
    UNITED STATES of America, Plaintiff-Appellee, v. Paul Photiadis BOCCONE, Defendant-Appellant. United States of America, Plaintiff-Appellee, v. Charles Brown, Jr., Defendant-Appellant.
    Nos. 12-4949, 12-4952.
    United States Court of Appeals, Fourth Circuit.
    Argued: Oct. 31, 2013.
    Decided: Feb. 20, 2014.
    
      ARGUED: John O. Iweanoge, II, The Iweanoges’ Law Firm, P.C., Washington, D.C.; Emma Mittelstaedt Burnham, Baker Botts, L.L.P., Washington, D.C., for Appellants. Michael Phillip Ben’Ary, Office of the United States Attorney, Alexandria, Virginia, for Appellee.
    ON BRIEF: William H. Jeffress, Jr., Nicholas C. Margida, Baker Botts L.L.P., Washington, D.C., for Appellant Charles Brown, Jr. Neil H. MacBride, United States Attorney, Marc J. Birnbaum, Special Assistant United States Attorney, Office of the United States Attorney, Alexandria, Virginia, for Appellee.
    Before NIEMEYER and WYNN, Circuit Judges, and LOUISE W. FLANAGAN, United States District Judge for the Eastern District of North Carolina, sitting by designation.
   Affirmed by unpublished opinion. Judge FLANAGAN wrote the opinion, in which Judge NIEMEYER and Judge WYNN joined.

Unpublished opinions are not binding precedent in this circuit.

FLANAGAN, District J.

Following a four-day trial, a jury convicted appellants Paul Photiadis Boccone and Charles Brown, Jr., of multiple charges related to illegal distribution of prescription drugs. Boccone was convicted of additional health care fraud and tax charges. The convictions arose from Boc-cone’s operation of Chantilly Specialists, a pain management clinic in Chantilly, Virginia, and Brown’s participation as a licensed nurse practitioner in the clinic’s operations. On appeal, Boccone and Brown challenge their convictions and sentences on several grounds, including admissibility of expert testimony, sufficiency of the evidence, and procedural reasonableness of the sentences. For the reasons presented below, we affirm.

I.

In an indictment filed December 22, 2011, the government charged Boccone and Brown with conspiracy to distribute controlled substances, under 21 U.S.C. § 846 (Count 1), and distribution of controlled substances, in violation of 21 U.S.C. § 841(a)(1) and 18 U.S.C. § 2 (Boccone, Counts 2-9; Brown, Counts 2, 7, 9). Boc-eone also was charged with possession of a firearm in relation to drug trafficking, under 18 U.S.C. § 924(c) (Count 10), health care fraud, under 18 U.S.C. § 1847 (Counts 11-16), and failure to pay employment taxes, under 26 U.S.C. § 7202 (Counts 17-28).

At trial, the government presented testimony by former employees and patients of Chantilly Specialists, relatives of patients, as well as an expert witness in the field of pain management. Appellants introduced testimony by Boccone, Brown, and an expert with respect to the cause of death of several patients. The evidence, viewed in the light most favorable to the government, may be summarized as follows.

Boccone was the owner and president of Chantilly Specialists from late 2005 to around December, 2011. He has a Juris Doctor degree, but no medical training. He employed several medical providers at Chantilly Specialists, including Brown, who was a nurse practitioner licensed to prescribe medication under Virginia law under the supervision of a physician. When Brown began work at Chantilly Specialists in July 2009, Dr. Carol Currier was a physician employed at the clinic, designated as supervising physician for Brown. Dr. Joel Match took over in this position from Dr. Currier in 2011. During the time that Dr. Currier was designated as supervising physician, and for some of the time that Dr. Match was designated as supervising physician, Boccone also provided direction to Brown in his treatment of patients and prescribing of medication.

