Robert Sloan and Kenneth Y. Sunew (collectively “plaintiffs”)1 appeal from a judgment entered on February 25, 2000, in accordance with a Memorandum and Order entered on February 23, 2000 (Loretta A. Preska, Judge), denying plaintiffs’ motion for “summary expedited final judgment” and granting defendants motion for summary judgment on the question of *229what process was due to plaintiffs with respect to the calculation of the Medicare-approved charges for the provision of certain services. We affirm the district court’s denial of plaintiffs’ requested relief, but reverse its due process determination and grant of defendants’ motion for summary-judgment.
I. Background
This ease is before us for the second time. See Furlong v. Shalala, 156 F.3d 384 (2d Cir.1998). Because a thorough account of the facts, and of the relevant regulatory scheme, is provided in our earlier opinion, see id. at 386-90, we presume familiarity with the background of this case. However, it will be useful for the discussion that follows to reiterate a few key points.
This case concerns various statutory and regulatory provisions that govern the Medicare “Part B” program — a voluntary program offering supplemental insurance coverage for those persons already enrolled in the Medicare “Part A” program, which offers basic health insurance to people who are 65 or older, or who are disabled. See 42 U.S.C. § 1395c-1395d; 1396j-1395k (1992). Under the Part B program, physicians must choose whether to accept assignment of their patients’ rights to reimbursement. See id. § 1395u(b)(3)(B)(ii) & (h)(1). If a physician accepts assignment, he must agree to accept the Medicare-approved charge (set by the Department of Health and Human Services) as payment in full. See id. § 1395u(b)(3)(B)(ii). These “assignee-physicians” generally receive 80% of the Medicare-approved charge from the Federal Supplementary Medical Insurance Trust Fund (“Trust Fund”) and the remaining 20% from the patient. See id. § 1395i(a)(l). Physicians electing not to accept assignment are also limited in the amount they can charge for their services, but the limit is higher than the Medicare-approved charge; they are permitted to charge an amount in excess of the Medicare-approved amount so long as it is not more than a specified “limiting charge.” See id. § 1395w-4(g). Since 1992, the limiting charge has been 115% of the Medicare-approved charge for non-participating physicians. See id. § 1395w-4(g)(2)(C). These “non-assigned physicians” bill their patients directly for the Medicare-approved charge plus any additional amount allowed by the limiting charge. See id. §§ 1395i(a)(l) & 1395u(b)(3)(B)(i). The patient is then reimbursed by the Trust Fund for 80% of the Medicare-approved charge. See id.
The Part B program is administered by the Secretary of the Department of Health and Human Services (the “Department”) acting through the Health Care Financing Administration (“HCFA”), but the day-today management of the program is handled by private insurance carriers under contract with the Department. See id. § 1395u. HCFA’s policies and rulings are binding on the carriers, see, e.g., 42 C.F.R. 405.502(d), 405.860(a)(1) (2000), and directives are communicated at least in part through the Medicare Carriers’ Manual (“MCM”), as well as through the Federal Register. In 1991, HCFA adopted a policy which provides that “[i]f a surgeon performs more than one procedure on the same patient on the same day, we will pay 100 percent of the global fee for the highest value procedure only, 50 percent of the global fee for the second most expensive procedure, and 25 percent of the global fee for the third, fourth, and fifth procedures.” 56 Fed.Reg. 59,502, 59,515 (Nov. 25, 1991); see 56 Fed.Reg. 59,601-02 (providing the Department’s response to comments on this rule).2 This so-called “one-and-one-half *230rule” applies by its terms only to surgical procedures.
A physician’s decision whether to accept assignment of patients’ claims affects not only the amounts that can be charged and the associated billing procedures, but also his or her ability to appeal an insurance carrier’s determination of the Medicare-approved charge for a given service. In our previous opinion, we summarized the appeal provisions available to assignee physicians as follows:
Following the carrier’s initial de novo determination, § 1395u(b)(3)(C) of the Act entitles the patient to a “fair hearing,” if the amount in controversy is at least $100, to be conducted by a carrier-designated hearing officer. See generally 42 C.F.R. § 405.807-405.815. If that hearing results in a decision adverse to the patient, and the amount in controversy equals or exceeds $500, the patient may request an evidentiary hearing and de novo review of the carrier’s decision by an Administrative Law Judge (ALJ). See § 42 U.S.C. 1395ff(b)(l)(C) (incorporating procedures for administrative review set forth at 42 U.S.C. § 405(b) & (b)(2)(B) (1994)). If that too is unsuccessful, the patient may appeal the ALJ’s decision to an appeals council. See id. Upon issuance of the appeals council’s ruling, which is the final administrative decision, a dissatisfied patient may within 60 days seek judicial review of the Secretary’s determination in the district court, but only if the amount in controversy equals or exceeds $1,000. See id. (incorporating procedures for judicial review set forth at 42 U.S.C. § 405(g)).
