Dr. Charles DeHaan appeals the sentence he received for engaging in a scheme to defraud Medicare in violation of 18 U.S.C. § 1347 . In estimating the loss attributable to DeHaan's conduct, the district court found that he was responsible for fraudulently certifying the eligibility of least 305 individuals for home health care services, resulting in wrongful billings to Medicare of nearly $2.8 million. DeHaan contends that the court's finding that he fraudulently certified 305 individuals is tainted by a legal error as to what was required to properly certify a patient as eligible for home care. He also argues that the loss figure for these individuals was inflated, as the government did not prove *801 that the individuals in question in fact were not eligible for the services billed. Finally, because he believes that this loss amount was erroneous, DeHaan contends that the court also erred in requiring him to pay restitution in the same amount. Finding no error in the district court's conservative loss-estimation methodology, we affirm.

I.

During the five-year time period relevant to this case, DeHaan was a licensed family-practice physician working in the Chicago and Rockford metropolitan areas of Illinois. He was president of Housecall Physicians Group of Rockford, S.C., was affiliated with other similar agencies providing medical services to homebound patients, and served as medical director of a number of home health agencies, assisted living facilities, and hospices. He was enrolled as a provider with Medicare and as such had a unique national provider number pursuant to which he would bill Medicare for services he provided to Medicare beneficiaries.

Among the services for which Medicare will reimburse qualified beneficiaries are home health services. In order to qualify for such services, an individual must be effectively confined to the home and must be certified as such by a physician.

DeHaan knew that Medicare authorized payment for physician house calls and other home health services only if those services were actually provided and were medically necessary due to a patient's disease, infirmity, or impairment. DeHaan also knew that Medicare did not authorize payment for services and treatment that were not actually provided or for which the patient did not meet the criteria necessary to justify the claimed service or treatment.

Beginning in January 2009 and continuing into January 2014, DeHaan participated in a scheme to defraud Medicare with the aim of obtaining monetary reimbursement from the Medicare program by means of materially false and fraudulent representations. The misrepresentations fell into two primary categories.

First, DeHaan would bill Medicare at the highest levels for services to homebound patients that were ostensibly time-consuming and/or complex, when in fact he had either conducted a routine, non-complex visit with the patient (perhaps lasting no more than a few minutes), or he had not seen (or served) the patient at all on the occasion for which he was billing. We shall refer to this as the overbilling aspect of the scheme.

Second, at the behest of home health agencies, DeHaan certified as homebound patients whom he either knew did not meet Medicare's criteria for home care or as to whom he lacked meaningful knowledge as to their health status. We shall refer to this as the fraudulent certification component of the scheme. Apropos of that aspect of the scheme, DeHaan at least twice acknowledged to one of the investigating agents that he had certified as homebound patients who did not, in fact, meet Medicare's criteria for being homebound. He added that the home health agencies would tell him what services their clients needed (and wanted, in many cases), and, in DeHaan's words, "I certify." R. 150 at 222. DeHaan questioned whether some of the patients truly qualified as homebound, but he told the agent that he could always find a reason why they needed home health services. "I will have some issues with this," he told the agent, R. 150 at 224, seemingly recognizing that some number of his certifications were of dubious legitimacy.

Medicare will authorize payment for health services-which include such things as intermittent skilled nursing, physical therapy, speech therapy, and occupational therapy-provided that three criteria are *802 satisfied. First, the beneficiary must in fact be homebound, meaning that his ability to leave the home is restricted due to illness or disability. Second, the beneficiary must be under the care of a physician who has created a specific plan of care for him. Third, the beneficiary's physician must complete and sign a Medicare Form 485 setting forth, among other things, the beneficiary's diagnosis, functional limitations, medications, and plan of care, along with a certification that the beneficiary is homebound, is under the physician's care, and is in need of home health services. See 42 U.S.C. § 1395n(a)(2)(A) ; 42 C.F.R. § 424.22 (a) ; United States v. Echols , 574 F. App'x 350 , 352 (5th Cir. 2014) (non-precedential decision); R. 93 at 5-6. Periodically, a physician will need to re-certify the beneficiary as homebound in order to preserve the beneficiary's eligibility for home health services. 42 C.F.R. § 424.22 (b). The certifying physician will bill Medicare for the certification or re-certification. Certification, of course, paves the way for home health agencies to provide services to the beneficiary and to bill Medicare for those services.