Boccone and Brown interacted nearly every day at the office. Boccone often was in the examination room with patients during medical appointments. Boccone interfered sometimes in medical treatment decisions, including by giving medical suggestions and opinions regarding medications and dosage. In some instances, Brown signed prescriptions that Boccone filled out with medication amounts specified. Boccone also wore a lab coat and sometimes referred to himself as “Dr. Boc-cone.”

In contrast to Boccone and Brown, Dr. Currier generally was present at Chantilly Specialists only once or twice a week. She was not told of positive drug screens, and she was not told of patient deaths, except once, although she had asked to be kept informed of such information.

After Dr. Match started employment at Chantilly Specialists, Boccone sometimes steered patients from Dr. Match to Brown, the result being that they would continue to get medications they were on before, whereas Dr. Match would have reduced medication pending clinical tests. After August 2011, Dr. Match realized that Brown did not always follow his instructions and ultimately recommended that Boccone terminate Brown. Dr. Match, like Dr. Currier, was not aware of the full extent of treatment practices at Chantilly Specialists.

Regarding typical practices at the clinic, patient visits generally were limited to fifteen to twenty minutes. Boccone directed use of an egg timer to limit visit times. Brown generally would see about four patients per hour. Patients typically did not get physical examinations. They sometimes received medications without clinical information in their charts or documentation of treatment at other facilities. A lead medical assistant employed at the clinic between January 2011 and March 2012 observed that he “found unusual the massive amounts of medications people were getting.” (JA 128).

The waiting room was extremely crowded, and some patients had track marks and exhibited other indicia that they were suffering from addiction or were in recovery. Many patients at the clinic traveled long distances for their prescriptions, including six or seven hours away from locations in Kentucky, West Virginia, and Tennessee. Some patients became agitated or angry if they did not get medications they sought, and police frequently responded to reports of unruly patients at the clinic. As a result of the conditions in the office, Boc-cone carried a firearm at work.

The government presented testimony and evidence regarding several former patients of Chantilly Specialists who received prescriptions following office visits with Brown. Justin McConnell was a patient between about 2008 and October 2011. At his first visit, McConnell did not provide medical records from prior providers. He received a prescription including 15 milligrams of oxycodone, which was an increase over the amount he claimed he was receiving from a podiatrist at the time. McConnell never received a physical examination while a patient at Chantilly Specialists, and he never saw Dr. Currier. As his tolerance grew for pain medications, McConnell received an increase in prescriptions to the point that he was addicted to the medication, and he was receiving prescriptions for 80 milligram OxyContin and 30 milligram oxycodone pills, in addition to other medications. At times, Brown called McConnell on his personal cell phone, and McConnell was nervous about prescriptions being changed depending on whether he called Brown back. Brown made McConnell uncomfortable by giving him “bear hug[s]” and sitting on his lap in the office. (JA 192).

Eric Honesty was a patient from about August 2008 until February 2011. Honesty’s typical appointments took ten to fifteen minutes, and he never received any physical examination at Chantilly Specialists. Boccone and Brown were involved jointly with some of Honesty’s medical visits at Chantilly Specialists, and they increased his prescriptions over time up to 680 to 700 narcotic pain pills per month. At one visit, Honesty agreed to return 80 milligram OxyContin pills to Boccone and Brown in exchange for a prescription increase. Honesty returned “thousands” of 80 milligram pills in this manner. (JA 337). Three times when he attempted to take the medications as written in his prescriptions, he overdosed. At one point, Boccone and Brown instructed Honesty to take only half of the pills they had prescribed for him. During the time that Honesty was a patient at Chantilly Specialists, Honesty was charged with unlawful distribution of oxycodone, some of which he obtained by filling prescriptions issued by Brown.

King Dao was a patient from approximately 2009 to 2011. He received pain medications, including 80 milligram Oxy-Contin and 30 milligram oxycodone pills, following appointments with Brown and at times at direction of Boccone. He received medications despite having been tested positive for cocaine, and at one point he received medications after having spent 78 days in jail following an arrest for prescription fraud at Chantilly Specialists, with no medical examination.