Furlong, 156 F.3d at 388; see 42 C.F.R. § 405.801. The difference in the rights accorded to assignee and non-assigned physicians arises because while Congress, in 42 U.S.C. § 1395ff, stated that “[a]ny individual dissatisfied with any determination” as to the amount of benefits awarded is entitled to the types of review summarized above, see 42 U.S.C. § 1395ff (b)(1)(C) (emphasis added), the Department, through 42 C.F.R. § 405.801, has determined that “the rights of a beneficiary ... to appeal the carrier’s initial determination are granted also to ... [a] physician or supplier that furnishes services to a beneficiary and that accepts an assignment from the beneficiary,” 42 C.F.R. § 405.801(b)(1), but does not extend the rights provided by § 1395ff to non-assigned physicians, see Furlong, 156 F.3d at 388. As we observed in our previous opinion, this policy “encourag[es] physicians to accept assignments and allow[s] patients to avoid additional charges and administrative responsibilities.” Id. at 391.
Plaintiffs here are non-assigned anesthesiologists who performed what the parties have called “concurrent invasive monitoring” during major surgeries. Such monitoring is “invasive” in that it involves the placement of equipment into the patient’s arteries and veins in order to monitor vital signs such as blood pressure, blood gases, and heart performance. See Furlong, 2000 WL 194843, at *2 (S.D.N.Y. Feb.18, 2000). It is “concurrent” because more than one type of equipment is used at the same time. See id. Prior to January 1, 1994, carriers classified concurrent invasive monitoring as surgical, and therefore applied the one-and-one-half rule to the procedures involved. See id. at *3. On that date, the HCFA apparently indicated through changes in the Medicare Physician Fee Schedule database that such monitoring was medical, rather than surgical, in nature, and was therefore exempt from application of the one-and-one-half rule.3 *231Given that the limiting charge for a service provided under Part B by a non-assigned physician is linked to the Medicare-approved charge for those services, the application of the one-and-one-half rule to concurrent invasive monitoring lowered the amount that plaintiffs could charge for their services. Throughout this case plaintiffs have argued that concurrent invasive monitoring is a “medical” and not a “surgical” procedure, and that the carriers therefore erroneously applied the one-and-one-half rule to such monitoring. And, as defendants conceded at oral argument and in their brief, assignee physicians who performed concurrent invasive monitoring during this period and who exercised their rights to appeal the application of the rule to these procedures before Administrative Law Judges (“ALJs”), appear to have been consistently successful in getting the application of the rule overturned on grounds that the procedures at issue were “medical” in nature. Plaintiffs claim that the total difference in benefits among the class of anesthesiologists affected by the application of the rule is $2,089,510.30.
In July 1997, the district court, having already dismissed the claims of the assign-ee physician plaintiffs for failure to exhaust their administrative remedies, see Furlong v. Shalala, No. 94 Civ. 4187, 1996 WL 393526 (S.D.N.Y. July 12, 1996), granted defendants’ motion for summary judgment, finding that (1) the HCFA regulation limiting appeal rights to assignee physicians did not violate the Administrative Procedure Act (“APA”); (2) that the regulation did not violate plaintiffs’ rights to equal protection; and (3) that plaintiffs had no property right in charging the higher rates that would have resulted if the one-and-one-half rule were not applied, see Furlong v. Shalala, 1997 WL 371174 (S.D.N.Y. July 3, 1997). On appeal, we affirmed the first two holdings, but concluded that, by virtue of a consistent line of ALJ decisions finding that the concurrent invasive monitoring procedures were medical and were therefore inappropriate for the application of the one-and-one-half rule, plaintiffs had a property interest in having the limiting charge for their services calculated without application of the one-and-one-half rule. See Furlong, 156 F.3d at 392-96. We remanded the case to the district court for a determination of what process was due to plaintiffs based on this right. See id. at 396.
On remand, plaintiffs made a motion for “summary expedited final judgment” in which they argued that this Court had effectively decided the substantive issue of whether the one-and-one-half rule should be applied, and that the district court should therefore proceed directly to recalculating the benefits to be paid to the beneficiaries without reference to the rule. Defendants moved for summary judgment on the issue of what process was due, arguing that plaintiffs’ interests would be sufficiently protected if they were granted the right to a paper review determination, and, in cases in which the disputed amount is at least $100, a “fair hearing” conducted by an officer of the carrier.