DeHaan elected to plead guilty to two counts of a 23-count superseding indictment. Although DeHaan denied certain aspects of the scheme to defraud as the government had framed it, he did admit to engaging in each of the two categories of misrepresentations that we have discussed: overbilling and fraudulent certifications. As it happens, the two counts of the indictment to which DeHaan pleaded guilty both involved overbilling as we have described it. Count 9 alleged that DeHaan had sought reimbursement for an in-home visit to a beneficiary, "SJ," whom DeHaan had actually not seen on the occasion in question. And Count 21 alleged that DeHaan had sought reimbursement for an in-home visit to a beneficiary, "CH," who had died some six weeks prior to the date of the fictitious visit.

The parties were unable to reach an agreement as to the loss resulting from DeHaan's criminal conduct, and the probation officer did not propose a loss amount in the pre-sentence report. The district court took evidence on the loss amount over the course of two days, after which the parties filed post-hearing briefs setting forth their widely-divergent views as to the appropriate loss amount.

Judge Kapala entered his findings as to the loss in a written order. After observing that "it is not possible to determine with precision the actual amount of loss in this case," R. 134 at 1, he endeavored to make a reasonable estimate of the loss. See U.S.S.G. § 2B1.1 cmt. n.3(c) (Nov. 2015). 1 The judge rejected DeHaan's argument that the loss amount should be limited to the $828.42 billed in connection with the Medicare beneficiaries identified in the two counts of the superseding indictment to which DeHaan had pleaded guilty. He also rejected the government's threshold position that the entirety of the billings attributable to DeHaan over the life of the scheme should be presumed fraudulent and that the burden should be shifted to DeHaan to prove otherwise. See United States v. Hebron , 684 F.3d 554 , 563 (5th Cir. 2012). But the judge was satisfied that the evidence presented by the government enabled him to make a reasonable estimate of the loss resulting from DeHaan's conduct.

As to the overbilling aspect of the scheme, the judge went on to find that DeHaan's conduct had resulted in a loss of $478,520.29. That figure is not at issue in this appeal; DeHaan accepts it as accurate.

*803 With respect to the loss associated with DeHaan's fraudulent certification of "homebound" patients-which DeHaan does dispute on appeal-the district court endorsed the government's view that one could reasonably estimate this component of the loss by tallying the number of Medicare beneficiaries certified by DeHaan as homebound who appeared not to be under his care. Government Exhibit 94A listed 471 patients certified by DeHaan as to whom there was no record of any in-home visit by DeHaan with those individuals. Exhibit 94B reduced that total to 411 by excluding patients who were certified by DeHaan but for whom there was never any subsequent billing by home health agencies. Exhibit 94C reduced the total further to 305 by eliminating patients who had additional certifications by someone other than DeHaan. Because the physician completing a Form 485 certification must have under his care the Medicare beneficiary he is certifying as homebound, and because there was no evidence of any billing by DeHaan as to these beneficiaries (other than for the certification or re-certification itself), Judge Kapala concluded it was reasonable to infer that the certifications as to these beneficiaries were fraudulent, and it was also reasonable to infer that the home healthcare billings associated with these patients, totaling $2,787,054.58 were part of the loss resulting from DeHaan's fraud. R. 134 at 10.

The judge acknowledged DeHaan's "brief[ ]" contention that a beneficiary could be certified as homebound based on a face-to-face encounter conducted by a medical professional other than the certifying physician himself. R. 134 at 10 n.10.

