                                                                   FILED
                                                       United States Court of Appeals
                                                               Tenth Circuit

                                        PUBLISH                 April 21, 2020
                                                            Christopher M. Wolpert
                        UNITED STATES COURT OF APPEALS          Clerk of Court

                                      TENTH CIRCUIT


 HAYS MEDICAL CENTER; MERCY
 HOSPITAL LEBANON; MERCY
 HOSPITAL ARDMORE, INC.; NORTH
 PLATTE NEBRASKA HOSPITAL
 CORPORATION, d/b/a Great Plains
 Medical Center; HANOVER HOSPITAL,
 INC.; KNOX COMMUNITY HOSPITAL;
 LABETTE COUNTY MEDICAL
 CENTER; MEMORIAL HOSPITAL OF
 SWEETWATER COUNTY; NEWMAN
 MEMORIAL COUNTY HOSPITAL, d/b/a
 Newman Regional Health;
 NORTHWESTERN MEDICAL CENTER,
 INC.; POCATELLO HOSPITAL, LLC,
 d/b/a Portneuf Medical Center,

           Plaintiffs - Appellants,                      No. 17-3232

 and

 RICHLAND MEMORIAL HOSPITAL,

           Plaintiff,

 v.

 ALEX M. AZAR, II, in his official
 capacity as Secretary of Health and Human
 Services, *

           Defendant - Appellee.

       *
        Pursuant to Fed. R. App. P. 43(c)(2), Eric Hargan is replaced by Alex M.
Azar II as the Secretary of Health and Human Services.
                 Appeal from the United States District Court
                          for the District of Kansas
                    (D.C. No. 2:15-CV-09893-JTM-GEB)


Daniel J. Hettich (Elizabeth N. Swayne with him on the briefs), King & Spalding
LLP, Washington D.C., for Plaintiffs - Appellants.

Carleen M. Zubrzycki, Attorney, Appellate Staff (Chad A. Readler, Acting
Assistant Attorney General, Stephen McAllister, United States Attorney, and
Michael S. Raab and Abby Wright, Attorneys, with her on the brief), United
States Department of Justice, Washington, D.C., for Defendant - Appellee.


Before TYMKOVICH, Chief Judge, HOLMES and PHILLIPS, Circuit Judges.


HOLMES, Circuit Judge.


      Plaintiff-Appellants are eleven rural hospitals (the “Hospitals”). They

challenge the methodology that the U.S. Secretary of Health and Human Services

(the “Secretary”) uses to calculate their Medicare reimbursements. The question

before us is whether that methodology is arbitrary and capricious. We hold that it

is not. Accordingly, exercising jurisdiction under 28 U.S.C. § 1291, we affirm

the district court’s judgment.

                                        I

      This case plunges us into the “labyrinthine world” of Medicare

reimbursement. Adirondack Med. Ctr. v. Sebelius, 740 F.3d 692, 694 (D.C. Cir.


                                        2
2014). 2 In order to navigate this world, we first lay out the necessary background,

which we do in three steps. First, we outline the basics of the Medicare

reimbursement system. Second, we explain the Secretary’s methodology at issue

and trace its application over the years. Third, we recount how this appeal

unfolded.

                                         A

      The Medicare program provides federally funded healthcare to persons over

sixty-five years old, as well as to disabled persons. See Social Security

Amendments of 1965, Pub. L. No. 89-97, § 102, 79 Stat. 291 (1965) (codified as

amended at 42 U.S.C. § 1395 et seq.). Medicare enrollees obtain their healthcare

through different “parts.” This case involves what is known as Medicare Part A.

See 42 U.S.C. §§ 1395c–1395i-5. 3 That part provides eligible persons with

      2
              Throughout this opinion, we cite to four decisions bearing the case
caption (or some substantially similar version thereof) Adirondack Medical
Center v. Sebelius. Three out of four of these decisions were different
dispositions within the same case. As such, the citations for each of these three
decisions contain a Roman numeral, corresponding to the chronological order in
which the respective disposition was rendered in that case (e.g., “Adirondack I,”
“Adirondack II,” and “Adirondack III”). The fourth decision is Adirondack
Medical Center v. Sebelius, 740 F.3d 692 (D.C. Cir. 2014), which, despite bearing
the same case caption as the aforementioned three decisions, is not connected to
that same case. Accordingly, that decision is not denoted by a Roman numeral
identifier as are the other three, but rather is cited to hereinafter in traditional
shortcite form (e.g., Adirondack Med. Ctr., 740 F.3d at 692).
      3
             Notwithstanding certain adjustments to dates and other minor
changes, the statutory and regulatory provisions involved here have remained
substantively unchanged over the relevant years. Thus, for convenience, we cite

                                         3
insurance covering, among other things, certain inpatient hospital services. See

id. § 1395d(a). The Secretary administers this program through the Centers for

Medicare & Medicaid Services (“CMS”), 4 a division of the Department of Health

and Human Services.

      The Secretary reimburses participating hospitals for certain inpatient care

they provide to Medicare Part A patients through what is called the “inpatient

prospective payment system,” a regime established by Congress in the 1980s

aimed at encouraging more cost-efficient management of medical care by

hospitals. See Social Security Amendments of 1983, Pub. L. No. 98-21, § 601, 97

Stat. 65, 149 (1983) (codified as amended at 42 U.S.C. § 1395ww). Through this

system, the Secretary reimburses hospitals for inpatient services on a prospective

basis, doing so “at a fixed amount per patient, regardless of the actual operating

costs they incur in rendering these services.” Sebelius v. Auburn Reg’l Med. Ctr.,

568 U.S. 145, 149 (2013). “By establishing predetermined reimbursement rates

that remain static regardless of the costs incurred by a hospital, Congress sought

‘to reform the financial incentives hospitals face, promoting efficiency in the


the most recent iteration of these provisions. When a provision has been changed
and that change is relevant for purposes of this appeal, we note that change and
cite the controlling language.
      4
             For simplicity’s sake, we use the term “the Secretary” as a catchall to
cover any governmental actor—including CMS—involved in administering the
hospital-reimbursement scheme at issue here.


                                         4
provision of services by rewarding cost/effective hospital practices.’” County of

Los Angeles v. Shalala, 192 F.3d 1005, 1008 (D.C. Cir. 1999) (quoting H.R. R EP .

N O . 98–25, at 132 (1983), as reprinted in 1983 U.S.C.C.A.N. 219, 351).

                                          1

      At its most basic, a hospital’s reimbursement for a given Medicare Part A

patient is the mathematical product of two figures—the payment rate and the

patient’s diagnosis-related group weight. We turn first to providing an overview

of the latter figure, the diagnosis-related group weight (the payment rate is

explored in the immediately succeeding subsection infra). Ascertaining this

figure begins with the Secretary sorting the Medicare Part A patient into a

“diagnosis-related group” (periodically referred to hereinafter as “DRG”). These

groups are essentially “categor[ies] of inpatient treatment” that reflect the

differing costs of treating various types of diagnoses, with each Part A patient

being sorted into a group at the time of discharge, based on that patient’s

diagnosis. Adirondack Med. Ctr., 740 F.3d at 694 n.1; see also 42 U.S.C.

§ 1395ww(d)(4)(A). The Secretary assigns each diagnosis-related group a

“weighting factor” that “reflects the relative hospital resources used” to treat

patients in that group “compared to [patients] classified within other groups.”

§ 1395ww(d)(4)(B). There are several hundred different diagnosis-related

groups, with individual weights “ranging from less than 1.000 to more than


                                          5
7.000.” Adirondack Med. Ctr. v. Sebelius (Adirondack II), 29 F. Supp. 3d 25, 30

(D.D.C. 2014). The more complicated and expensive the diagnoses, “the greater

the weight assigned to that particular [diagnosis-related group] will be.” County

of Los Angeles, 192 F.3d at 1008. The Secretary then multiplies the Medicare

Part A patient’s diagnosis-related group weight by the payment rate (again, we

discuss this latter figure infra). The product of that calculation is the hospital’s

reimbursement for treating a particular patient. 5 See id.; see also 42 U.S.C.

§ 1395ww(d)(3)(D).

      In order to account for changes in resource consumption, Congress

recognized that it would be necessary to periodically recalculate the diagnosis-

related group weighting factors. Changes to the Inpatient Hospital Prospective

Payment System and Fiscal Year 1991 Rates, 55 Fed. Reg. 35,990, 36,008 (“FY

1991 Final Rule”). Accordingly, at Congress’s direction, the Secretary annually

“adjust[s]” the diagnosis-related group “classifications and weighting factors.” Id.

(citing § 1395ww(d)(4)(C)(i)); see also Changes to the Hospital Inpatient

Prospective Payment Systems and Fiscal Year 2010 Rates, 74 Fed. Reg. 43,754,

43,895 (Aug. 27, 2009) (“FY 2010 Final Rule”) (noting that the Secretary makes


       5
              We offer a simplified example. A hospital treats two patients.
Patient 1 had a heart attack, placing her in a diagnosis-related group with a weight
of 3.0. Patient 2 had the flu, which has a diagnosis-related group weight of 1.0.
Assume that the Secretary pays the hospital using a payment rate of $1,000. For
Patient 1, the hospital would get $3,000. For Patient 2, it would get $1,000.

                                           6
“changes to the [diagnosis-related-group] classifications and weighting factors”).

This adjustment in the classifications and weighting factors is designed “to reflect

changes in treatment patterns, technology . . ., and other factors which may change

the relative use of hospital resources.” § 1395ww(d)(4)(C)(i). 6

      We focus here on the Secretary’s annual adjustment of the diagnosis-related

group weighting factors, or, in the common parlance of regulators, his

“recalibration” of the weights. The Secretary starts this process by assembling “a

dataset of recent patients.” J.A. at 159 (Mem. in Opp’n to Pls.’ Mot. for Summ. J.

& in Supp. of Def.’s Cross-Mot. for Summ. J., filed Oct. 20, 2016); see also 55

Fed. Reg. at 36,033 (FY 1991 Final Rule) (“One of the basic issues in

recalibration is the choice of a data base that allows us to construct relative DRG

weights that most accurately reflect current relative resource use.”). Based on this

dataset, the Secretary then calculates the average cost of treating patients across all

diagnosis-related groups and “the average cost of treating a patient in each

diagnosis-related group.” J.A. at 159. The Secretary then divides the average cost

for each diagnosis-related group by the overall average cost. See id. Using this

ratio, he then assigns a new weighting factor to each diagnosis-related group. See


       6
             For context, we note that the process of adjusting the diagnosis-
related group classifications entails, inter alia, moving some diagnoses from one
diagnosis-related group to another and sometimes creating new diagnosis-related
groups altogether. See, e.g., 55 Fed. Reg. at 36,010 (FY 1991 Final Rule) (adding
thirteen new DRGs).

                                          7
id.; see also 42 C.F.R. § 412.60(a) (noting that the Secretary “assigns, for each

DRG, an appropriate weighting factor that reflects the estimated relative cost of

hospital resources used with respect to discharges classified within that group

compared to discharges classified within other groups”). 7

      The recalibration process has the potential of leading to higher payments to

hospitals systemwide. However, Congress requires the Secretary to recalibrate “in

a manner that assures that the aggregate payments . . . are no greater or less than

those that would have been made [pre-recalibration].” 42 U.S.C.

§ 1395ww(d)(4)(C)(iii). In other words, Congress mandates that aggregate

payments remain budget neutral notwithstanding recalibration. See, e.g.,

Adirondack II, 29 F. Supp. 3d at 32 (“[T]he annual DRG recalibration must ‘be

made in a manner that assures that the aggregate payments . . . for discharges in

the fiscal year are not greater or less than those that would have been made for

discharges in the year without such adjustment.’” (omission in original) (quoting

§ 1395ww(d)(4)(C)(iii)), aff’d sub nom. Adirondack Med. Ctr. v. Burwell, 782

F.3d 707 (D.C. Cir. 2015)).