Michael Rogers was a patient from 2007 to the date of his death, on April 8, 2010. He drove about six hours from Johnson City, Tennessee to receive prescriptions at the clinic. Boccone directed an increase in his pain medications in February 2009, to 80 milligram OxyContin and 30 milligram Roxicodon'e pills, a level that was maintained by providers, including Brown, until Rogers’s death. Brown admitted making changes to Rogers’s medical chart after learning of Rogers’s death.

The government also introduced testimony and a report of an expert witness qualified in the field of pain management, Dr. Robin Hamill-Ruth. Testifying as to standards of practice in the field of pain management, she summarized guidelines for prescribing medications for chronic pain, as well as standards for evaluations, referrals, documentation, periodic review and examinations. Dr. Hamill-Ruth also identified “red flags” indicating patients with problems with addiction, abuse, or diversion of medication, which would signal to a provider that there is not legitimate medical purpose for prescriptions. These include traveling long distances to receive medications, early refills, frequent calls, lost prescriptions, violent behavior, and receiving treatment from multiple providers. She also described the significance of 80 milligram OxyContin pills, which is a high dosage amount that she had never prescribed in her twenty-five years of pain management practice.

In addition,' Dr. Hamill-Ruth outlined her review of certain patient records, including those for Honesty, Dao, and Rogers, underlying individual distribution charges in this case. For each patient reviewed, Dr. Hamill-Ruth concluded that the entire course of treatment was outside the bounds of the accepted standard of care for pain management practice and for no legitimate medical purpose. She cited in each case indicia that should have led a reasonable, licensed medical practitioner to cease or reduce making prescriptions, require diagnostic examinations, and monitor patients to ensure legitimate medical care.

Finally, the government introduced testimony regarding Boccone’s health care billing fraud and failure to pay taxes. With respect to billing fraud, the provider listed in the medical record for one medical visit was Boccone, whereas the provider billed to Medicare was a physician’s assistant. With respect to the tax charges, Boccone failed to pay employment taxes despite withholding tax from employee paychecks.

Upon the close of the government’s evidence, the government voluntarily moved to dismiss three of the health care fraud charges (Counts 11, 12, and 13), which motion the district court granted. Defendants moved for judgment of acquittal at that time, and again moved for judgment of acquittal following the close of their case, which the district court denied.

Following closing argument and jury instructions, the jury found Boccone guilty of the conspiracy charge (Count 1), six of the distribution charges (Counts 2, 3,-4, 5, 7, and 9), one health care fraud charge (Count 14), and all of the tax charges (Counts 17-28). The jury found Boccone not guilty of two of the distribution charges (Counts 6 and 8), and possession of a firearm in furtherance of a drug trafficking crime (Count 10). The jury found Brown guilty of the conspiracy charge (Count 1) and all three of the distribution charges against him (Counts 2, 7, 9). Finally, the jury found that death did not result from the use of the substance distributed in Count 9, for patient Rogers.

In preparation for sentencing, the probation office prepared a presentence report, which calculated a guideline range of 360 months to life imprisonment for Boc-cone and a guideline range of 188 to 235 months imprisonment for Brown. After adopting the guideline ranges in the pre-sentence reports without change, the court varied downward, sentencing Boccone to 180 months imprisonment and Brown to 60 months imprisonment. These appeals followed.

II.

A.

We address first Boccone’s argument that the district court erred in allowing admission of the expert report and testimony of Dr. Hamill-Ruth.

“We review for abuse of discretion the district court’s decision to admit expert testimony under Federal Rule of Evidence 702.” United States v. Wilson, 484 F.3d 267, 273 (4th Cir.2007) (citing Kumho Tire Co. v. Carmichael, 526 U.S. 137, 152, 119 S.Ct. 1167, 143 L.Ed.2d 238 (1999)). “We will not vacate a conviction unless we find that the district court judge acted arbitrarily or irrationally in admitting evidence.” United States v. Basham, 561 F.3d 302, 326 (4th Cir.2009) (internal quotations omitted). In addition, evidentiary rulings are subject to harmless error review. United States v. Mouzone, 687 F.3d 207, 216 (4th Cir.2012).