It is not clear to the court how this is relevant, ... [as it] does not change the fact that the defendant certified that the patients listed in Exhibit 94C were under his care ..., even though there is no record of him providing any medical care to those patients. Accordingly, this undeveloped argument does not persuade the court that the government's loss calculation on this issue is incorrect, or that the government is somehow "attempting to pile on."

R. 134 at 10 n.10 (quoting defendant's post-hearing brief regarding sentencing enhancements, R. 119 at 22).

Coupled with the overbilling figure, the total loss attributable to DeHaan's conduct amounted to $3,265,574.87, which the court found to be a fair and reasonable estimate of the loss. R. 134 at 10. That loss amount triggered a 16-level enhancement pursuant to section 2B1.1(b)(1)(I) for losses exceeding $1.5 million, along with another two-level enhancement pursuant to section 2B1.1(b)(7) because the loss to Medicare exceeded $1 million. R. 134 at 10.

The court subsequently ordered DeHaan to serve a within-Guidelines sentence of 108 months in prison. It also ordered him to pay restitution in the amount of $2,787,054.58, which was the loss figure associated with his fraudulent homebound certifications. 2

*804 II.

DeHaan's appeal focuses on the district court's estimate of the loss attributable to the fraudulent certification aspect of the scheme. He makes three principal arguments: (1) The district court committed legal error when it concluded that DeHaan's certifications of the 305 Medicare beneficiaries identified in Exhibit 94C as homebound were fraudulent in the absence of evidence that he had ever made a home visit to these patients, when the law did not require DeHaan himself to meet with the patient as a condition of certifying him or her as homebound; (2) the court committed a second legal error in adopting as the loss figure the total billings associated with these fraudulent certifications, without proof that none of these 305 patients was in fact homebound and thus qualified for home health benefits; (3) for the same reasons the estimate of the loss resulting from the fraudulent certifications was erroneous, the court committed plain error when it required DeHaan to make restitution to Medicare in this amount. 3

DeHaan's first argument assumes that the district court treated as fraudulent the certifications of the 305 individuals set forth in Exhibit 94C because there was no evidence that DeHaan met with these individuals face to face before certifying them as homebound. DeHaan does not dispute that he certified certain individuals as homebound without first meeting them in person, but he points out that the face-to-face requirement for certification was first adopted with the passage of the Affordable Care Act in 2010, and did not take effect until January 1, 2011, a full two years into his criminal scheme. See Patient Protection and Affordable Care Act, Pub. L. No. 111-148, § 6407, 124 Stat. 119 , 769-70 (Mar. 23, 2010); 42 U.S.C. § 1395f ; CMS Manual System, Pub. 100-02, Transmittal 139 (Feb. 16, 2011) ("Clarifications for Home Health Face-to-Face Encounter Provisions") (amending § 30.5 of Medicare Benefits Policy Manual), available at www.cms.gov/Regulations-and-Guidance/Guidance/Transmittals/downloads/R1398BP.pdf (visited July 17, 2018). Even then, the face-to-face meeting could be conducted by a non-physician practitioner, such as a nurse practitioner or physician's assistant, working in collaboration with or under the supervision of the certifying physician rather than the physician himself. Affordable Care Act § 10605, 124 Stat. at 1006; 42 U.S.C. §§ 1395f(a)(2)(C), 1395n(a)(2)(A). DeHaan notes testimony below that "at various times relevant to the scheme," he did have nurse practitioners working with him. DeHaan Br. 26. So the lack of a face-to-face meeting between DeHaan and any of the 305 individuals listed in Exhibit 94C did not by itself establish that the certifications were fraudulent, as he may have relied on a face-to-face encounter with one of these nurse practitioners in certifying these individuals as homebound.