       7
             Here is a grossly simplified example. Say, after recalibration, the
overall average cost of treating Medicare patients is $1,000. And assume that the
average cost of treating patients in diagnosis-related group A is $1,500. Dividing
$1,500 by $1,000 (i.e., $1,500 ÷ $1,000) yields a new (post-recalibration)
weighting factor of 1.5 for that diagnosis-related group.

                                          8
      To achieve budget neutrality in aggregate payments, the Secretary takes two

steps. The Secretary’s first step is to “normalize” the recalibrated diagnosis-

related group weights to offset any change in the average weight caused by

recalibration. 74 Fed. Reg. at 4395 (FY 2010 Final Rule). The Secretary has

explained that normalization negates any increase in average diagnosis-related

group weights by “equating the average case weight after recalibration to the

average case weight before recalibration.” Changes to the Hospital Inpatient

Prospective Payment Systems and Fiscal Year 1994 Rates, 58 Fed. Reg. 46,270,

46,291 (Sept. 1, 1993) (“FY 1994 Final Rule”). 8 More specifically, the Secretary

applies a numerical adjustment “in order to ensure that the average [diagnosis-

related group] weight after recalibration is equal to the average [diagnosis-related

group] weight prior to recalibration.” Proposed Changes to the Hospital Inpatient




       8
             When the Secretary refers to normalized average diagnosis-related
group weights, he frequently uses the phrase “average case weight.” See, e.g., 74
Fed. Reg. at 43,896 (FY 2010 Final Rule); Changes to the Hospital Inpatient
Prospective Payment Systems and Fiscal Year 2006 Rates, 70 Fed. Reg. 47,278,
47,322 (Aug. 12, 2005) (“FY 2006 Final Rule”). Throughout this opinion, to
avoid introducing yet another term for readers to keep straight, we do not use the
phrase “average case weight.” We instead use “average diagnosis-related group
weight” or “average DRG,” which is the terminology the parties most often use.
See, e.g., Aplts.’ Opening Br. at 11 (“[W]hen the Secretary calculates the
hospital-specific rate by dividing by the hospital’s average DRG weight.”);
Aplee.’s Resp. Br. at 7 (referring to “the average diagnosis-related group weight”
(emphasis omitted)).

                                          9
Prospective Payment Systems and Fiscal Year 2010 Rates, 74 Fed. Reg. 24,080,

24,184 (May 22, 2009) (“FY 2010 Proposed Rule”). 9

      Normalization, however, “does not necessarily achieve budget neutrality

with respect to aggregate payments to hospitals because payment to hospitals is

affected by factors other than average [diagnosis-related group] weight.” 58 Fed.

Reg. at 46,291 (FY 1994 Final Rule); see also 74 Fed. Reg. at 43,895 (FY 2010

Final Rule) (noting that “our analysis has indicated that the normalization

adjustment does not usually achieve budget neutrality with respect to aggregate

payments to hospitals” (emphasis added)). For example, Congress requires the

Secretary to apply wage-index adjustments to hospital reimbursement rates to

account for varying labor costs of hospitals located in different geographic areas

of the country, as well as in urban and rural settings, and to do this “in a manner

that assures that aggregate payments to hospitals are not affected by the change in

the wage index.” 58 Fed. Reg. at 46,346 (FY 1994 Final Rule); see 42 U.S.C.



       9
             A simplified example might help. Assume that the average
diagnosis-related-group weight before recalibration was 2.0. And say that after
recalibration the average weight is 2.5. To offset this increase, the Secretary
would apply a normalization factor of 0.8 (i.e., 2.0 ÷ 2.5) to each patient’s post-
recalibration diagnosis-related group weight. See, e.g., Aplee.’s Resp. Br. at 25
(“To normalize the average weights across the two years (i.e., to ensure that the
average [diagnosis-related group] weight does not change), the Secretary would
multiply each patient’s diagnosis-related group weighting factor by 3/6 (the
pre-recalibration average weight, divided by the post-recalibration average
weight).”).

                                         10
1395ww(d)(3)(E) (“[T]he Secretary shall adjust the proportion . . . of hospitals’

costs which are attributable to wages and wage-related costs, of the DRG

prospective payment rates . . . for area differences in hospital wage levels by a

factor (established by the Secretary) reflecting the relative hospital wage level in

the geographic area of the hospital compared to the national average hospital wage

level.”); see also 58 Fed. Reg. at 46,291 (FY 1994 Final Rule) (“Under the

Medicare prospective payment system, different payment rates are calculated for

hospitals located in rural, urban, and large urban areas.”).

      Payment to hospitals is also affected by Congress’s requirement that the

Secretary “provide for an additional payment amount for” teaching hospitals “with

indirect costs of medical education.” § 1395ww(d)(5)(B); see Rush Univ. Med.

Ctr. v. Burwell, 763 F.3d 754, 755 (7th Cir. 2014) (“Teaching hospitals provide a

valuable service to the public by training the next generation of doctors and

medical professionals, but that benefit comes at a price: such hospitals experience

significantly higher per-patient care costs than their non-teaching counterparts. To

compensate them for taking on this extra financial burden, the federal Medicare

program provides additional reimbursement for expenses beyond the immediate

costs of patient care. One such adjustment is for ‘indirect medical education’

(IME) costs.”); Henry Ford Health Sys. v. Dep’t of Health & Human Servs., 654

F.3d 660, 663 (6th Cir. 2011) (“Under the Medicare program, teaching hospitals


                                          11
receive additional payments, above and beyond the reimbursement rate for treating

Medicare patients, to cover the ‘direct’ and ‘indirect costs of medical education.’”

(quoting § 1395ww(d)(5)(B), (h))).

      In light of such factors, normalization of the average diagnosis-related

group weights will not necessarily result in budget neutrality of aggregate

payments systemwide. That is because those factors affect—and frequently

increase—the hospitals’ payment rate and, in computing a hospital’s

reimbursement, “a patient’s [normalized] diagnosis-related group weight is

multiplied by the hospital’s applicable [payment] rate.” Aplee.’s Resp. Br. at 7. 10




       10
              The Secretary argues that “[g]iven the interaction of other Medicare
payment adjustments . . . normalization usually does not lead to budget
neutrality.” Aplee.’s Resp. Br. at 24. He contends that this is especially so when
the high-weight diagnosis-related group weights are disproportionately found in
hospitals that receive higher payments because of adjustments, like the wage
index. See id. (“[I]f urban hospitals with high wage-index adjustments have a
disproportionate number of patients with a high diagnosis-related group weighting
factor, then normalization will not result in budget neutrality.” (emphasis added));
see also 55 Fed. Reg. at 36,074 (FY 1991 Final Rule) (noting that “urban
hospitals generally have a greater proportion of cases concentrated in the
high-weighted DRGs . . . weights will tend to increase the average DRG weight
for these hospitals and, therefore, raise their payments under the prospective
payment system”). The Secretary offers a mathematical hypothetical to support
this view in which normalization of average diagnosis-related group weights does
not result in budget neutrality in part because a patient with a comparatively high
diagnosis-related group weight is admitted to a hospital with a very high payment
rate “due, for instance, to a high wage index or an adjustment for teaching
hospitals.” Aplee.’s Resp. Br. at 24.

                                          12
      Accordingly, to ensure budget neutrality in aggregate payments, the

Secretary takes a second step: he calculates “a budget neutrality adjustment” to

account for those other factors, such that the adjustment is in fact “budget

neutral.” 58 Fed. Reg. at 46,291 (FY 1994 Final Rule); see 55 Fed Reg. at

36,073–74 (FY 1991 Final Rule) (noting the “interactive effect of the wage index

and DRG weights on aggregate payments” and that the Secretary applied a “budget

neutrality adjustment factor” to the hospital-specific rates because unless he did

so, he would not be able to “meet the statutory requirement that aggregate

payments neither increase nor decrease”). “This budget-neutrality adjustment

takes the form of a multiplier that the Secretary applies in calculating the

hospital’s base payment rate[.]” Aplee.’s Resp. Br. at 8.

      Since Fiscal Year (“FY”) 1994, the Secretary has applied the budget-

neutrality adjustment “in a cumulative manner,” commencing with the FY 1993

adjustment factors for that inaugural cumulative computation. Aplts.’ Opening Br.

at 10; see 70 Fed. Reg. at 47,429 (FY 2006 Final Rule). That is to say, he “does

not remove the prior year’s budget-neutrality adjustment before calculating and

applying the current year’s adjustment.” Aplee.’s Resp. Br. at 8; see id. (“[A]ll

diagnosis-related group budget-neutrality adjustments that were applied each fiscal

year from FY 1993 onward are permanently incorporated into a later year’s

rates.”); see also 58 Fed. Reg. at 46,346 (FY 1994 Final Rule) (explaining that the


                                          13
“budget neutrality adjustment factor is applied . . . without removing the effects of

the FY 1993 budget neutrality adjustment”). The Secretary then applies this

cumulative budget-neutrality adjustment factor to the payment rate used in the

reimbursement formula. See 74 Fed. Reg. at 43,895 (FY 2010 Final Rule).

                                           2

      Having defined and described the term “diagnosis-related group weight,” we

turn now to explicating the other major component undergirding a hospital’s

reimbursement: the payment rate. The Secretary reimburses most hospitals using

what is called the federal rate. The starting point in calculating the federal rate in

a given year is the “average standardized amount,” which is essentially the

estimated average per-patient operating costs of inpatient hospital services for all

hospitals within a geographic region. See 42 U.S.C. § 1395ww(d)(1)(A)(iii),

(d)(3)(A); 42 C.F.R. § 412.64. Each year, the Secretary updates the standardized

amount to account for variables such as inflation and wage levels. See 42 U.S.C.

§ 1395ww(b)(3)(B)(i), (d)(3)(E). Once an updated standardized amount is

calculated, the Secretary multiplies it by the cumulative budget-neutrality

adjustment. 58 Fed. Reg. at 46,358 (FY 1994 Final Rule) (in context of discussion

about calculating the federal rate for FY 1994, explaining that the budget-

neutrality adjustment “is applied to the standard Federal payment rate”). To

calculate the actual reimbursement for a specific patient’s inpatient care, the


                                          14
mathematical product of the standardized amount and the budget neutrality

adjustment is multiplied by the patient’s diagnosis-related group weight. 42

U.S.C. § 1395ww(d)(3)(D).

      Although, as discussed, the above-noted federal rate is the mode of

reimbursement that is employed for most hospitals, because certain rural hospitals

“provide critical services to the underserved and uninsured, Congress has adopted

special payment provisions for them.” J.A. at 286 (Dist. Ct. Mem. & Order, dated

Aug. 31, 2017) (quoting Adirondack II, 29 F. Supp. 3d at 32). As relevant here,

those rural hospitals are “sole community” and “Medicare-dependent” hospitals. 11

See, e.g., Cmty. Hosp. v. Sullivan, 986 F.2d 357, 358 (10th Cir. 1993) (noting

Congress has evinced special concern for sole community hospitals). It is

undisputed that each of the Hospitals here is either a sole community or Medicare-

dependent hospital.