The district court denied plaintiffs motion, finding that because the carriers’ determinations of the benefits due are not subject to direct judicial review, that court *232had no jurisdiction to simply recalculate the benefits and order payment. See Furlong, 2000 WL 194843, at *5-*6. The court also granted defendants’ motion, finding that, under the test set forth in Mathews v. Eldridge, 424 U.S. 319, 335, 96 S.Ct. 893, 47 L.Ed.2d 18 (1976), plaintiffs’ right to due process with respect to their right to accurate calculation of the approved charges would be satisfied by a paper review and a fair hearing before the carrier. See id. at *6-*7. Plaintiffs now appeal the district court’s rulings on both motions.
II. Discussion
A Standard of Review
We review a district court’s grant of summary judgment de novo, construing the evidence in the light most favorable to the non-moving party. See, e.g., Tenenbaum v. Williams, 193 F.3d 581, 593 (2d Cir.1999), cert. denied 529 U.S. 1098, 120 S.Ct. 1832, 146 L.Ed.2d 776 (2000). Because plaintiffs’ requested relief is, in essence, a summary judgment motion, we review the denial of that motion, as well as the grant of defendants’ motion, under this standard.
B. Due Process
Our analysis begins with the provisions of the Medicare Act governing the review of benefits determinations:
The findings and decision of the [Secretary] after a hearing shall be binding upon all individuals who were parties to such hearing. No findings of fact or decision of the [Secretary] shall be reviewed by any person, tribunal, or governmental agency except as herein provided. No action against the United States, the Commissioner of Social Security, or any officer or employee thereof shall be brought under section 1331 or 1346 of Title 28 to recover on any claim arising under this subchapter.
42 U.S.C. § 405(h); see id. § 1395Ü (incorporating § 405(h)). At first blush, given that no review is available to non-assigned physicians under HCFA’s regulations interpreting the Act, section 405(h) seems to mean, by virtue of that section’s explicit statement that no review apart from that provided by the Act was available, and that plaintiffs have no cognizable right to review of their claims. However, our inquiry does not end with this interpretation, and we to conclude that the matter before us falls outside the reach of section 405(h) as incorporated by the Medicare Act.
Prior to the Supreme Court’s decision in Shalala v. Illinois Council on Long Term Care, Inc., 529 U.S. 1, 120 S.Ct. 1084, 146 L.Ed.2d 1 (2000), courts distinguished between determinations of “the amount of the Medicare payment to be made on a particular claim,” (“amount” claims) which have been held to fall within the channeling provisions of section 405(h), Bowen v. Michigan Academy of Family Physicians, 476 U.S. 667, 675, 106 S.Ct. 2133, 90 L.Ed.2d 623 (1986) (quoting United States v. Erika, 456 U.S. 201, 208, 102 S.Ct. 1650, 72 L.Ed.2d 12 (1982) (internal quotation marks omitted)), and “challenges to the validity of the Secretary’s instructions and regulations” (“methodology” claims), which have been held not to be the kinds of determinations delegated by Congress to the insurance carriers and to be therefore exempt from the 405(h) bar, see id. at 678, 106 S.Ct. 2133. Michigan Academy was decided before the Medicare Act was amended in 1987 to afford individuals challenging Medicare Part B determinations the same appeals procedures as individuals challenging Part A determinations. See Omnibus Budget Reconciliation Act of 1986, Pub.L. No. 99-509, § 9341, 100 Stat. 1874, 2037-38 (1986) (codified at 42 U.S.C. § 1395ff (1992)); Abbey v. Sullivan, 978 F.2d 37, 40 (2d Cir.1992). At the time of Michigan Academy, Part B claimants were limited to a de novo review determination by the carrier and, if the claim exceeded $100, a “fair hearing” conducted by the carrier. See Schweiker v. McClure, 456 U.S. 188, 191, 102 S.Ct. 1665, 72 L.Ed.2d 1 (1982); Erika, 456 U.S. at 203, 102 S.Ct. 1650; Abbey, 978 F.2d at 40. In *233Erika, the Supreme Court found that Congress had intended to foreclose judicial review of Part B claims, see Erika, 456 U.S. at 206-11, 102 S.Ct. 1650, and in McClure, it found that the limited review available to Part B comported with constitutional requirements of due process, see McClure, 456 U.S. at 196-99, 102 S.Ct. 1665.
The Michigan Academy Court considered the question whether the jurisdictional bar contained in § 405(h) prevented the district court from hearing a challenge to a regulation that claimed that the regulation was inconsistent with the Medicare statute. See 476 U.S. at 669, 106 S.Ct. 2133. Beginning with the “strong presumption that Congress intends judicial review of administrative action” unless “there is a persuasive reason to believe that [precluding such review] was the purpose of Congress,” see id. at 670, 106 S.Ct. 2133, the Court determined that a challenge to the validity of a regulation is not the kind of question that is considered in a “fair hearing,” see id. at 676, 106 S.Ct. 2133, and that, in light of the relevant statutes and legislative history, “those matters which Congress did not leave to be determined in a ‘fair hearing’ conducted by the carrier-including challenges to the validity of the Secretary’s instructions and regulations-are not impliedly insulated from judicial review by 42 U.S.C. § 1395ff,” see id. at 678, 106 S.Ct. 2133. Instead, the Court held that Congress had intended to foreclose judicial review of determinations of the amounts of benefits due to individual claimants. See id. at 677, 106 S.Ct. 2133.