Federal Rule of Evidence 702 provides: A witness who is qualified as an expert by knowledge, skill, experience, training, or education may testify in the form of an opinion or otherwise if: (a) the expert’s scientific, technical, or other specialized knowledge will help the trier of fact to understand the evidence or to determine a fact in issue; .(b) the testimony is based on sufficient facts or data; (c) the testimony is the product of reliable principles and methods; and (d) the expert has reliably applied the principles and methods to the facts of the case.

Fed.R.Evid. 702. “A ‘trial judge must have considerable leeway in deciding in a particular case how to go about determining whether particular expert testimony is reliable.’ ” Wilson, 484 F.3d at 273 (quoting Kumho Tire, 526 U.S. at 152, 119 S.Ct. 1167). “Thus, ‘Rule 702 grants the district judge the discretionary authority, reviewable for its abuse, to determine reliability in light of the particular facts and circumstances of the particular case.’ ” Id. (quoting Kumho Tire, 526 U.S. at 158, 119 S.Ct. 1167).

The government contends as an initial matter that we need not reach Boccone’s arguments as to admissibility of Dr. Hamill-Ruth’s testimony because it was irrelevant with respect to Boccone’s distribution of controlled substances. The government points out correctly that to convict Boccone of distribution of controlled substances, it need only show that Boccone, not a licensed medical provider, distributed or caused the distribution of a controlled substance. See 21 U.S.C. § 841(a)(1); 18 U.S.C. § 2.

Nevertheless, Boccone is charged in this case not only with distributing controlled substances individually, but also in concert with and in conspiracy with other medical providers, particularly Brown. In order to convict a licensed medical provider of unlawful distribution of controlled substances, the government must prove that the provider’s “ ‘actions were not for legitimate medical purposes in the usual course of his professional medical practice or [were] beyond the bounds of medical practice.’” United States v. Singh, 54 F.3d 1182, 1187 (4th Cir.1995) (quoting United States v. Tran Trong Cuong, 18 F.3d 1132, 1141 (4th Cir.1994)). As discussed below in addressing the sufficiency of the evidence, Boccone’s convictions may rest at least in part on the theory that Boccone directed Brown to issue prescriptions that were not for legitimate medical purposes or were beyond the bounds of medical practices.

Accordingly, expert testimony regarding whether treatment in this case was beyond the bounds of medical practice is relevant to the counts of conviction against both Brown and Boccone. We turn, therefore, to address Boccone’s arguments as to the admissibility of that testimony.

Boccone contends that Dr. Hamill-Ruth’s testimony and report does not meet the standards set forth in Fed.R.Evid. 702 for multiple reasons, including that Dr. Hamill-Ruth (1) did not accurately set forth the standards of model policies and guidance on prescribing narcotics, (2) used only sixteen hours to review thousands of pages of medical records, (3) did not examine any of the patients referred in her report, (4) did not adequately specify records reviewed, and (5) stated legal conclusions such as “it is illegal” within her written report.

This court previously has upheld the use of expert medical testimony similar in many respects to the testimony of Dr. Hamill-Ruth. For example, in United States v. McIver, 470 F.3d 550 (4th Cir.2006), the government offered testimony of an anesthesiologist qualified as an expert in pain management, who concluded, “[b]ased on his review of certain patient records,” that the “treatment of several of Appellant’s patients fell outside the parameters of legitimate medical practice.” Id. at 556. For one patient, he opined that “there was ‘no legitimate reason to be prescribing1 combinations of opioids in such high doses based on the patient’s medical conditions,” and in light of the patient’s “history of drug abuse.” Id. For another, he testified that it was “outside the legitimate practice of medicine for Appellant to prescribe high doses of opioids given [the patient’s] history of negative drug screens.” Id.