       11
             A sole community hospital is one that is (1) “located more than 35
road miles from another hospital,” (2) “the sole source of inpatient hospital
services reasonably available” to Medicare Part A patients in the area, and (3)
“located in a rural area and designated by the Secretary as an essential access
community hospital.” 42 U.S.C. § 1395ww(d)(5)(D)(iii). A Medicare-dependent
hospital is one (1) that is “located in a rural area,” (2) that has fewer “than 100
beds,” (3) that “is not classified as a sole community hospital,” and (4) “for which
not less than 60 percent of its inpatient days or discharges . . . were attributable to
inpatients entitled to benefits under [Medicare Part A].” Id.
§ 1395ww(d)(5)(G)(iv).

                                         15
      Chief among the special payment provisions Congress has adopted for sole

community and Medicare-dependent hospitals is the option of selecting

reimbursement for covered healthcare based on a “hospital-specific rate,” instead

of the federal rate. See 42 U.S.C. § 1395ww(d)(5)(D)(i), (d)(5)(G)(i)–(ii);

Adirondack Med Ctr., 740 F.3d at 695 (noting that these rural hospitals “have the

option” of receiving the higher of the hospital-specific and the federal rate

“[b]ecause these facilities typically serve underserved communities”). As its name

suggests, the hospital-specific rate is different for each eligible hospital.

      The Secretary’s starting point for calculating a hospital-specific rate is the

hospital’s “target amount” in a given “base year.” See 42 U.S.C.

§ 1395ww(d)(5)(D), (d)(5)(G). A target amount is a hospital’s “historic operating

costs” in a specific year. Adirondack Med. Ctr., 740 F.3d at 695; see also 42

U.S.C. § 1395ww(b)(3)(A). Base years are certain statutorily designated years that

Congress has authorized for use in determining a hospital’s corresponding historic

operating costs—viz., its target amount—with hospitals being free to select the

base year that will yield them the highest payment. 12 See 42 U.S.C.


       12
              Sole community hospitals, for example, are authorized to select
either FY 1982, 1987, 1996, or 2006 as a base year. Medicare-dependent
hospitals, for their part, may select either FY 1982, 1987, or 2002 as a base year.
See 74 Fed. Reg. at 43,760–61 (FY 2010 Final Rule). The Hospitals are sole
community hospitals that the Secretary paid based on their FY 2006 base-year
rates and a Medicare-dependent hospital that the Secretary paid based on its FY
2002 base-year rate. See Aplts.’ Opening Br. at 7.

                                           16
§ 1395ww(b)(3)(C), (b)(3)(D). Of particular relevance here, and as further

discussed infra, Congress periodically adds new base years. See, e.g., id.

§ 1395ww(b)(3)(G).

      As with the federal rate, the Secretary annually adjusts the hospital-specific

rate to account for variables such as inflation and wage levels. See id.

§ 1395ww(b)(3)(B)(i), (d)(3)(E); 42 C.F.R. §§ 412.78(e), 412.79(d). He also

applies the cumulative budget-neutrality adjustment to the hospital-specific rate.

See 74 Fed. Reg. at 43,895 (FY 2010 Final Rule); see also 42 C.F.R. §§ 412.77(j),

412.79(i). Finally, to determine payment for a specific patient, the Secretary

multiplies the hospital-specific rate by each patient’s diagnosis-related group

weight, with the product being the hospital’s reimbursement.

      Although both sole community and Medicare-dependent hospitals may select

a “payout” based on a hospital-specific rate, the nature of the payout “differs

slightly” between the two hospitals. Adirondack Med. Ctr., 740 F.3d at 695 n.2.

Reimbursement for sole community hospitals is “fairly straightforward”: they are

to be paid the higher of either the hospital-specific rate or the federal rate. Id.; see

42 U.S.C. § 1395ww(d)(5)(D)(i). On the other hand, Medicare-dependent

hospitals are to be paid the federal rate plus “75% of the difference between the

federal rate payment and the hospital-specific rate payment.” Adirondack Med.

Ctr., 740 F.3d at 695 n.2; see 42 U.S.C. § 1395ww(d)(5)(G)(ii)(II).


                                           17
                                           B

      Having laid out the basics of the Medicare Part A reimbursement system, we

can focus on the part of that system at issue here—the Secretary’s methodology for

calculating the hospital-specific rate when Congress adds a new base year. In the

following subsections, we explain how that methodology works and how the

Secretary has applied it over the years.

                                           1

      When Congress adds a new base year, the hospital-specific rate for that new

year is calculated according to the following four-step formula:

      Step One: Divide the hospital’s target amount for the new base year “by
      the number of discharges in the base [year].” 42 C.F.R. §§ 412.78(c),
      412.79(b).
      Step Two: Divide the figure from step one by the hospital’s normalized
      average diagnosis-related group weight for the new base year. See id.
      §§ 412.78(d), 412.79(c).
      Step Three: Apply an update factor to account for specific variables
      such as inflation and wage levels. See id. §§ 412.73(c), 412.78(e),
      412.79(d).
      Step Four: Apply a cumulative budget-neutrality adjustment to the
      resulting rate figure. See id. §§ 412.78(j), 412.79(i); 74 Fed. Reg. at
      43,895–96 (FY 2010 Final Rule). In this context, “cumulative” means
      that the Secretary does not remove the budget adjustments from years
      predating the new base year. 13



       13
             The formula is stated here in highly simplified form to highlight the
area of contention between the parties: the interaction between step 2 and step 4.
The Secretary, for example, states the formula in eight steps, detailing matters not
directly bearing on this dispute. See Aplee.’s Resp. Br. at 29–30.

                                           18
      The amount this formula yields is the hospital-specific rate for a given

hospital in the new base year. That rate is then multiplied by each patient’s

diagnosis-related group weight, which yields the hospital’s reimbursement for each

patient’s inpatient care.

      The Hospitals do not challenge steps one and three. And much of steps two

and four is also uncontroversial. The Hospitals agree, for instance, “that the

average DRG weight used as a divisor [in step two] has been normalized.” Aplts.’

Reply Br. at 17. And they “do not object to the fact that DRG weights are used as

a divisor” in step two. Aplts.’ Opening Br. at 9 n.4. Likewise, “[t]he Hospitals do

not object to prior-year adjustments being applied once.” Id. at 18. In fact, the

Hospitals do not even complain about the cumulative nature of this adjustment.

See Aplts.’ Reply Br. at 2 (“The Hospitals explicitly stated on several occasions . .

. that their contention is not that the prior-year budget-neutrality adjustments

should not be applied once . . . .”). Nor do they “necessarily take issue with the

Secretary’s decision to apply the [cumulative budget-neutrality adjustment] to the

rates instead of the weights.” Aplts.’ Opening Br. at 24.

      What the parties do vigorously dispute, however, are the consequences of

the Secretary applying a cumulative budget-neutrality adjustment in step four.

Above all, they contest whether that adjustment is being applied twice—once in

step two and then again in step four. Going forward, the focal point of our


                                          19
analysis will be unpacking how those steps interact. Before delving into that

disagreement, however, it helps to understand how the Secretary has applied his

methodology over the years.

                                         2

        As discussed supra, Congress has periodically added new base years.

Whenever this happens, the Secretary issues “rebasing” instructions to fiscal

intermediaries. 14 See, e.g., J.A. at 339–43 (CMS Transmittal A-01-123, dated

Sept. 27, 2001) (“2000 Instructions”). These are technical instructions, which tell

the intermediaries how to calculate the hospital-specific rates for the new base

year.

        In 1999, Congress added FY 1996 as a base year for sole community

hospitals. See Medicare, Medicaid, and SCHIP Balanced Budget Refinement Act

of 1999, Pub. L. No. 106-113, § 405, 113 Stat. 1501 (codified as amended at 42

U.S.C. § 1395ww(b)(3)(G)). In response, the Secretary issued the 2000

Instructions. See J.A. at 339–43 (2000 Instructions). The instructions, as it turned

out, were not a model of clarity. Notably, they failed to expressly state whether


        14
             Fiscal intermediaries, also referred to as “Medicare Administrative
Contractors,” are private entities that, acting as the Secretary’s agent, process
Medicare claims. See 42 U.S.C. § 1395h; 42 C.F.R. §§ 421.3, 421.100. As
relevant here, reimbursement of participating hospitals’ Medicare Part A costs is
sought and made through these intermediaries, and as part of that process, the
intermediaries are responsible for actually performing the reimbursement
calculations described at length in this opinion. See 42 C.F.R. § 421.100.

                                         20
the intermediaries were to apply a cumulative budget-neutrality adjustment to the

hospital-specific rate for the new base year. The closest the instructions came to

addressing the issue was in the statement that the FY 1996 hospital-specific rate

was to be multiplied “by a factor of 1.02547 to update it from 1996 to 2000.” Id.

at 342.

      But that remark is ambiguous. On the one hand, the 1.02547 figure might

have included the budget-neutrality adjustments from FY 1993 (the first year for

such adjustments) to FY 1996. See Aplts.’ Opening Br. at 11–12 (acknowledging

this possibility); Aplee.’s Resp. Br. at 15 (arguing that the 2000 Instructions

directed fiscal intermediaries to “apply the cumulative diagnosis-related group

budget-neutrality adjustment from the first year the adjustment was applied”); cf.

Adirondack Med. Ctr. v. Sebelius (Adirondack I), 935 F. Supp. 2d 121, 132

(D.D.C. 2013) (explaining that the 2000 Instructions directed intermediaries to

apply “cumulative DRG budget neutrality adjustment factors from FY 1993 to FY

2000”). On the other hand, the intermediaries were instructed to update the

hospital-specific rate “from 1996 to 2000,” implying the budget-neutrality

adjustment was not cumulative. J.A. at 342 (2000 Instructions) (emphasis added).

      In 2006, Congress added FY 2002 as a new base year for Medicare-

dependent hospitals. See Deficit Reduction Act of 2005, Pub. L. No. 109-171,

§ 5003(b), 120 Stat. 4, 32 (codified as amended at 42 U.S.C. § 1395ww(b)(3)(K)


                                         21
(2006)). The Secretary again issued rebasing instructions. See J.A. at 324–38

(CMS Transmittal 1067, dated Sept. 25, 2006) (“2006 Instructions”). This time,

the instructions seemed to speak clearly—the Secretary did not instruct

intermediaries to apply prior years’ budget-neutrality adjustments to the new base

year. See id. at 328. Instead, he instructed that the budget-neutrality adjustments

were to be applied prospectively only, i.e., for years after the new FY 2002 base

year. See Aplee.’s Resp. Br. at 15 (acknowledging that “unlike the 2000

instructions, these instructions inadvertently failed to tell the [Medicare]

contractors to apply the cumulative diagnosis-related group budget-neutrality

adjustment from FY 1993 forward”).

      Two years later, Congress added FY 2006 as a new base year for sole

community hospitals. See Medicare Improvements for Patients and Providers Act

of 2008, Pub. L. No. 110-275, § 122(a), 122 Stat. 2494 (codified as amended at 42

U.S.C. § 1395ww(b)(3)(L) (2008)). As before, the Secretary issued rebasing

instructions. See J.A. at 344–49 (CMS Transmittal 1610, dated Oct. 3, 2008)

(“2008 Instructions”). Like the 2006 Instructions, the 2008 Instructions did not

direct intermediaries to apply prior years’ budget-neutrality adjustments to the new

base year; again, they were directed to apply the adjustments only

prospectively—that is, for years after FY 2006. See id. at 349; see also Aplee.’s

Resp. Br. at 15 (“In 2008, when Congress added FY 2006 as a possible base year


                                          22
for sole community hospitals, the technical instructions that CMS first sent to

contractors contained the same mistake as the 2006 instructions regarding

Medicare-dependent, small rural hospitals.”).