In Illinois Council, the Supreme Court sought to clarify the scope of Michigan Academy. The Court stated that Michigan Academy did not stand for the proposition that the § 405(h) bar applied only to “amount determinations,” and that “it is more plausible to read Michigan Academy as holding that § 1395Ü does not apply section 405(h) where its application would not simply channel review through the agency, but would mean no review at all.” Illinois Council, 120 S.Ct. at 1096-97. By “review,” the Court meant judicial review. It noted the concern expressed in Michigan Academy that “ ‘a serious constitutional question’ ... would arise if we construed § 1395Ü to deny a judicial forum for constitutional claims arising under Part B,’ ” id. at 1096 (quoting Michigan Academy, 476 U.S. at 681 n. 12, 106 S.Ct. 2133 (quoting Weinberger v. Salfi, 422 U.S. 749, 762, 95 S.Ct. 2457, 45 L.Ed.2d 522 (1975))), and conditioned its finding that the plaintiffs in that case were required to pursue their challenges through the agency on the assurance that judicial review would be available both for questions addressed by the agency and for any questions that the agency could not consider, see id. at 1099. However, the Court also confirmed that the section 405(h) bar “clearly applies] in a typical Social Security or Medicare benefits case, where an individual seeks a monetary benefit from the agency (say, a disability payment, or payment for some medical procedure), the agency denies the benefit and the individual challenges the lawfulness of that denial.” Id. at 1092. Thus, the status of the amount/methodology distinction after Illinois Council is somewhat unclear. On one hand, the Court has held that application of the section 405(h) bar is not limited to “amount determinations.” On the other, it confirmed that the kinds of challenges previously termed “amount determinations” were well within the scope of the section 405(h) bar and further confirmed the continued validity of the result in Michigan Academy, reformulating its “methodology” analysis by stating that the Michigan Academy Court “applied § 1395Ü with one important change of detail — a change produced by not applying § 405(h) where its application to a particular category of cases, such as Medicare Part B ‘methodology’ challenges, would not lead to a channeling of review through the agency, but would mean no review at all.” Id. at 1095-96.
It is this last statement that guides our opinion in the instant appeal. Whatever *234else the Illinois Council Court may have intended to do with respect to the recognition of federal court jurisdiction over Medicare challenges, it clearly stated that the review scheme available for Medicare Part B claims prior to 1987 — the scheme considered in Michigan Academy — is the kind of scheme which not only postpones judicial review, but forecloses it, and that the courts should not interpret section 1395Ü as requiring such a problematic foreclosure of review in all circumstances. And, as explained above, the plaintiff non-assignee physicians in the present appeal are, in effect, in the same position as Medicare B beneficiaries prior to 1987. Therefore, it appears to this Court — assuming plaintiffs’ claims are not the kind of “amount” claims found by the Illinois Council Court to fall squarely within the channeling provisions of section 405(h), but are rather akin to the “methodology” claims brought by the plaintiffs in Michigan Academy under the pre-1987 Medicare B review scheme — that plaintiffs claims fall outside the scope of section 405(h), and that this section cannot be used to answer the question of what process is due plaintiffs.
We are convinced that plaintiffs’ claims are challenges to agency policy (or, in the language of Michigan Academy, “methodology claims”) rather than challenges to the calculation of benefits. We described this distinction in our opinion in Abbey v. Sullivan, 978 F.2d 37, 42 (2d Cir.1992), stating that “federal jurisdiction exists where there is a challenge to the validity of an agency rule or regulation, but jurisdiction is lacking where the claim is merely that the insurance carrier misapplied or misinterpreted valid rules and regulations,” see id. (quoting Kuritzky v. Blue Shield of W. N.Y., Inc., 850 F.2d 126, 128 (2d Cir.1988) (per curiam) (internal quotation marks omitted)). While we went on in that opinion to suggest that the amount/methodology distinction was not a meaningful one after the 1987 amendments extending review rights to Medicare B recipients, see id. at 42-43, that is obviously not the case with respect to non-assigned physicians, whose rights to review under the present statute are nearly identical to those of Medicare B beneficiaries in general under the pre-1987 statutory scheme described in Michigan Academy.