Similarly, in United States v. Alerre, 430 F.3d 681 (4th Cir.2005), a physician qualified as an expert reviewed selected medical files in evaluating whether prescriptions were issued outside the scope of legitimate medical practice. Id. at 686. The expert testified that “many of the prescriptions lacked appropriate documentation or had no ‘follow up’ treatment, that the defendants ignored ‘red flags’ indicative of drug abuse, and that certain prescriptions and dosages were inappropriate.” Id.

Likewise, in Tran Trong Cuong, an expert provided testimony following a medical file review, opining, for example, “that persons claiming ... severe pain over a long period of time should have had additional reports in their files of x-ray examinations, blood tests and other procedures attempting to identify the source of the pain.” Id.; see also United States v. Hurwitz, 459 F.3d 463, 467 (4th Cir.2006) (“The government’s expert witnesses testified that a doctor who knowingly prescribed opioids to an addict or to a patient the doctor knew was selling the drugs on the street was acting outside the bounds of legitimate medical practice”); Singh, 54 F.3d at 1187 & n. 3 (expert testified as to “the inappropriateness of the prescriptions,” upon review of “information relating to” each patient).

In this case, Dr. Hamill-Ruth was qualified, without objection, as an expert in pain management. Similar to the expert testimony in McIver, Alerre, and Tran Trong Cuong, Dr. Hamill-Ruth described her understanding of the standard of care for treating patients in a pain management context and then compared the treatment shown in the medical records in the case with that standard of care, finding the treatment shown to be outside legitimate medical practice. In doing so, she cited red flags similar to those identified by experts in the cases noted above, including negative drug screens, lack of documentation and follow up treatment for medical conditions, prescriptions over a long period of time without medical examinations, high dosage combinations, and prescriptions despite signs of drug addiction or street sales. (JA 3827-3836; 536-551).

In light of Dr. Hamill-Ruth’s qualifications and detailed manner in which she outlined her review of patient records and evidence considered as a basis for her opinions, we conclude that her testimony and report were both scientifically valid and helpful to the jury. Contrary to Boccone’s argument here, there is no requirement in our precedent that the expert must examine the patients whose files are reviewed, or set forth a particular model policy or standard, or cite to particular records or amounts of records for any particular patient. Rather, the points of criticism raised by Boccone go to the weight of the testimony, and these points were open for exploration upon cross-examination of the expert witness. Indeed, as the court noted in Mclver, such cross-examination enabled the appellants to point out “varying theories of pain management, ... differences in points of view as to appropriate levels of pain medication,” and make challenges to the expert’s “opinions regarding [the appellant’s] treatment of specific patients.” McIver, 470 F.3d at 556.

We address separately Boccone’s argument that the report improperly states a legal conclusion, referencing in particular the statement by Dr. Hamill-Ruth that “[i]t is illegal and grossly substandard for a person without medical license and DEA registration to make therapeutic decisions and alter prescribing of controlled substances.” (JA 3828). This statement is made in the context of Dr. Hamill-Ruth’s review of Rogers’s medical file, in which Boccone directs medication dosage and treatment for Rogers in an office visit note. (Id.).

This court has observed that “opinion testimony that states a legal standard or draws a legal conclusion by applying law to the facts is generally inadmissible.” McIver, 470 F.3d at 562. Nevertheless, an expert may testify that treatment was “outside the bounds of ... professional medical practice,” or that “treatment of certain patients was either illegitimate or inappropriate.” Id. Such language “falls within the limited vernacular that is available to express whether a doctor acted outside the bounds of his professional practice.” Id.