      But about six weeks later, the Secretary revised the 2008 Instructions in a

Joint Signature Memorandum. See J.A. at 350–53 (Joint Signature Mem., dated

Nov. 17, 2008). In this memorandum, the Secretary no longer instructed

intermediaries to apply the budget-neutrality adjustments prospectively only, as he

had in his initially issued 2008 Instructions. Rather, he instructed the

intermediaries to apply to the new FY 2006 base year all budget-neutrality

adjustments extending back to FY 1993. See id. at 350–51.

      Another six months passed before the Secretary issued a proposed rule

pertaining to Medicare-dependent hospitals that explained to the public his

methodology for FY 2010. 74 Fed. Reg. at 24,183–85 (FY 2010 Proposed Rule).

The FY 2010 Proposed Rule reiterated the Secretary’s policy of applying a

cumulative budget-neutrality adjustment “to both the standard Federal rate and

hospital specific rates” without “remov[ing] the prior years’ budget neutrality

adjustment.” Id. at 24,184. To do otherwise, the Secretary explained, “would not

satisfy” Congress’s mandate to achieve budget neutrality. Id.

      In explaining why a cumulative budget-neutrality adjustment was needed,

the Secretary said that “[i]f we were to remove this budget neutrality adjustment


                                          23
factor for years prior to the base year, we believe the normalized DRG weights

applied to the hospital-specific amounts would be artificially high, thus resulting

in higher aggregate payments than permitted under the statute.” Id. This notion of

“artificially high” normalized average diagnosis-related group weights was new.

For years, the Secretary had explained that normalization negated any increase in

diagnosis-related group weights by “equating the average [diagnosis-related group]

weight after recalibration to the average [diagnosis-related group] weight before

recalibration.” 58 Fed. Reg. at 46,291 (FY 1994 Final Rule). But normalization

did not always “achieve budget neutrality with respect to aggregate payments . . .

because payment . . . is affected by factors other than average [diagnosis-related

group] weight.” Id. (emphasis added). The cumulative budget-neutrality

adjustment accounted for these other factors—not “artificially high” average

diagnosis-related group weights. 74 Fed. Reg. at 24,184 (FY 2010 Proposed

Rule). These longstanding positions of the Secretary were inconsistent with the

idea of “artificially high” normalized average diagnosis-related group weights.

      Although the FY 2010 Proposed Rule introduced some uncertainty to the

regulatory landscape, it also shed substantial light on the lingering question

surrounding application of the cumulative budget-neutrality adjustment. As

explained above, the 2000 Instructions had left in doubt whether the Secretary’s

instructions required application of a cumulative budget-neutrality adjustment to


                                          24
calculate the hospital-specific rates for the FY 1996 base year. The FY 2010

Proposed Rule removed that doubt. The proposed rule clarified that “the

instructions for implementing both the FY 1996 and FY 2006” base years applied

“cumulative budget neutrality adjustment factors” including each year’s

adjustment “since FY 1993.” Id. And those instructions were in keeping with the

Secretary’s “established policy.” Id.

      The FY 2010 Proposed Rule brought the 2006 Instructions in line with that

declared policy. Recall, those instructions had directed intermediaries to apply

“budget adjustment factors” prospectively for the new FY 2002 base year—that is,

“for FYs 2003 through 2007.” Id. The failure to include the budget-neutrality

adjustments from “FYs 1993 through 2002,” the Secretary opined, was

“inconsistent with [his] stated policy of applying a cumulative budget neutrality

adjustment” and led to about a “1.74 percent” overpayment to Medicare-dependent

hospitals using the FY 2002 base year. Id. So going forward, the Secretary

announced, intermediaries were to once again apply a cumulative budget-neutrality

adjustment for all base years. Id. Of course, he admitted, this change would

potentially “lower the hospital-specific rate” for some Medicare-dependent

hospitals using the FY 2002 base year, to the point that the federal rate would

result in higher payments than the hospital-specific rate. Id. at 24,185. But the

cumulative adjustment was necessary to achieve budget neutrality and maintain “a


                                         25
meaningful comparison between payments under the Federal rate, which is

adjusted by the cumulative budget neutrality factor, and payments based on the

hospital-specific rate.” Id. at 24,184.

      The FY 2010 Proposed Rule drew many public comments. Several

commenters argued that a cumulative budget-neutrality adjustment for new base

years was unnecessary. Indeed, they believed this adjustment was already baked

into step two of the Secretary’s methodology—i.e., by dividing the hospital’s

average per-patient expenses in the new base year by its normalized average

diagnosis-related group weight. See J.A. at 312–13 (Rural Referral Center/Sole

Community Hospital Coalition, Comment Letter on FY 2010 Proposed Rule (June

25, 2009)). After all, these commenters pointed out, the Secretary had admitted

that those average diagnosis-related group weights were “artificially high”—even

after normalization. Id. at 312 (quoting 74 Fed. Reg. at 24,184 (FY 2010 Proposed

Rule)). And using these inflated weights as a divisor, the commenters explained,

resulted in a hospital-specific rate that was lower than it would have otherwise

been. See id. at 313. The same was not true for the federal rate, however, because

the Secretary did not use the inflated weights as a divisor in calculating that rate.

Hence, they argued, a cumulative budget-neutrality adjustment was appropriate for

the federal-rate hospitals, but it was unnecessary—indeed, duplicative—for sole

community and Medicare-dependent hospitals. Id. at 314–15.


                                           26
      The Secretary responded to these comments in the preamble to the FY 2010

Final Rule. See 74 Fed. Reg. at 43,895–96 (FY 2010 Final Rule). Retreating from

the “artificially high” language in the proposed rule, the Secretary rejected the

claim that the normalized average diagnosis-related group weights were too high.

See id. at 43,896. Rather, he explained that “[b]ecause the weights are

normalized,” they were no higher than they were pre-recalibration. Id. For that

reason, the Secretary denied that “the cumulative budget neutrality adjustment”

was meant to “offset[] an average [DRG] weight increase due to recalibration.”

Id. Thus, he reasoned that “[t]he cumulative budget neutrality adjustment [was]

not already being accounted for” in step two. Id. Satisfied that he put down the

confusion, the Secretary published the FY 2010 Final Rule.

                                          C

      This case unfolded against that backdrop. After the publication of the FY

2010 Final Rule, the Hospitals took issue with the Secretary’s methodology for

calculating the hospital-specific rate for new base years. And dissatisfied with

their reimbursements under that methodology, the Hospitals filed administrative

appeals with the Provider Reimbursement Review Board, an independent panel

authorized to hear appeals from the Secretary’s final determinations. See, e.g.,

J.A. at 354–81 (Hannover Hosp. Appeal Request, dated May 7, 2010); see 42

U.S.C. § 1395oo(a)(1). Though the Board concluded that it “lack[ed] the authority


                                          27
to decide the legal question” the Hospitals raised, it granted their request for

expedited judicial review. J.A. at 322, 323 (Bd. Decision, dated Oct. 8, 2015); see

42 U.S.C. § 1395oo(f)(1).

      The Hospitals then sued the Secretary in the district court. See J.A. at

50–108 (First Am. Compl., filed Feb. 16, 2016). Their complaint alleged that the

Secretary’s methodology violated the Administrative Procedure Act (the “APA”).

See id. at 59–62. Specifically, the Hospitals argued that the Secretary’s

application of the cumulative budget-neutrality adjustment to the hospital-specific

rate for new base years was “arbitrary, capricious, . . . or otherwise not in

accordance with law.” 15 Id. at 61 (quoting 5 U.S.C. § 706(2)(A)).

      Both parties moved for summary judgment. The Hospitals argued that the

Secretary’s methodology was arbitrary and capricious for three reasons. See id. at

133–47 (Pls.’ Mem. of P. & A. in Supp. of Mot. for Summ. J., filed Sept. 6, 2016).

First, they claimed that the Secretary applied the same cumulative budget-


       15
             The Hospitals’ complaint also alleged that the cumulative budget-
neutrality adjustment was “in excess of statutory jurisdiction” under 5 U.S.C.
§ 706(2)(C) and contrary to the notice-and-comment requirements in § 553(b)–(c).
See J.A. at 59–63. On appeal, the Hospitals have waived these arguments by
inadequately briefing them. See Aplts.’ Opening Br. at 22–23 (mentioning only
§ 706(2)(A)); see also Allen v. United Servs. Auto. Ass’n, 907 F.3d 1230, 1236
n.3 (10th Cir. 2018) (ruling that party’s “cursory argument” on appeal was
“waived”); Sierra Club, Inc. v. Bostick, 787 F.3d 1043, 1060 n.18 (10th Cir.
2015) (concluding that because parties “have not developed” their argument, “it is
waived”). Thus, we need not and do not consider whether the Secretary’s
methodology violates §§ 553(b)–(c) or 706(2)(C).

                                           28
neutrality adjustment twice—once by using inflated normalized diagnosis-related

group weights as a divisor in step two and then again in step four. See id. at

133–43. Second, the Hospitals contended that the Secretary’s methodology

yielded different payments than “would have been made had [he] . . . applied the

budget-neutrality adjustments to the DRG weights themselves.” Id. at 132. Third,

they claimed that the Secretary acted arbitrarily and capriciously by not calculating

the hospital-specific rate for new base years “based on 100 percent” of a hospital’s

base-year “target amount.” 16 42 U.S.C. § 1395ww(d)(5)(D)(i)(I); see J.A. at

143–46. For those reasons, the Hospitals asked the district court to order “the

Secretary to recalculate [their] base-year hospital-specific rates and compensate

[them] accordingly.” J.A. at 148.




       16
             This “based on 100 percent” language applies only to sole community
hospitals. Compare 42 U.S.C. § 1395ww(d)(5)(D)(i)(I), with id.
§ 1395ww(d)(5)(G)(ii) (omitting that language for Medicare-dependent hospitals).
But the statute does command the Secretary to reimburse both sole community
and Medicare-dependent hospitals based on their “allowable operating costs” in
the base year. See id. § 1395ww(b)(3)(C)(i)(I) (sole community hospitals); id.
§ 1395ww(b)(3)(D)(i)(I) (Medicare-dependent hospitals). Both before the district
court and on appeal, the Hospitals have read these provisions as demanding the
Secretary reimburse both sole community and Medicare-dependent hospitals for
100% of their base-year operating costs. See J.A. at 143–46; Aplts.’ Opening Br.
at 34–41, 37 n.20. For simplicity, in addressing this argument, we refer to the
“based on 100 percent” language without distinguishing between sole community
and Medicare-dependent hospitals because that language best captures the
substance of the Hospitals’ argument as it pertains to both types of hospitals.

                                          29
      The Secretary cross-moved for summary judgment. See J.A. at 150–84

(Def.’s Mem. in Opp’n to Pls.’ Mot. & in Supp. of Cross-Mot. for Summ. J, filed

Oct. 20, 2016). First, the Secretary denied that his methodology applied the

budget-neutrality adjustment twice. See id. at 181. That argument, the Secretary

noted, turned on the false premise that the normalized average diagnosis-related

group weights were “too high.” Id. Instead, normalization guaranteed that the

weights were exactly the same as they were pre-recalibration. Id. at 181 & n.10;

see id. at 181. That the FY 2010 Proposed Rule had used the phrase “artificially

high” was an unfortunate and imprecise “way of stating that without a cumulative

budget-neutrality adjustment the payments under the hospital-specific rate would

be higher.” Id. at 181 n.10. Second, the Secretary pointed out that the Hospitals

had conceded that the Medicare statute did not compel him to apply the budget-

neutrality adjustment to the weights rather than to the rates. As a result, whether

his methodology yielded a different payment than if he had applied the adjustment

to the weights was irrelevant. See id. at 176–77. Lastly, the Hospitals’ “based on

100 percent” argument failed, too, the Secretary observed: that argument wrongly

assumed that a new base year was “a kind of reset” entitling the Hospitals to 100%

of their operating costs rather than a starting point from which the Secretary must

make adjustments. Id. at 178. Thus, the Secretary argued that he was entitled to

summary judgment.