Defendants, as well as the district court, construe plaintiffs’ claims as “amount” claims. The district court first touched on the issue in its 1996 Memorandum and Order, when it considered whether it lacked subject matter jurisdiction to hear plaintiffs claims because of the Medicare Act provision that “[a] regulation or instruction which relates to a method for determining the amount of payment under part B of this subchapter and which was initially issued before January 1, 1981, shall not be subject to judicial review.” 42 U.S.C. § 1395ff(b)(4); see Furlong v. Shalala, 1996 WL 393526, at *4-*6. The district court found the amount/methodology dichotomy to have some application to the question whether plaintiffs’ challenge was a challenge to a “method” set forth in a pre-1981 regulation. See id. at *6. The district court found that 1395ff(b)(4) did not bar jurisdiction, stating:
[P]laintiffs’ claims are amount claims, not methodology claims, and therefore are not precluded from judicial review by Section 1395ff(b)(4).
Plaintiffs do not attack the validity of [the Medicare Manual provision allowing carriers to elect to award partial payment for multiple surgeries]. Instead, they challenge its application by Medicare carriers to their concurrent invasive monitoring procedures.... “Plaintiffs claims allege only a misapplication of valid regulations” and therefore are characterized as amount claims under Erika. Thus, they do not fall within the limitation in Section 1395ff(b)(4) on judicial review of Part B methodology claims.
Id. (citations omitted). Defendants in their brief rely on the reasoning of the district court in its 1996 Memorandum and Order *235in arguing that plaintiffs’ claims are appropriately viewed as “amount” claims.4
We disagree. In the complaint, plaintiffs challenge, inter alia, “the deliberate, unlawful and discriminatory action of the Health Care Financing Administration in ... authorizing and directing Medicare Part B carriers to make reduced payments for these medical procedures under the ‘one and one half surgical rule prior to December 31, 1993.” Moreover, plaintiffs state that HCFA explicitly approved the carriers’ application of the rule to concurrent invasive monitoring both in writing ánd in the form of the reimbursement codes assigned to these procedures in the official Medicare Physician Fee Schedule database. Plaintiffs’ allegation regarding the reimbursement codes has been conceded by the defendants. See note 3, supra; Letter of Michael M. Krauss, dated December 12, 2000, at 3-5. The written approval alleged is supported by a February 12, 1993 letter from a Reimbursement Specialist in the Medicare Division of the Department of Health and Human Services to an employee of the New York State Federation of Anesthesiologists declaring that “current national surgery rules” apply the one-and-one-half rule to concurrent anesthesia procedures. Although this written confirmation from a Department employee is insufficient to show that the agency had a policy requiring the carriers to apply the one-and-one-half rule to concurrent invasive monitoring prior to 1994, the use of codes in the Medicare Physician Fee Schedule database indicating that these monitoring procedures were appropriate for application of the multiple surgery rules does credibly evince such a policy.
Defendants protest that this Court cannot now find that the Department mandated the application of the one-and-one-half rule to concurrent invasive monitoring because of the statement in our prior opinion that “[njeither [the Medicare Manual provision allowing carriers to award partial payment for concurrent surgeries nor the subsequent HCFA regulation mandating application of the one-and-one-half rule to multiple surgical procedures] — nor for that matter any publication, regulation or fee schedule — affirmatively mandated application of the ‘one-and-one-half rule to concurrent invasive monitoring by requiring carriers to treat the service as ‘surgical.’ ” Furlong, 156 F.3d at 393-94; see Letter of Michael M. Krauss, dated December 12, 2000, at 1-4. While that was indeed our understanding at the time of our last opinion, we now, due only to supplemental briefing specifically requested by the *236Court following oral argument, have sufficient information in the record before us to conclude otherwise: that while the Carriers’ Manual and the HCFA regulation setting forth the one-and-one-half rule may be silent on the application of the rule to concurrent invasive monitoring, the Medicare Physician Fee Schedule database, distributed to the carriers to aid them in their calculations, apparently was not. On the basis of this new information, we therefore find that the Fee Schedule database did direct carriers to apply the rule to the services performed by plaintiffs. Moreover, even if one takes the defendants’ view that application of the one-and-one-half rule was not mandated but was instead left to the carriers’ discretion, the decision to allow the carriers to make such determinations is itself an agency policy. Therefore, in the view of this Court, plaintiffs’ claims are best construed neither as challenges to the one-and-one-half rule itself, nor as mere challenges to the mechanical application of the one-and-one-half-rule, but rather as challenges to the separate agency policy that either mandated application of the one-and-one-half rule to concurrent invasive monitoring or delegated that decision to the carriers.