But DeHaan is mistaken to think that the court characterized these certifications as fraudulent based on the lack of face-to-face meetings with the individuals listed. Certainly it is true that both the government's counsel and some of its witnesses made statements which could be understood as asserting that DeHaan was required to have a face-to-face meeting with a patient before certifying that patient as homebound. R. 158 at 173, 183, 223. But it is not at all apparent that the district *805 judge ever labored under the misimpression that DeHaan was required to meet in person with a patient before he certified that individual as homebound. The judge appeared to challenge that very notion when the government advanced it. R. 158 at 182-83. More to the point, in concluding that the certifications of the individuals in Exhibit 94C were fraudulent, the judge relied not on the lack of face-to-face encounters, but on the absence of evidence that these patients were under DeHaan's care. R. 134 at 10 n.10. Indeed, in his order, Judge Kapala expressly acknowledged DeHaan's argument that the required face-to-face meeting could be performed by someone other than the certifying physician, but he dismissed the relevance of this argument given his conclusion that the patients set forth in Exhibit 94C were not under DeHaan's care. R. 134 at 10 n.10. So the notion that the district court relied on the lack of a face-to-face meeting between DeHaan and the patients prior to certification is a non-starter.

More relevant is DeHaan's secondary contention that the patients in question could have been under DeHaan's care without him necessarily providing services directly to the patients and billing Medicare for those services. Certainly it is true that a physician may supervise the care of a patient but rely on someone like a nurse practitioner or another non-physician professional from a home health agency to provide care to the patient. Because a non-physician professional will typically have his or her own Medicare provider number, that individual's services will be billed under that number rather than the number of the supervising physician. Moreover, the 2014 Medicare Benefits Policy Manual in effect at the conclusion of the scheme indicated that there was no requirement that the physician himself see the homebound patient at any particular time or with any particular frequency:

The patient must be under the care of a physician who is qualified to sign the physician certification and plan of care in accordance with 42 C.F.R. § 424.22 .

A patient is expected to be under the care of the physician who signs the plan of care and the physician certification. It is expected, but not required for coverage, that the physician who signs the plan of care will see the patient, but there is no specified interval of time within which the patient must be seen.

Medicare Benefits Policy Manual, Ch. 7 § 10 (2014), available at doczz.net/doc/6541500/medicare-benefit-policy-manual-chapter-7-home health-se... (visited July 17, 2018). So in theory, DeHaan might have been supervising the care of a particular patient without seeing that patient or billing Medicare for direct services to that patient at any particular time or interval of time. Thus, in DeHaan's view, the lack of such billings by him does not by itself suggest fraud in the Form 485 certifications, just as his lack of a face-to-face meeting in connection with the certification does not necessarily mean the certification was fraudulent.

But we agree with the district court that the lack of billings by DeHaan as to any of the patients set forth in Exhibit 94C does support the reasonable inference that the certifications of these patients as homebound were fraudulent. Given that a homebound patient must be under the certifying physician's care, one would naturally expect that the physician will, at one point or another, bill Medicare for some visit or service apart from the certification itself. Whatever the 2014 Medicare Benefits Policy Manual may or may not have required of the certifying physician in this respect, it did not suggest that the physician would routinely be so detached from the patient's care that he would never see the patient or provide a service for which he would bill *806 Medicare directly. Indeed, in view of the government's case as to the overbilling aspect of the scheme, which included testimony from multiple patients recounting DeHaan's practice of making brief visits to their residences for perfunctory inquiries as to their status and needs (sometimes not venturing beyond their doorways in the course of the visit)-and for which he would later bill Medicare for hundreds if not thousands of dollars for examinations and services he did not perform-it is all the more noteworthy that DeHaan forsook the opportunity to bill the government for services to any of the beneficiaries identified in Exhibit 94C. The lack of any apparent followup by DeHaan with these beneficiaries once certified for home care readily supports the inference that DeHaan did not, in fact, have the patients identified in Exhibit 94C under his care. Having in mind that the district court's task was to make a reasonable estimate of the loss rather than to assess it with precision, we are satisfied that its reliance upon Exhibit 94C was both acceptable and proper. For this purpose, the government was not required to rule out every theoretical possibility that a given patient listed in that exhibit could have been under DeHaan's care without the doctor himself having seen and/or provided a billable service to that patient at some point during the life of the scheme. The lack of any billing for a visit or service by DeHaan reasonably suggests fraud, and the court was within its rights to base its loss estimate on that inference.