                                          30
      The district court agreed with the Secretary. It viewed the Secretary’s

choice “to apply pre-base year budget neutrality adjustments” as a “consistent and

rational” one. Id. at 295, 297 n.8. And the district court thought the Secretary had

adequately explained in the FY 2010 Final Rule why his methodology did not in

fact apply the budget-neutrality adjustment twice. See id. at 297–98. Likewise,

the court agreed with the Secretary’s view that “an amount based on 100 percent

of the hospital’s target amount,” 42 U.S.C. § 1395ww(d)(5)(D)(i)(I), was “the

starting point—not the end point—for the Secretary’s calculations,” J.A. at 301.

The district court added that it would “not second-guess the Secretary’s policy”

just because there may have been “other ways of calculating payments.” Id. at

300. And so the court denied the Hospitals’ summary-judgment motion, granted

the Secretary’s cross-motion, and entered final judgment.

                                         II

      The Hospitals now appeal from the final judgment. Their appeal raises one

issue: Is the Secretary’s methodology for calculating the hospital-specific rate for

a new base year arbitrary and capricious under 5 U.S.C. § 706(2)(A)? 17 In


       17
              The Hospitals style their appeal as raising three issues. See Aplts.’
Opening Br. at 6. In truth, those three issues are permutations of the same
issue—whether the Secretary’s methodology is arbitrary and capricious. We
therefore address the Hospitals’ three issues as three arguments within the one
larger legal issue. Similarly, though the Hospitals cite both §§ 706(2)(A) and
706(2)(C) in their statement of the issues, see id., their standard-of-review section
discusses only § 706(2)(A), see id. at 22. By inadequately briefing their

                                         31
answering that question, we review the district court’s grant of summary judgment

de novo. See McKeen v. U.S. Forest Serv., 615 F.3d 1244, 1253 (10th Cir. 2010).

During our review, “[w]e apply the same standard of review as the district court.”

WildEarth Guardians v. U.S. Bureau of Land Mgmt., 870 F.3d 1222, 1233 (10th

Cir. 2017).

      In Medicare-reimbursement cases, the APA supplies the standard we use to

review the Secretary’s actions. See 42 U.S.C. § 1395oo(f)(1); accord Thomas

Jefferson Univ. v. Shalala, 512 U.S. 504, 512 (1994). We will invalidate an

agency action under § 706(2)(A) only if it is “arbitrary, capricious, an abuse of

discretion, or otherwise not in accordance with law.” 5 U.S.C. § 706(2)(A);

accord W. Watersheds Project v. U.S. Bureau of Land Mgmt., 721 F.3d 1264, 1273

(10th Cir. 2013). To assess the agency’s action, we look to “the agency’s

contemporaneous explanation in light of the existing administrative record.”

Dep’t of Commerce v. New York, ---- U.S. ----, 139 S. Ct. 2551, 2573 (2019)

(recognizing “a narrow exception” when there is “a strong showing of bad faith or

improper behavior”). But we do not consider the agency’s “post hoc

rationalizations” for the action. Sorenson Commc’ns, Inc. v. FCC, 567 F.3d 1215,

1221 (10th Cir. 2009). That said, if the agency relied on impermissible




§ 706(2)(C) argument, the Hospitals waive it. See, e.g., Allen, 907 F.3d at 1236
n.3.

                                          32
considerations or “entirely failed to consider an important aspect of the problem,”

then it acted arbitrarily and capriciously. Ukeiley v. EPA, 896 F.3d 1158, 1164

(10th Cir. 2018) (quoting US Magnesium, LLC v. EPA, 690 F.3d 1157, 1164 (10th

Cir. 2012)). The same is true if the agency’s stated rationale “runs counter to the

evidence before [it] or is so implausible that it could not be ascribed to a

difference in view or the product of agency expertise.” Id.

      But APA review is narrow. And the arbitrary-and-capricious standard “is

very deferential to the agency.” W. Watersheds, 721 F.3d at 1273 (quoting

Hillsdale Envtl. Loss Prevention, Inc., v. U.S. Army Corps of Eng’rs, 702 F.3d

1156, 1165 (10th Cir. 2012)). Indeed, we presume that an agency action is valid

unless the party challenging the action proves otherwise. See Dine Citizens

Against Ruining Our Env’t v. Bernhardt, 923 F.3d 831, 839 (10th Cir. 2019).

“Our deference to the agency is ‘especially strong where the challenged decisions

involve technical or scientific matters within the agency’s area of expertise.’” Id.

(quoting Morris v. U.S. Nuclear Regulatory Comm’n, 598 F.3d 677, 691 (10th Cir.

2010)). Above all, we may not “substitute our judgment for that of the agency” on

matters within its expertise. Judulang v. Holder, 565 U.S. 42, 53 (2011) (quoting

Motor Vehicle Mfrs. Ass’n of U.S., Inc. v. State Farm Mut. Auto. Ins. Co., 463 U.S.

29, 43 (1983)).




                                          33
       The parties agree that § 706(2)(A)’s arbitrary-and-capricious standard

governs this appeal. The Hospitals frame their entire argument as arising under

that subsection. See Aplts.’ Opening Br. at 22. For his part, the Secretary agrees

that we should review his actions “under the familiar standards of the [APA].”

Aplee.’s Resp. Br. at 19. And, though he does not expressly argue in the language

of arbitrary-and-capricious review, the Secretary fully engages with the Hospitals’

arbitrary-and-capricious arguments. See, e.g., id. at 22–30 (responding to the

Hospitals’ divisor argument but never using the words “arbitrary” or “capricious”).

Thus, we take it as undisputed that § 706(2)(A)’s arbitrary-and-capricious standard

applies here. 18


        18
              The Secretary also invokes the familiar standard from Chevron,
U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837 (1984).
See Aplee.’s Resp. Br. at 19. But after a threadbare citation, the Secretary never
again mentions Chevron, never recites its well-known two steps, and never
applies those steps to the facts here. Instead, the Secretary dresses his arguments
in “reasonableness” garb. See, e.g., id. at 20 (arguing “[t]he Secretary reasonably
adopted [his] methodology”). “Reasonableness,” however, is relevant under both
the arbitrary-and-capricious standard and Chevron. See Chevron, 467 U.S. at 844;
W. Watersheds, 721 F.3d at 1273. So the Secretary’s perfunctory and fleeting
invocation of Chevron waives his argument for Chevron deference. See, e.g.,
Dutcher v. Matheson, 840 F.3d 1183, 1203 & n.12 (10th Cir. 2016) (declining to
perform a Chevron analysis when a plaintiff raised argument for first time in a
motion to reconsider and rejecting argument that courts must “sua sponte
undertake a Chevron reasonableness analysis any time an agency interpretive
regulation is implicated”); Bronson v. Swensen, 500 F.3d 1099, 1104 (10th Cir.
2007) (“[W]e routinely have declined to consider arguments that are not raised, or
are inadequately presented, in an appellant’s opening brief.”); see also Neustar,
Inc. v. FCC, 857 F.3d 886, 893–94 (D.C. Cir. 2017) (“The FCC’s brief nominally
references Chevron’s deferential standard in its standard of review but did not

                                         34
invoke this standard with respect to rulemaking. Consequently, it has forfeited
any claims to Chevron deference.”); Commodity Futures Trading Comm’n v.
Erskine, 512 F.3d 309, 314 (6th Cir. 2008) (“[T]he CFTC waived any reliance on
Chevron by failing to raise it to the district court.”); Faris v. Williams WPC-I,
Inc., 332 F.3d 316, 319 (5th Cir. 2003) (“This [Chevron] argument was not
presented to nor passed on by the district court, and therefore may not be
considered on appeal.”); cf. Lubow v. U.S. Dep’t of State, 783 F.3d 877, 884 (D.C.
Cir. 2015) (“The applicability of the Chevron framework does not go to our
court’s jurisdiction, and a party therefore can forfeit an argument against
deference by failing to raise it.”); cf. also Gardner v. Galetka, 568 F.3d 862, 878
(10th Cir. 2009) (answering in the negative the following question: “can the
congressionally mandated deferential standard of review [of the Anti-terrorism
and Effective Death Penalty Act] be waived by counsel?” (emphasis added)). In
any event, eliding a formal Chevron analysis does not materially alter our
resolution of the issue before us or, more specifically, our consideration of the
parties’ arguments. After all, the Secretary engages fully with the Hospitals’
arbitrary-and-capricious arguments. See, e.g., Aplee.’s Resp. Br. at 22–30. And
insofar as the Secretary’s reasonableness arguments involve a tacit claim for
deference at the second step of Chevron, the Secretary is effectively arguing that
his methodology is not “arbitrary or capricious in substance.” Judulang, 565 U.S.
at 52 n.7 (quoting Mayo Found. for Med. Ed. & Research v. United States, 562
U.S. 44, 53 (2011)). Consequently, whether we apply Chevron or arbitrary-and-
capricious review does not materially alter the outcome or change our analysis.

                                        35
                                           III

         With the standard of review laid out, we can turn to the question before us:

Is the Secretary’s methodology for calculating the hospital-specific rate for a new

base year arbitrary and capricious?

         The Hospitals answer that question in the affirmative, for three reasons.

First, they argue that the “Secretary acted arbitrarily and capriciously in applying

the same budget-neutrality adjustments twice.” Aplts.’ Opening Br. at 6. Second,

the Hospitals claim that the Secretary’s methodology is arbitrary and capricious

and contrary to Congress’s statutory command because it “yields a different

payment than had he budget-neutralized the weights themselves.” Id. Third, they

contend that the Secretary’s methodology is arbitrary and capricious because it

“would not reimburse a hospital its full base-year allowable operating costs.” Id.

         The Secretary disagrees. He denies that applying a cumulative budget-

neutrality adjustment to a new base year mistakenly applies that adjustment twice.

The Secretary likewise refutes the claim that he must apply the cumulative budget-

neutrality adjustment to the diagnosis-related group weights themselves. Finally,

the Secretary disagrees that his methodology must be arbitrary and capricious

because it would not reimburse the Hospitals for 100% of their base-year operating

costs.




                                           36
      We agree with the Secretary. That is to say, for the reasons below, we hold

that the Secretary’s methodology is not arbitrary and capricious. Thus, we affirm

the district court’s judgment.

                                          A

      The centerpiece of the Hospitals’ position is their argument that the

Secretary mistakenly applies the cumulative budget-neutrality adjustment twice

when calculating the hospital-specific rate for a new base year. This double

application is, the Hospitals say, “arbitrary and capricious on its face.” Id. at 27.

“[B]ut at a minimum,” they argue, this error proves that the Secretary

misunderstood his own methodology and its consequences. Id. For those reasons,

the Hospitals claim that the Secretary’s methodology is arbitrary and capricious.

      We disagree. We explain our disagreement in three sections. First, we

recount the Hospitals’ double-application argument in more detail. Second, we

conclude that this argument rests on flawed premises. Third, we reject the

Hospitals’ suggestion that the Secretary misunderstood his own methodology.