This close reading of the plaintiffs’ complaint leads us in turn to the conclusion that, under the analysis of Michigan Academy and Illinois Council set forth above, plaintiffs’ claims fall outside the scope of § 405(h), and that therefore the review provisions set forth in the Medicare Act cannot guide our due process analysis. Instead, we must undertake a traditional due process analysis under Mathews v. Eldridge, 424 U.S. 319, 335, 96 S.Ct. 893, 47 L.Ed.2d 18 (1976). While not explicitly stated in our prior opinion, it is this analysis that allowed us to hold that the Department did not abuse its discretion in denying review to non-assigned physicians while finding that those physicians had a property interest in charging higher fees.
Under the due process analysis set forth in Mathews v. Eldridge, a court must consider “(1) the private interest that will be affected by the official action; (2) the risk of an erroneous deprivation of such interest through the procedures used and the probable value of additional or substitute procedural safeguards; and (3) the fiscal and administrative burdens that the additional or substantive procedures entail.” Isaacs v. Bowen, 865 F.2d 468, 476 (2d Cir.1989)(citing Eldridge, 424 U.S. at 335, 96 S.Ct. 893). As to the first of these factors, the district court found the plaintiffs’ private interest in charging the higher rate to be “considerable, albeit limited,” because the plaintiffs had not been completely deprived of their right to recover for their services, but instead were merely prevented from recovering higher fees. Furlong, 2000 WL 194843, at *7 (citing Isaacs, 865 F.2d at 476). As to the second factor, it found that if the plaintiffs were limited to carrier fair hearings, the carrier officers could refer both to the ALJ decisions reversing carrier decisions on the application of the one-and-one-half rule to concurrent invasive monitoring in the appeals brought by assignee physicians and to the Department’s subsequent change in policy in making their determinations, and that therefore a carrier review would be sufficient to prevent an erroneous deprivation of the interests at stake. See id. As to the final factor, the district court found that, given the number of cases, ordering ALJ review would place a heavy burden on the Department. The court also noted that carrier review had been found to pass constitutional muster in Schweiker v. McClure, 456 U.S. 188, 195-200, 102 S.Ct. 1665, 72 L.Ed.2d 1 (1982). See id.
While we agree with the district court’s assessment of the importance of the interest at stake, we find that the other two factors, which address the risk of error and the administrative burden on the agency, weigh in favor of granting agency review of the determinations made at the fair hearings conducted by the carriers. By agency review, we mean review by the ALJs and, as appropriate, by the De*237partment’s Appeals Board (the final administrative stop within the agency). In reaching this conclusion, we need not, and indeed do not, take a position, as plaintiffs would have us do, that hearings conducted by carrier officers are inherently biased or unfair.5 See Br. for Plaintiffs Appellants at 18. Rather, we are concerned that, on the record before us, there is evidence that would suggest a significant likelihood of erroneous deprivation of plaintiffs’ property interests. First and foremost, we are troubled that, as conceded by the government, ALJs have consistently reversed the decisions of the carriers with respect to their application of the one-and-one-half rule to concurrent invasive monitoring. This high rate of reversal — spanning several years' — causes us to doubt whether the carriers can effectively construe and apply the agency policy on this issue. We give great weight to the government’s acknowledgment of the consistent reversals. Moreover, there is no indication in the record or through available sources that the ALJ opinions are published or otherwise made routinely available to the carrier officers, which makes us less certain than the district court that the carriers can be expected to follow the lead of the ALJs on this question. This is not to say that we have any view as to whether the only correct determination would be one which did not apply the one-and-one-half rule to concurrent invasive monitoring. Here, we merely determine that the high rate of reversal shows that the carriers have consistently failed to apply agency policy as set by the agency itself, in the form of decisions by the administrative law judges. This leads us to conclude that the second Mathews v. Eldridge factor weighs in favor of agency review.
While we understand the district court’s concern about the possible administrative burden to be placed on the agency if such review is made available, we find that this burden is more than counterbalanced by the risk of error posed by limiting review to a carrier fair hearing. Moreover, if the Department agrees with the previous ALJ opinions that the one-and-one-half rule should not be applied to these procedures — consistent with its explicit policy since January 1994 — it may, of course, instruct the carriers to grant the increase in reimbursements in the first instance, and thereby lessen the need for ALJ review'. In so noting, we take no position as to what the Department should do.
As to whether ALJ review and any subsequent agency review by the Department’s Departmental Appeals Board would suffice to protect plaintiffs’ due process rights, Illinois Council seems to suggest that, at least for claims traditionally thought of as “methodology” claims, judicial review must be available. See Illinois Council, 120 S.Ct. at 1096-97. That is, that plaintiffs would have the right to appeal the agency’s final administrative decision to the federal courts. Moreover, because there is no allowance made in Illinois Council requiring claimants to meet a jurisdictional amount before appealing their claims, we are precluded from instituting such a requirement. In practice, of course, *238it is questionable whether plaintiffs will choose to take these- appeals, given our deference to the agency on policy matters. The determination of whether concurrent invasive monitoring is medical or surgical is squarely within the discretion and expertise of the agency, and it is highly unlikely that the courts would disturb agency findings on this issue. See Chevron, U.S.A., Inc. v. Natural Resources Defense Council, Inc., 467 U.S. 837, 842-45, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984).