That the government bore the burden of proof as to the loss, e.g. , United States v. Williams , 892 F.3d 242 , 250 (7th Cir. 2018), does not counsel differently. The government satisfied that burden by supplying the court with evidence which, as we have just explained, established a reasonable estimate of the loss. Its approach to the loss attributable to DeHaan's fraudulent certifications was, if anything, "conservative," as Judge Kapala described it. R. 134 at 9. As the perpetrator of the scheme, DeHaan had the means to present the court with a different view of the scope of his fraud, if he wished, or to demonstrate that the government's evidence or methodology was in some way unreliable. See United States v. Durham , 766 F.3d 672 , 686 (7th Cir. 2014) (once government has presented explicit proof of loss, it is defendant's obligation to present evidence to counter that showing) (citing United States v. Gordon , 495 F.3d 427 , 432 (7th Cir. 2007) ). Judge Kapala gave DeHaan every chance to do just that. DeHaan did not avail himself of that opportunity.

In short, we reject the notion that the district court committed legal error in relying on the lack of direct billings by DeHaan to infer that the patients identified in Exhibit 94C were not, in fact, under his care, as required by the relevant statutes and regulations.

DeHaan next argues that the district court improperly calculated the monetary loss to Medicare resulting from the fraudulent certification of these 305 patients. As we noted earlier, the district court found that Medicare paid roughly $2.8 million to home health agencies under Medicare Part A for services rendered pursuant to DeHaan's certification that these patients were homebound. R. 134 at 10. DeHaan contends that he can only be held to account for the loss that was proximately caused by his conduct, and for two reasons he believes it was error for the court to treat the total amount paid by Medicare for services to these patients as the relevant loss amount.

First, he notes that the home health agencies had an independent duty to bill Medicare only for such services as were reasonably necessary. The government declined to treat the home health agencies as co-schemers with DeHaan, such that any *807 fraud on his part was attributable to the agencies who proceeded to bill Medicare for services to the patients he certified, or vice-versa. Thus, as DeHaan sees things, if the agencies concluded that a given patient warranted home health services, then the bills they submitted to and were paid by Medicare were not fraudulent. And if the agencies were knowingly billing Medicare for services that were unnecessary, then that was an independent fraud in which DeHaan was not implicated. Either way, in his view, "[a]gency independence is an intervening act breaking the causal chain between DeHaan's certifications and any agency bills-fraudulent or not." DeHaan Br. 37.

Second, and relatedly, DeHaan argues that Medicare only suffered a loss to the extent that any of these patients in fact could not qualify as homebound and thus should not have received the services for which Medicare was billed. In his view, absent proof that none of the 305 patients was actually eligible for home health services, it was error for the court to treat the entire amount paid by Medicare for services to these patients as a loss.

Neither of these arguments was made below, so our review is for plain error only. Fed. R. Crim. P. 52(b) ; see also , e.g. , United States v. Carson , 870 F.3d 584 , 593 (7th Cir. 2017), cert. denied , --- U.S. ----, 138 S.Ct. 2011 , --- L.Ed.2d ---- (2018). We are satisfied that the district court committed no obvious error in treating the amounts paid by Medicare as the loss amount for which DeHaan should be held responsible. See Puckett v. United States , 556 U.S. 129 , 135, 129 S.Ct. 1423 , 1429, 173 L.Ed.2d 266 (2009) (to meet plain error standard error must be clear or obvious) (citing United States v. Olano , 507 U.S. 725 , 734, 113 S.Ct. 1770 , 1777, 123 L.Ed.2d 508 (1993) ).