                                          1

      To understand the Hospitals’ double-application argument, recall three

features of the Medicare-reimbursement system:

      Recalibration: Congress requires the Secretary to “recalibrate” (i.e.,
      adjust) the diagnosis-related group weights every year. See 42 U.S.C.
      § 1395ww(d)(4)(C)(i). Because recalibration can change aggregate
      payments to hospitals systemwide, Congress requires the Secretary to

                                          37
      recalibrate the weights “in a manner that assures that aggregate
      payments” neither increase nor decrease. Id. § 1395ww(d)(4)(C)(iii); 74
      Fed. Reg. at 43,895 (FY 2010 Final Rule).
      Normalization: Achieving budget neutrality is a two-step process. To
      that end, the Secretary’s first step is to “normalize” the recalibrated
      weights. Normalization guarantees “that the average [diagnosis-related
      group] weight after recalibration is equal to the average . . . weight prior
      to recalibration.” 58 Fed. Reg. at 46,291 (FY 1994 Final Rule). For
      example, in 1990, recalibration increased the average diagnosis-related
      group weight by 1.35%. See Changes to the Inpatient Hospital
      Prospective Payment System and Fiscal Year 1990 Rates, 54 Fed. Reg.
      36,452, 36,470 (Sept. 1, 1989) (“FY 1990 Final Rule”). So to offset the
      1.35% increase in average weight caused by recalibration, the Secretary
      normalized the post-recalibration weights. See id.
      Budget-Neutrality Adjustment: Normalization, however, does not always
      “achieve budget neutrality” because “factors other than average
      [diagnosis-related group] weight” affect payments. 58 Fed. Reg. at
      46,291 (FY 1994 Final Rule). So the Secretary’s second step to achieve
      budget neutrality is to calculate and apply “a budget neutrality
      adjustment” to account for those other factors. Id.

      Now recall the Secretary’s four-step methodology for calculating the

hospital-specific rate for a new base year:

      Step One: Divide the hospital’s target amount for the new base year by
      the number of discharges that year .
      Step Two: Divide the figure from step one by the hospital’s normalized
      average diagnosis-related group weight for the new base year.
      Step Three: Apply an update factor to account for specific variables
      such as inflation and wage levels.
      Step Four: Apply the cumulative budget-neutrality adjustment.

      The nub of the dispute is whether the Secretary effectively applies the

budget-neutrality adjustment twice—once in step two and then again in step four.

The Hospitals argue that they can prove that step two includes the cumulative

                                          38
budget-neutrality adjustment. This argument rests on two premises. First, that the

normalized diagnosis-related group weights are “too high to be budget neutral.”

Aplts.’ Opening Br. at 2–3. Second, that these weights are inflated by the precise

amount necessary to achieve budget neutrality. And, because these inflated

weights are used as a divisor in step two, the hospital-specific rate for a new base

year is reduced by the exact percentage that the Secretary later reduces the rates

through application of the cumulative budget-neutrality adjustment in step four.

      Consider the following hypothetical that the Hospitals say proves their

double-application argument. 19 Imagine that Congress adds FY 2002 as a new

base year. And assume that the Secretary calculates a cumulative budget-

neutrality adjustment factor of 0.986. (This figure would be the product of

budget-neutrality adjustments from 1996 to 2002.) When the Secretary multiplies

this adjustment factor by the federal rate and does the same for the hospital-

specific rate in step four, he reduces those rates by 1.4%. And, from this “1.4

percent budget-neutrality adjustment,” the Hospitals reason that “the DRG weights

have increased by 1.4 percent” from 1996 to 2002. Aplts.’ Reply Br. at 19. Put



       19
             The Hospitals crafted this hypothetical in their reply brief,
responding to the Secretary’s own less extensive hypothetical in which the
Secretary concludes that, at bottom, the Hospitals seek to “avoid the impact of
budget neutrality adjustments from 1996 through 2002”—the new hypothetical
base fiscal year. Aplee.’s Resp. Br. at 32. We convey that hypothetical in all
material respects, see Aplts.’ Reply Br. at 18–24, and subsequently analyze it.

                                          39
differently, the Hospitals think that—even after normalization—the average

diagnosis-related group weights for the new FY 2002 base year are 1.4% too high.

See id. at 20–21. And by using these inflated weights as a divisor in step two, the

Secretary applies the same 1.4% budget-neutrality reduction to the hospital-

specific rate that he later applies in step four. See id.

      Here is how this hypothetical would play out under the Hospitals’

assumptions. Assume that in 1996 Hospital X’s per-patient target amount was

$1,000, and its average diagnosis-related group weight that year was 1.0. So

Hospital X would have “receive[d] $1,000 for treating its average patient” in 1996.

Id. at 19. And assume that nothing changed from 1996 to 2002; that is, the per-

patient target amount in 2002 remained $1,000, and the patients that Hospital X

treated in 2002 had identical ailments to those treated in 1996. Despite this lack

of change, Hospital X’s average diagnosis-related group weight for FY

2002—even after normalization—would have increased by 1.4% to 1.014. See id.

So when the Secretary in step two divides Hospital X’s per-patient target amount

for 2002 ($1,000) by its inflated average diagnosis-related group weight (1.014),

he gets $986.19. Id. Then, in step four, “the Secretary . . . would mistakenly

believe that he had to apply another 1.4 percent reduction [in the form of a

cumulative budget-neutrality adjustment of 0.986] to the hospital’s 2002

hospital-specific rate of $986.19, leading to a hospital-specific rate of $972.38.”


                                            40
Id. at 20. This rate is about 2.8% less than the 1996 rate. Thus, the Hospitals

posit that the Secretary mistakenly applied the 1.4% cumulative budget-neutrality

adjustment twice—once in step two and then again in step four.

                                          2

      The Hospitals’ double-application argument, however, rests on flawed

premises. The Hospitals assume that the normalized average diagnosis-related

group weights used as a divisor in step two are “artificially high” or “too high to

be budget neutral.” Aplts.’ Opening Br. at 24 & n.12. This assumption turns on

the validity of the claim “that a hospital that had an average DRG weight of 1.0 in

1996 would have a [normalized average] DRG weight of 1.014 in 2002 if it treated

the same type of patients.” Aplts.’ Reply Br. at 23; see id. at 21 (noting that “the

one point of disagreement between the parties regarding this hypothetical” pertains

to “whether the hospital’s DRG weight in 2002 would necessarily be 1.014 . . . as

the Hospitals contend”). According to the Hospitals, it is “necessarily” true that

the DRG weight would be 1.014 “because the 1.4 percent budget neutrality

adjustment means that, based solely on DRG recalibrations, the [normalized] DRG

weights have increased by 1.4 percent.” Id. at 19.

      These assumptions evince a misunderstanding of the role of normalization

and the budget-neutrality adjustment. Recall that after the Secretary recalibrates

the diagnosis-related group weights, he normalizes them. The parties seem to


                                         41
agree that normalization “ensure[s] that the average DRG weight is the same after

recalibration as it was before.” Aplts.’ Opening Br. at 10. It should ineluctably

follow, then, that under the Hospitals’ hypothetical, the average diagnosis-related

group weight of Hospital X in FY 1996 should be the same as in FY 2000—that is,

1.0. See 74 Fed. Reg. at 24,184 (FY 2010 Proposed Rule) (noting that, in

normalizing the weights, the Secretary applies a numerical adjustment “in order to

ensure that the average [diagnosis-related group] weight after recalibration is

equal to the average [diagnosis-related group] weight prior to recalibration”). In

short, normalization—not the application of a budget-neutrality

adjustment—removes any year-to-year increase in the average diagnosis-related

group weights. And, relatedly, with respect to those group weights, it is

normalization—not a budget-neutrality adjustment—that serves the statutory

mandate (though not necessarily completely) of establishing budget neutrality in

aggregate payments systemwide. See 58 Fed. Reg. at 46,291 (FY 1994 Final Rule)

(noting that normalization “does not necessarily achieve budget neutrality with

respect to aggregate payments to hospitals because payment to hospitals is affected

by factors other than average [diagnosis-related group] weight”).

      Correcting these misunderstandings exposes the logical hole in the

Hospitals’ double-application argument. They assume that the existence of a “1.4

percent budget neutrality adjustment means that, based solely on DRG


                                         42
recalibrations, the [normalized average] DRG weights have increased by 1.4

percent.” Aplts.’ Reply Br. at 19. But, by its very nature, normalization makes

that impossible. And in any event, the Hospitals’ reasoning begs the question of

what the cumulative budget-neutrality adjustment accounts for. Underlying their

reasoning appears to be their answer: the Hospitals repeatedly assert that “the

entire purpose of the budget-neutrality exercise is simply to budget neutralize the

DRG weights.” Id. at 26 (emphasis added); see id. at 1 (“The budget-neutrality

adjustments at issue here are meant to keep the recalibrated DRG weights budget

neutral and ensure that Medicare payments neither increase nor decrease based

simply on the adjustments to the DRG weights.”); see also Aplts.’ Opening Br. at

19 (noting that “since the budget-neutrality adjustments were instituted to fulfill

the Congressional mandate to budget-neutralize the DRG weights”); id. at 31

(noting that “the entire point of the [budget-neutrality] adjustment is to render

DRGs weights budget neutral”). But the Hospitals are wrong.

      Congress’s statutory directive to the Secretary is not to budget neutralize the

DRG weights per se but rather to ensure that the process of recalibration of those

weights is performed “in a manner that assures that the aggregate payments” are

budget neutral. See § 1395ww(d)(4)(C)(iii) (requiring the Secretary to recalibrate

“in a manner that assures that the aggregate payments . . . are no greater or less

than those that would have been made [pre-recalibration]” (emphasis added));


                                          43
accord Adirondack II, 29 F. Supp. 3d at 32. Despite their repeated assertions to

the contrary, the Hospitals cite no on-point authority that supports their position.

The Secretary has discretion on how to accomplish this statutory budget-neutrality

directive. See Adirondack Med. Ctr. v. Burwell (Adirondack III), 782 F.3d 707,

710 (D.C. Cir. 2015) (noting “the wide discretion afforded the Secretary to

implement the Medicare reimbursement formula, including determining how to

meet Medicare’s budget neutrality requirements”). And, as noted, he does so

primarily through the normalization process. And, notwithstanding the Hospitals’

contrary view, the budget-neutrality adjustment comes into play, not to budget

neutralize the DRG weights themselves, but rather to ensure that, after

normalization, the budget-neutrality job is done by addressing the effects of other

factors in the Medicare system, such as wage-index and teaching-hospital

adjustments, that could hinder achievement of budget neutrality. See, e.g., 42

U.S.C. 1395ww(d)(3)(E) (providing for a wage-index adjustment); id.

§ 1395ww(d)(5)(B) (directing the Secretary to “provide for an additional payment

amount for” teaching hospitals with “with indirect costs of medical education”).

      In fact, the Hospitals’ own hypothetical (discussed above) undercuts their

argument. In that scenario, we assumed that the average diagnosis-related group

weights for the new FY 2002 base year were 1.4% higher than the weights from

1996. See Aplts.’ Reply Br. at 19 (“[B]ased solely on DRG recalibrations, the


                                          44
DRG weights have increased by 1.4 percent.”). But we now know that

normalization guarantees that the 2002 weights are exactly the same as the 1996

weights. See Aplts.’ Opening Br. at 10 (explaining that normalization “ensure[s]

that the average DRG weight is the same after recalibration as it was before”).

Even so, the cumulative budget-neutrality adjustment is needed to offset a 1.4%

increase in aggregate payments caused by “other Medicare payment adjustments.”

