicaid proxy is unambiguous in its exclusion of KHCP patient days, we have no need to address the hospitals’ equal protection and arbitrary-and-capricious arguments. As the Secretary must follow the clear directive of Congress, she had no discretion in how to apply the Medicaid proxy and thus lacked the statutory authority to interpret the statute in a way that would have included KHCP patient days in the numerator of the Medicaid proxy.

III.

For the foregoing reasons, we affirm the district courts’ grants of summary judgment to the Secretary. 
      
      . The Third Circuit in Cooper University Hospital affirmed “substantially for the reasons set forth in [District] Judge Simandle’s excellent [o]pinion.'' 636 F.3d at 45.
     
      
      . From language in the rest of Ky. Rev. Stat. § 205.640, it is clear that "medical assistance” in Ky. Rev. Stat. § 205.640(5) is meant to refer to “medical assistance” as it is defined in the Medicaid statute. For example, Ky. Rev. Stat. § 205.640(1) states that “[t]he commissioner of Medicaid services shall adopt a disproportionate share program consistent with the requirements of Title XDÍ of the Social Security Act,” thereby linking Ky. Rev. Stat. § 205.640 to the Medicaid statute.
     