First, although the home health agencies had their own obligations to Medicare, their independent role in ascertaining what services a patient genuinely required and in billing Medicare for those services in no way mitigated or limited DeHaan's culpability for the resulting loss to Medicare. The certifying physician plays the role of gatekeeper in ascertaining whether a patient is homebound and qualifies for home health services; Medicare relies on the independent and honest professional judgment of the certifying physician for that purpose. See United States v. Patel , 778 F.3d 607 , 617 (7th Cir. 2015). DeHaan certified as homebound hundreds of patients either knowing that they did not qualify as homebound under Medicare's criteria or without knowing at all whether they so qualified. In doing so, he breached his duty to Medicare and opened the door for the agencies to bill Medicare for millions of dollars worth of services. See id. He knew this is what the agencies would do-after all, in at least some instances, he certified the patients as homebound at the agencies' behest. He may be held to account for the foreseeable consequences of the scheme. See U.S.S.G. § 2B1.1, comment. (n.3(A)(i) ) (" 'Actual loss' means the reasonably foreseeable pecuniary harm that resulted from the offense.").

Second, it is not plain that this is the sort of case in which the loss amount should be reduced by the value of services provided to patients who, although fraudulently certified as homebound by DeHaan, in fact were homebound and thus could have been properly certified. The fraud at issue in this appeal does not involve overbilling for services that were otherwise legitimate. Cf. United States v. Mahmood , 820 F.3d 177 , 193-94 (5th Cir.), cert. denied , --- U.S. ----, 137 S.Ct. 122 , 196 L.Ed.2d 41 (2016) (defendant entitled to credit for value of legitimate hospital services that only became tainted by fraud *808 after the fact, when defendant had billing codes altered to result in overcharges); United Statesv. Vivit , 214 F.3d 908 , 915-18 (7th Cir. 2000) (where fraud involved overstatement of care provided to patients, and evidence indicated that some services provided were medically necessary, district court appropriately credited defendant for value of those services in loss calculation). Medicare requires a patient to be certified as a precondition to receiving home health services. Absent a proper certification, a patient is not eligible for such services as far as Medicare is concerned, whether he is actually homebound or not. Thus, any patients whom DeHaan fraudulently certified as homebound without actually knowing anything about their status were, from Medicare's point of view, ineligible for home health services, in the same way that a patient who has not yet been evaluated and certified as homebound by a physician is ineligible. In this way, one may see the entire amount paid by Medicare for services to these patients as a loss even if, in theory, some number of these patients were in fact homebound and could therefore have qualified for home services had they been certified as homebound in good faith by an honest physician. Cf. United States v. Jones , 664 F.3d 966 , 984 (5th Cir. 2011) (noting that from Medicare and Medicaid's perspective, medical services provided by unlicensed therapists were of no value; it was thus appropriate to treat entire amount paid by Medicare and Medicaid for those services as loss); United States v. Triana , 468 F.3d 308 , 320-23 (6th Cir. 2006) (where defendant was barred by prior conviction from participating in Medicare program, full amount paid by Medicare to his firms was properly treated as loss, even if billings were for legitimate services provided to Medicare-eligible patients by licensed professionals). 4

Finally, we may quickly dispatch DeHaan's contention that the district court committed plain error in ordering him to pay restitution in the amount of $2,787,054.58-equal to the loss amount attributed to the wrongful certification component of his fraud. This challenge largely amounts to a rehash of the challenges DeHaan made to the loss amount and which we have already rejected. We need add only that the restitution order does not, in our view, effectuate joint and several liability for the actions of the home health agencies who billed Medicare for the services provided to the patients whom DeHaan fraudulently certified as homebound. As we have already discussed, regardless of whether the agencies themselves engaged in independent wrongdoing when they billed Medicare for these services, the billings were the direct and foreseeable result of DeHaan's fraud as the gatekeeper in certifying the patients; without his certification, the agencies could not have billed Medicare and Medicare would not have compensated the agencies for the services they provided. The Medicare payments are a reasonable approximation of the loss resulting from DeHaan's own criminal conduct, and as such it was entirely appropriate for the district court to order DeHaan to make restitution for that loss.

*809 III.

Finding no error in the district court's calculation of the loss owing to DeHaan's wrongful certification of patients as homebound or its order that DeHaan make restitution to Medicare for that loss, we AFFIRM the sentence.