Aplee.’s Resp. Br. at 24. So, in our hypothetical, we may derive Hospital X’s

2002 hospital-specific rate based on the following formula: its per-patient target

amount for 2002 ($1,000) divided by its normalized average diagnosis-related

group weight (1.0) and then multiplied by the cumulative budget-neutrality

adjustment (0.986). The result is a hospital-specific rate for the new FY 2002 base

year of $986.00 (i.e., $1,000 ÷ 1.0 × 0.986 = $986.00). And that rate is 1.4% less

than the 1996 hospital-specific rate. Simply put, the Secretary’s methodology does

not apply the cumulative budget-neutrality adjustment twice. 20

                                          3

      That said, the confusion that seemingly underlies the Hospitals’ double-

application argument is understandable. In fact, the Secretary arguably invited


       20
              This fact also scuttles the Hospitals’ claim that the Secretary’s
methodology, “[r]ather than creating comparability with the Federal rate . . . ,
destroys it.” Aplts.’ Opening Br. at 43. The premise for this argument is that the
Secretary uses “inflated” average diagnosis-related group weights “as the
divisor.” Id. As explained above, that premise is false.

                                         45
that confusion. Recall that in the FY 2010 Proposed Rule the Secretary reiterated

that he “normalize[s] DRG weights by an adjustment factor in order to ensure that

the average [DRG] weight after recalibration is equal to the average . . . weight

prior to recalibration.” 74 Fed. Reg. at 24,184 (FY 2010 Proposed Rule); see also

58 Fed. Reg. at 46,291 (FY 1994 Final Rule) (making essentially same statement).

But, unlike past rules, the FY 2010 Proposed Rule went on to say that if the

Secretary “were to remove this budget neutrality adjustment factor for years prior

to the base year, . . . the normalized DRG weights applied to the hospital-specific

amounts would be artificially high.” 74 Fed. Reg. at 24,184 (FY 2010 Proposed

Rule). In this imprecise wording, the Secretary seemingly planted the seeds for

the Hospitals’ confusion.

      In the FY 2010 Final Rule, the Secretary confronted the confusion

apparently wrought by his imprecise wording. He wrote, “[s]ome commenters

[had] asserted that the application of a cumulative budget neutrality adjustment

factor . . . doubles the impact of this adjustment on the hospital-specific rates.” 74

Fed. Reg. at 43,896 (FY 2010 Final Rule). These same commenters, the Secretary

recognized, had thought that the normalized average “weight from FYs 1993

through 2002 [had] increased and that the cumulative budget neutrality adjustment

. . . offsets this average . . . weight increase.” Id. And he observed that, on this




                                           46
assumption, the commenters had concluded “that this budget neutrality adjustment

[was] already being accounted for [in step two] when [the Secretary] divides the

. . . average cost per discharge by the hospital’s [normalized average DRG

weight].” Id.

      The Secretary then disabused the commenters of this notion. The Secretary

repeated his longstanding position that “the recalibrated DRG weights are

normalized each year . . . so that the national average [DRG] weight after . . .

recalibration is equal to the . . . average [DRG] weight before recalibration.” Id.;

see 58 Fed. Reg. at 46,291 (FY 1994 Final Rule) (reiterating same position). And

“[b]ecause the weights are normalized,” the Secretary explained, “they do not

reflect . . . average [DRG] weight change due to recalibration.” 74 Fed. Reg. at

43,896 (FY 2010 Final Rule) (emphasis added). He repeated that “DRG weights

after normalization, do not reflect . . . average [DRG] weight change.” Id.

(emphasis added). To put a finer point on it, the Secretary wrote that he

“disagree[d] with commenter’s assertions that the average [DRG] weight from FYs

1993 through 2002 increased due to recalibration.” Id. The Secretary also

disagreed with the idea “that the cumulative budget neutrality adjustment . . . for

this time period offsets an average [DRG] weight increase due to recalibration.”

Id. For that reason, he explained, “[t]he cumulative budget neutrality adjustment

is not already being accounted for [in step two] when [the Secretary] divides the


                                          47
FY 2002 average cost per discharge for a hospital by the hospital’s [normalized

average DRG weight] for FY 2002.” Id.

      The FY 2010 Final Rule should have stifled the Hospitals’ double-

application argument. After all, the Secretary refuted the central premise of that

argument—that the normalized average diagnosis-related group weights were

inflated. Those weights, the Secretary had explained, were not inflated. What’s

more, he had clarified that the cumulative budget-neutrality adjustment was not

meant “to offset any increase or decrease in the . . . average [DRG] weight due to

recalibration.” Id. In other words, the Secretary had effectively refuted the

Hospitals’ later assumption in its briefing here that a budget adjustment of 1.4%

means that, “if the hospital’s average DRG weight was 1.0 in 1996, then its

average DRG weight for treating the same patient in 2002 would necessarily be 1.4

percent higher.” Aplts.’ Opening Br. at 43.

      Nevertheless, the Hospitals are immovable in their belief that the Secretary

has everything “exactly backwards” and fails to understand his own methodology.

Id. Indeed, the Hospitals argue that the Secretary “acted arbitrarily and

capriciously” by straying from his “prior practice” and failing “to consider an

important aspect of the issue”—i.e., the ostensibly inflated DRG weight. Id. at 27.




                                         48
Once again, however, an examination of the record belies this argument. 21 Though

the FY 2010 Final Rule itself is proof enough, looking to earlier rules confirms

that the Secretary has long understood his methodology. Take the FY 1994 Final

Rule. In that rule, the Secretary explained that the recalibrated “weights are

normalized by an adjustment factor, so that the average [DRG] weight after

recalibration is equal to the average . . . weight prior to recalibration.” 58 Fed.

Reg. at 46,291 (FY 1994 Final Rule). But normalization does not always “achieve

budget neutrality with respect to aggregate payments to hospitals because payment

to hospitals is affected by factors other than average [DRG] weight.” Id.

(emphasis added). “Therefore,” the Secretary explained, he applies “a budget



       21
              In their briefing, the Hospitals make hay out of a supposedly
erroneous example that government counsel offered the D.C. district court during
similar litigation. See, e.g., Aplts.’ Opening Br. at 19–21, 30, 34, 42. Whether
this example offered to a different court in a different case is indeed inaccurate is
irrelevant here. Absent a “strong showing of bad faith or improper behavior,” we
assess the Secretary’s actions against his “contemporaneous explanation in light
of the existing administrative record.” Dep’t of Commerce, 139 S. Ct. at 2573,
2574 (citations omitted). We do not retroactively attribute an alleged
misunderstanding by government counsel in a highly technical case to the
Secretary when he acted, most notably, in the FY 2010 Final Rule. Cf. Sorenson,
567 F.3d at 1221 (“The court must rely on the reasoning set forth in the
administrative record and disregard post hoc rationalizations of counsel.”); Lewis
v. Babbitt, 998 F.2d 880, 882 (10th Cir. 1993) (“Judicial review under these
[APA] standards is generally based on the administrative record that was before
the agency at the time of its decision, and reviewing courts may not rely on
litigation affidavits that provide post hoc rationalizations for the agency’s action.”
(citations omitted)). We therefore refuse to consider the supposedly erroneous
example from the D.C. district court proceedings.

                                          49
neutrality adjustment to assure the requirement of [budget neutrality in aggregate

payments] is met.” Id. Simply put, since 1994, the Secretary has understood

that—contrary to the Hospitals’ claims now—normalization offsets any increase in

the recalibrated weights, but other factors necessitate a cumulative budget-

neutrality adjustment to ensure that the statutory mandate of budget neutrality in

aggregate payments is achieved. That explanation guts the assumptions on which

the Hospitals’ double-application argument rests. And the Secretary has reiterated

this same explanation over the years. 22

      To be sure, imprecise language has sometimes plagued the Secretary. The

FY 2010 Proposed Rule, for example, included the unfortunate phrase “artificially

high.” 74 Fed. Reg. at 24,184 (FY 2010 Proposed Rule). And in the 2000

Instructions, the Secretary did not clarify whether he applied a cumulative budget-

neutrality adjustment to the new FY 1996 base year. See J.A. at 342 (2000

Instructions). But the Secretary rectified both semantic oversights in the FY 2010

Final Rule. As we have explained, that rule made clear that the normalized

diagnosis-related group weights are not artificially high—a position the Secretary



       22
            See, e.g., Changes to the Hospital Inpatient Prospective Payment
Systems and Fiscal Year 1996 Rates, 60 Fed. Reg. 45,778, 45,792 (Sept. 1, 1995)
(“FY 1996 Final Rule”); Changes to the Hospital Inpatient Prospective Payment
Systems and Fiscal Year 2001 Rates, 65 Fed. Reg. 47,054, 47,070 (Aug. 1, 2000)
(“FY 2001 Final Rule”); 70 Fed. Reg. at 47,322 (FY 2006 Final Rule).


                                           50
had long held. See, e.g., 58 Fed. Reg. at 46,291 (FY 1994 Final Rule). And the

FY 2010 Final Rule clarified that “the instructions for implementing . . . the [new]

FY 1996” base year—i.e., the 2000 Instructions—did in fact apply the “cumulative

budget neutrality adjustment.” 74 Fed. Reg. at 43,895 (FY 2010 Final Rule). So,

despite these occasional imprecise word choices, the Secretary’s longstanding

position has been that the normalized diagnosis-related group weights are not

artificially high, and his current methodology is the same as that which he used the

first time Congress added a new base year. 23

      With this understanding, one can see the 2006 Instructions and the initial

2008 Instructions for what they were—mistakes. Recall that in those instructions,

the Secretary did not apply prior years’ budget-neutrality adjustments to the new

base years. See J.A. at 328 (2006 Instructions); id. at 349 (2008 Instructions). But



       23
             Notably, the Hospitals concede that the 2000 Instructions “may have
contained the [cumulative budget-neutrality] adjustments from the three prior
years.” Aplts.’ Opening Br. at 11–12. They also do not expressly challenge the
correctness of the Secretary’s interpretation of those instructions as having in fact
applied a cumulative adjustment to the new FY 1996 base year. See generally id.
Thus, we have no reason to doubt that the Secretary did in fact apply a cumulative
budget-neutrality adjustment to the new FY 1996 base year when calculating the
hospital-specific rate. Cf. Adirondack III, 782 F.3d at 709 (“Prior to 2006, the
budget neutrality adjustments applied to the hospital-specific . . . rates in a
straightforward way: once a base year was chosen and the rate was calculated, the
Secretary applied every budget neutrality adjustment from 1993 . . . to the
present.”); Adirondack I, 935 F. Supp. 2d at 132 (explaining that the 2000
Instructions applied “cumulative DRG budget neutrality adjustment factors from
FY 1993 to FY 2000”).

                                         51
just six weeks after issuing the 2008 Instructions, the Secretary corrected his error

in those instructions by including the budget-neutrality adjustments from the years

before the new base year. See id. at 351 (Joint Signature Mem.). The FY 2010

Proposed Rule did the same for the 2006 Instructions. 74 Fed. Reg. at 24,184 (FY

2010 Proposed Rule). In that proposed rule, the Secretary even explained the

reasons behind the corrections. Applying the cumulative budget-neutrality

adjustment to new base years, the Secretary noted, was consistent with his

“established policy” and necessary for “a meaningful comparison between

payments under the Federal rate, which is adjusted by the cumulative budget

neutrality factor, and payments based on the hospital-specific rate.” Id. And

admitting that correcting the past errors “would lower the hospital-specific rate”

for some hospitals going forward, the Secretary declined to retroactively reduce

payments that had already been made to hospitals under the erroneous instructions.

Id. at 24,185. The 2006 Instructions and the initial 2008 Instructions, then, were

aberrations, and the Secretary’s current methodology the norm. Cf. Adirondack

III, 782 F.3d at 709 (“Prior to 2006, the budget neutrality adjustments applied to

the hospital-specific . . . rates in a straightforward way: once a base year was

chosen and the rate was calculated, the Secretary applied every budget neutrality

adjustment from 1993 . . . to the present.”).