Both defendants and the district court argue that to allow plaintiffs full administrative and judicial review on these claims will undermine the Department’s choice to afford fewer remedies to physicians who do not elect to accept assignment of their patients’ claims. But this argument misses a key point: our decision does nothing to disturb the different opportunities for review accorded to assignee and non-assigned physicians with respect to “amount” challenges. Under our interpretation of the Michigan Academy/Illinois Council line of eases and of the review provisions governing review under the Medicare Act, while the avenues of review available to assignee and non-assigned physicians differ markedly with respect to challenges to the calculation of benefits, “methodology” challenges, such as the ones at issue in the instant ease, fall outside the scope of the Act, and therefore beyond the Act’s review provisions. Hence, as to methodology challenges, which are not addressed by the Department’s regulation providing that only assignee physicians are entitled to review of their Part B claims, assignee and non-assigned physicians are on equal footing.
C. Plaintiffs’Requested Relief
As stated above, the district court declined to grant plaintiffs’ request for “summary expedited final judgment” in the form of a simple recalculation of the benefits owed. It first stated that plaintiffs’ requested relief rested on the faulty assumption that this Court, in its prior opinion, had confirmed the findings of the ALJ opinions, and had, in effect, made a legal determination that concurrent invasive monitoring was a medical, and not a surgical, procedure, and that it was therefore proper to recalculate the benefits due without reference to the one-and-one-half rule. See Furlong, 2000 WL 194843, at *5. Second, the court found that it lacked jurisdiction to conduct such a recalculation. See id. It reasoned that the only way it would have jurisdiction to conduct the recalculation was if it found that due process required direct judicial review of the carriers’ benefit determinations, which it did not. See id. at *5-*6. Finally, the district court found that to grant plaintiffs’ requested relief would be to “prevent HCFA from correcting its own errors.” Id. at *6 (citing Abbey, 978 F.2d at 45).
We agree completely with the district court on its first observation. In our prior opinion, we did not adopt the findings of the ALJs that concurrent invasive monitoring was a medical procedure. We remain agnostic on this policy issue, which is well within the discretion of the Department. Our earlier opinion found that the ALJ opinions provided a basis for a property right, but did not confirm or adopt the findings of the ALJs as a matter of law. Therefore, it would have been inappropriate for the district court to enter judgment, as no determination of the relevant legal question had been made.
As to the second basis for the district court’s ruling, we agree that, because due process does not require direct judicial review of the carrier decisions, it would have been improper for the district court to grant the requested relief. However, because of our determination that this is a “methodology” case as opposed to an “amount” case, we are not troubled, as the district court was, with the effect that such review would have had on the decision of physicians to accept assignment; both assignee and non-assigned physicians bringing methodology challenges would have the same right to review, and this does *239nothing to disturb their different treatment with respect to amount challenges.
Finally,, and most importantly, this Court agrees with the district court that it would be improper to enter judgment as requested by the plaintiffs because to do so would be to take the responsibility for correctly construing agency policy from the agency itself. See Abbey, 978 F.2d at 45. As we stated in Abbey, “Giving the agency first crack at correcting its own errors ... conserves judicial resources.” Id. This ground suffices to support the district court’s ruling. The Department possesses the requisite expertise to construe its policies and to conduct the somewhat complicated calculations involved in resolving these claims. Putting aside any jurisdictional problems, it would have been unwise for the district court to have needlessly taken on these tasks. We therefore affirm the district court’s denial of plaintiffs’ motion.6
CONCLUSION
For the reasons explained above, we affirm the district court’s denial of the relief requested by plaintiffs, but reverse its grant of summary judgment on the issue of what process is due, and remand the ease to the district court so that it may enter a new judgment consistent with this opinion.
. The claims of plaintiffs Monica Furlong and Lawrence Schwartz, also listed as appellants on the notice of appeal, were long ago dismissed by the District Court for failure to exhaust their administrative remedies. See Furlong v. Shalala, No. 94 Civ. 4817, 1996 WL 393526, at *8-* 12 (S.D.N.Y. July 12, 1996). There was no appeal from this dismissal. See Furlong v. Shalala, 156 F.3d 384, 390 (2d Cir.1998). Therefore, only the claims of plaintiffs Sloan and Sunew remain.
. This regulation apparently grew out of the choice of some carriers to reimburse physicians in this manner pursuant to MCM § 4149, which provides that carriers should "[e]stablish guidelines for use in coding charges for surgery when more than one surgical procedure is performed during the same operation, through the same opening, through a different opening or by different surgical procedures. The guidelines should establish the allowable amount based upon (1) the major procedure only, or (2) the major proce*230dure plus partial amounts for other procedures.” Health Care Financing Authority, Medicare Carriers’ Manual § 4149. Presumably, the discretion of the carriers to elect between these two options has been circumscribed by the 1991 regulation quoted above.
. Although the parties agree that this shift in policy occurred, it is unclear given the state of the record how precisely this shift was communicated by HCFA. Despite this Court’s explicit request, defendants were unable to direct us to a regulation or policy statement announcing the change. The defendants, in *231the supplemental letter brief requested by the Court, do assert that in January 1994, the numeric code in the official Medicare Physician Fee Schedule database indicating whether the multiple surgical rules should be applied in calculating the benefits due changed from a "1,” indicating that these rules should be applied, to a "0,” indicating that they should not. See Letter of Michael M. Krauss, dated December 12, 2000, at 3-5; see also MCM § 4826(C) (confirming the meaning of these codes with respect to the application of multiple surgery rules). This comports with the facts alleged by plaintiffs in their complaint. While the only other evidence of this change in policy contained in the record is an excerpt from a newsletter published by the American Society of Anesthesiologists, see Letter of Peter James Clines, dated December 12, 2000, Ex. 5, the Court is satisfied that this change in policy did occur as of January 1, 1994, and that it was communicated to the insurance carriers through the coding system in the fee schedule database.
. Defendants argue in passing that because plaintiffs did not appeal from this ruling, it is the law of the case, and binding on plaintiffs here. See Appellee’s Br. at 33, note.
Plaintiffs respond that the district court in 1996 simply correctly determined that plaintiffs were not challenging the one-and-one-half rule itself, but rather "the decision of HCFA to endorse the carrier's application of the rule to concurrent invasive monitoring.” Appellants’ Reply Br. at 8. We do not think that this is a fair reading of the district court’s ruling. It is clear that the district court thought the claims were best construed as the carriers’ application of a valid agency regulation, and hence amount claims.
We understand the "law of the case” doctrine to be discretionary. See, e.g., Christianson v. Colt Indus. Operating Corp., 486 U.S. 800, 817, 108 S.Ct. 2166, 100 L.Ed.2d 811 (1988) (Brennan, J.); Tischmann v. ITT/Sheraton Corp., 145 F.3d 561, 564 (2d Cir.), cert. denied 525 U.S. 963, 119 S.Ct. 406, 142 L.Ed.2d 329 (1998); Doctor’s Assoc., Inc. v. Distajo, 107 F.3d 126, 131 (2d Cir.1997), cert. denied, 522 U.S. 948, 118 S.Ct. 365, 139 L.Ed.2d 284 (1997); North River Ins. Co. v. Philadelphia Reins. Corp., 63 F.3d 160, 164-65 (2d Cir.1995), cert. denied, 516 U.S. 1184, 116 S.Ct. 1289, 134 L.Ed.2d 233 (1996); United States v. Uccio, 940 F.2d 753, 757-59 (2d Cir.1991). Here, since the prior ruling was in favor of the plaintiffs, it is doubtful that they could have contested the court’s rationale. And even if they could have done so, it would not have been in their interest. Therefore, we are not dealing here with a situation in which a party with the incentive to appeal an order has failed to do so at one stage, and seeks to ignore the order at another. Thus, the application of the law of the case doctrine would be inappropriate under these circumstances, and we decline to apply it here.
. Plaintiffs, in support of their argument, quote a Conference Report from the time of the 1987 amendments enhancing review of Part B determinations, which states:
Numerous concerns have been expressed by beneficiaries about the fairness and adequacy of this Part B appeals process. Some have expressed the concern that the hearing officers are not properly qualified or are not objective, because many of them are former employees of the carrier or because their continued service as hearing officers may depend on the carriers being satisfied with the decisions they render. Other concerns deal with the way hearings are conducted, including the beneficiaries' inability to produce evidence or to challenge the hearing officers' decision rules or his reliance on unidentified experts and consultants.
The Committee bill would attempt to resolve these concerns by establishing an appeals procedure under Part B that is modeled after that available under Part A.
Blue Brief at 17-18 (quoting H.R.Rep. No. 99-727, at § 4532, reprinted in 1986 U.S.C.C.A.N. 3607).
. Defendants suggest that plaintiffs do not have standing to request the relief sought below. Because we affirm the district court’s denial of that relief on the ground discussed above, we need not address this issue.