                                          52
      In summary, the Secretary does not apply the cumulative budget-neutrality

adjustment twice. The Hospitals’ argument to the contrary rests on flawed

assumptions. And the Secretary has long understood his methodology and

explained it to the public. Thus, the Hospitals’ first argument for why the

Secretary’s methodology is supposedly arbitrary and capricious fails.

                                          B

      The Hospitals next argue that the Secretary’s methodology is arbitrary and

capricious and contrary to Congress’s statutory command because it “yields a

different payment than had he budget-neutralized the weights themselves.” Aplts.’

Opening Br. at 6. The logic behind this argument is as follows. “The budget-

neutrality adjustments have one purpose: to budget-neutralize the DRG weights.”

Id. at 27. The Secretary’s methodology is valid only if it “yields the same payment

as had [he] merely budget-neutralized the DRG weights themselves (rather than the

payment rates).” Id. at 19. The Secretary’s “methodology does not yield the same

payment” as the one he would have had he “budget-neutralized the DRG weights

themselves.” Id. at 20. Therefore, the Secretary’s methodology is arbitrary and

capricious.

      Largely for the reasons we already have discussed in Part III.A.2, supra, this

argument fails. Congress’s statutory directive to the Secretary is not to budget

neutralize the DRG weights per se but instead to ensure that the process of


                                         53
recalibration of those weights is performed “in a manner that assures that the

aggregate payments” are budget neutral. See § 1395ww(d)(4)(C)(iii) (requiring

the Secretary to recalibrate “in a manner that assures that the aggregate payments

. . . are no greater or less than those that would have been made [pre-

recalibration]” (emphasis added)); accord Adirondack II, 29 F. Supp. 3d at 32.

And the Secretary has discretion on how to accomplish this statutory budget-

neutrality directive. See Adirondack III, 782 F.3d at 710 (noting “the wide

discretion afforded the Secretary to implement the Medicare reimbursement

formula, including determining how to meet Medicare’s budget neutrality

requirements”). Stated otherwise, the statutory text teaches that the budget-

neutrality adjustment’s purpose is to achieve budget neutrality in aggregate

payments systemwide, not to guarantee that the diagnosis-related group weights

themselves are budget neutral. And the text leaves the “manner” in which the

Secretary achieves budget neutrality up to him. Thus, the Hospitals’ assertion that

the “one purpose” of the budget-neutrality adjustment under Congress’s statutory

scheme is “to budget neutralize the DRG weights” is incorrect. Aplts.’ Opening

Br. at 27. Whether the Secretary’s methodology yields the same payment as would

a methodology applying the adjustment to the weights is irrelevant; 24 the Secretary


       24
              Once again, the Hospitals try to cover up the logical holes in their
argument by reverting to the government counsel’s alleged claim before the D.C.
district court that the Secretary’s “methodology would yield the same payment as

                                          54
does not act arbitrarily or capriciously if his chosen methodology adheres to the

statutory command to achieve budget neutrality in aggregate payments. 25

Therefore, the Hospitals’ second argument meets the same fate as its first.

                                          C

      For their final argument, the Hospitals claim that the Secretary’s

methodology is arbitrary and capricious because, if applied to a new base year

itself, it would reimburse them for less than 100% of their actual base-year costs.

This argument relies on language from 42 U.S.C. § 1395ww(d)(5)(D)(i)(I). 26 That


would be yielded had he budget-neutralized the weights themselves.” Aplts.’
Opening Br. at 28. And once again, we decline to rely on statements outside of
the administrative record. See supra note 20; cf. Dep’t of Commerce, 139 S. Ct.
at 2573. Even if we could consider this extra-record statement, we would not do
so here. Notably, the government counsel later corrected the representation on
appeal, explaining “that the Secretary is ‘fully aware of the reduction in a base
year’s payment rate that occurs because of [his] methodology.’” Aplee.’s Resp.
Br. at 37 n.12 (quoting Gov’t’s Br. at 27, Adirondack III, No. 14-5122 (D.C. Cir.
Nov. 20, 2014)).
       25
              Notably, the Hospitals’ challenge is not about whether “the Secretary
has failed to maintain budget-neutrality,” Aplee.’s Resp. Br. at 21—that is, failed
to carry out his statutory mandate—but rather about “the precise methodology
used by the Secretary,” Adirondack III, 782 F.3d at 710. Though the Hospitals
push back on the notion that they have agreed that the Secretary has “successfully
achieve[d] the goal of budget neutrality,” id., they never directly say that he has
not but rather turn our gaze back to the Secretary’s ostensible failing in properly
handling the problem of “inflated” DRG weights, Aplts.’ Reply Br. at 15 n.12.
       26
             As explained in footnote 15, this provision applies only to sole
community hospitals. For our purposes, that distinction is irrelevant because the
Hospitals’ argument invoking that provision fails. In other words, given that not
even sole community hospitals are entitled to 100% of their actual base-year
costs, Medicare-dependent hospitals—to which this language does not strictly

                                         55
provision directs the Secretary to calculate the hospital-specific rate using “an

amount based on 100 percent of the hospital’s target amount for the cost reporting

period [i.e., the base year], as defined in subsection (b)(3)(C).”

§ 1395ww(d)(5)(D)(i)(I). Subsection (b)(3)(C), in turn, defines “target amount” as

a hospital’s “allowable operating costs” during the base year. Id.

§ 1395ww(b)(3)(C)(i)(I). The Hospitals read this language as a command for the

Secretary to reimburse them for 100% of their actual base-year costs. And they

reason that if the Secretary’s methodology—when applied to the new base year

itself—fails to satisfy that command, it must be arbitrary and capricious.

      The Hospitals, however, come up short again. To start, their argument

evinces a fundamental misunderstanding about the nature of the current Medicare-

reimbursement system. Under the original Medicare Act, the Secretary paid

hospitals for “the reasonable cost” of treating each Medicare patient. Social

Security Amendments of 1965 §§ 1814(b), 1861(v)(1). But this system quickly

became unwieldy; “[t]he more [hospitals] spent, the more they would receive” in

reimbursement. Billings Clinic v. Azar, 901 F.3d 301, 303 (D.C. Cir. 2018).

Consequently, Congress replaced the old system with the inpatient prospective

payment system. See Social Security Act Amendments of 1983 § 601. A central

premise of this current system is that hospitals “are reimbursed at a fixed amount



apply—necessarily are not entitled to such reimbursement.

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per patient, regardless of the actual operating costs they incur in rendering these

services.” Auburn Reg’l Med. Ctr., 568 U.S. at 149 (emphasis added). Against

this backdrop, the Hospitals’ claim to 100% of their actual base-year costs

looks—at the very least—suspect.

      Closer inspection of the Hospitals’ argument makes clear that it is flawed.

The whole exercise of inquiring as to whether a given methodology would

reimburse the Hospitals for 100% of their actual base-year costs is odd under the

inpatient prospective payment system. By statutory mandate, the Secretary never

uses the hospital-specific rate he calculates for a base year to reimburse a hospital

for discharges from that base year itself. Thus, for example, he never uses the rate

calculated for the FY 2002 base year to reimburse a hospital for its 2002

discharges. Rather, that rate applies only for “discharges occurring on or after

October 1, 2006.” 42 U.S.C. § 1395ww(b)(3)(K)(i). It is, after all, an inpatient

prospective payment system. So whether the rate the Secretary calculated for the

FY 2002 base year would reimburse a hospital for its full 2002 costs is seemingly

irrelevant.

      Moreover, the text on which the Hospitals rely further discredits their

argument. The transitive verb “base” ordinarily means “use as a point from which

(something) can develop.” Base, N EW O XFORD A MERICAN D ICTIONARY 134 (2d

ed. 2005). And as a noun, “base” often means “a main or important element or


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ingredient to which other things are added.” Id. So when Congress said that the

payment using the hospital-specific rate “shall be” an “amount based on 100

percent of the hospital’s target amount,” 42 U.S.C. § 1395ww(d)(5)(D)(i)(I), it was

telling the Secretary that 100% of the hospital’s target amount was the starting

point from which to develop the hospital-specific rate. And that is exactly what

the Secretary does: in simplified form, he starts with 100% of a hospital’s base-

year target amount, divides that amount by the normalized average diagnosis-

related group weight for that year, and then applies the budget-neutrality

adjustment. In hitching their wagon to the phrase “an amount based on 100

percent of the hospital’s target amount,” then, the Hospitals effectively undercut

their own position.

      And contrary to the Hospitals’ protestations, reading “based on” according

to its ordinary meaning does not “render[] the phrase ‘100 percent’ surplusage.”

Aplts.’ Opening Br. at 39. Under this commonsense reading, the phrase “100

percent” clarifies that the starting point for the Secretary’s calculations must be

100%—not 90%, 50%, or some other percentage—of the hospital’s target amount.

For example, if Hospital X’s base-year target amount was $1,000, the Secretary

could not begin with $900, divide that amount by the normalized average

diagnosis-related group weight, and then apply the budget-neutrality adjustment.

Without the phrase “100 percent,” the provision would instruct—without any


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specificity—the Secretary to arrive at the hospital-specific rate using “an amount

based on . . . the hospital’s target amount.” On that wording, it would be unclear

whether the Secretary must use an amount based on all or may use only a portion

of the hospital’s target amount. Cf. Anna Jaques Hosp. v. Sebelius, 583 F.3d 1, 5

(D.C. Cir. 2008) (agreeing that a provision instructing the Secretary to calculate

“the wage index . . . ‘on the basis of’” survey data was ambiguous because it was

“silent about whether she must use all of the survey data”). The phrase “100

percent” has the effect of clearing up the matter. And so the Hospitals are

mistaken in asserting that an interpretation of “based on” as meaning the starting

point renders “100 percent” surplusage. 27

      Aside from its conceptual and linguistic shortcomings, the Hospitals’

argument is logically inconsistent with the Hospitals’ overall approach.

Throughout their briefing, the Hospitals stress that they agree “that the Secretary

should apply all budget-neutrality adjustments once.” Aplts.’ Reply Br. at 12 n.10.

But if the Secretary had to pay hospitals 100% of their actual base-year costs, he



       27
             The Hospitals’ reading, however, does create surplusage. Congress
directs the Secretary to calculate the hospital-specific rate using “an amount based
on 100 percent of the hospital’s target amount.” 42 U.S.C.
§ 1395ww(d)(5)(D)(i)(I). The Hospitals read that language as a “command to use
‘100 percent’ of base-year costs.” Aplts.’ Opening Br. at 37. But that reading
gives no meaning to the words “an amount based on.” As the Hospitals
themselves point out, “every statutory word must be given meaning.” Id. Yet,
they are content to give four statutory words no meaning.

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could not apply any budget-neutrality adjustment at all. For example, say Hospital

X’s actual base-year costs were $1,000 and the budget-neutrality adjustment was

0.9. If the Secretary applied that adjustment to the base year, he would pay

Hospital X $900 for its base-year discharges. Under the logic of the Hospitals’

argument, the Secretary could not apply that adjustment at all because doing so

would be “an immediate reduction in their base-year costs.” Aplts.’ Opening Br.

at 39. Yet, the Hospitals have repeatedly asserted that the Secretary is not

prohibited from applying a budget-neutrality adjustment to the hospital-specific

rate for a new base year. Thus, if—as the Hospitals agree—the Secretary may

apply a budget-neutrality adjustment to the hospital-specific rate, then the

Secretary cannot also be required to pay a hospital 100% of its base-year operating

costs. Simply put, the Hospitals’ third argument—like its first two—fails to

establish that the Secretary’s methodology is arbitrary and capricious.

                                         IV

      For the foregoing reasons, we hold that the Secretary’s methodology is not

arbitrary and capricious and AFFIRM the district court’s judgment.




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