In accord with Melver, the expert’s statement here that “it is illegal and grossly substandard” for a person without medical license to make therapeutic decisions, in reference to Boccone’s involvement in treatment of Rogers, reasonably articulates the extent of departure from usual professional practice in this case. The statement thus is relevant to the jury’s determination that treatment of Rogers was “outside the bounds of ... professional medical practice.” Id. In any event, even assuming that the reference to “it is illegal” crossed outside of the “limited vernacular,” id., available in this context to describe legitimate medical practice, we conclude that the error was harmless, given the weight of evidence against Boccone apart from that reference in Dr. Hamill-Ruth’s report. See United States v. McLean, 715 F.3d 129, 143 (4th Cir.2013) (“[W]e need only say with fair assurance, after pondering all that happened without stripping the erroneous action from the whole, that the judgment was not substantially swayed by the error.”) (internal quotations omitted).

In sum, the district court properly admitted Dr. Hamill-Ruth’s testimony and report, and Boccone cannot establish error warranting reversal of his convictions on the basis of such testimony and report.

B.

Appellants argue that the evidence was insufficient to convict them of any of the counts of conviction.

We must sustain the jury’s verdict “if there is substantial evidence, taking the view most favorable to the Government, to support [the convictions].” United States v. Moye, 454 F.3d 390, 394 (4th Cir.2006) (en banc) (internal quotations omitted). “[Sjubstantial evidence is evidence that a reasonable finder of fact could accept as adequate and sufficient to support a conclusion of a defendant’s guilt beyond a reasonable doubt.” United States v. Burgos, 94 F.3d 849, 862 (4th Cir.1996) (en banc). In reviewing a sufficiency argument, we “must consider circumstantial as well as direct evidence, and allow the government the benefit of all reasonable inferences from the facts proven to those sought to be established.” United States v. Tresvant, 677 F.2d 1018, 1021 (4th Cir.1982). In addition, we “may not weigh the evidence or review the credibility of the witnesses,” as “those functions are reserved for the jury.” United States v. Wilson, 118 F.3d 228, 234 (4th Cir.1997).

1.

We address first the sufficiency of the evidence to convict appellants of the individual counts of distribution of controlled substances under 21 U.S.C. § 841.

Section 841 provides that “[e]xcept as authorized by this subchapter, it shall be unlawful for any person knowingly or intentionally ... to manufacture, distribute, or dispense ... a controlled substance.” 21 U.S.C. § 841(a)(1). An exception pertinent to this case is set forth in § 822(b), which provides:

Persons registered by the Attorney General under this subchapter to manufacture, distribute, or dispense controlled substances or list I chemicals are authorized to possess, manufacture, distribute, or dispense such substances or chemicals (including any such activity in the conduct of research) to the extent authorized by their registration and in conformity with the other provisions of this subchapter.

Id. § 822(b). As the court previously has observed, regulations promulgated by the Attorney General provide “that a prescription for a controlled substance is effective only if it is ‘issued for a legitimate medical purpose by an individual practitioner acting in the usual course of his professional practice.’ ” Hurwitz, 459 F.3d at 475 (citing 21 C.F.R. § 1306.04(a)).

Thus, to convict a medical practitioner under § 841(a)(1), the government must prove that (1) the defendant “distributed or dispensed a controlled substance,” (2) he “acted knowingly and intentionally,” and (3) his “actions were not for legitimate medical purposes in the usual course of his professional medical practice or were beyond the bounds of medical practice.” Singh, 54 F.3d at 1187 (quoting Tran Trong Cuong, 18 F.3d at 1141). “[T]here are no specific guidelines concerning what is required to support a conclusion that an accused acted outside the usual course of professional practice.” Id. (quoting United States v. August, 984 F.2d 705, 713 (6th Cir.1992)). “Rather, the courts must engage in a case-by-case analysis of evidence to determine whether a reasonable inference of guilt may be drawn from specific facts.” Id. (quoting August, 984 F.2d at 713).

A defendant’s “good faith” generally is relevant to a jury’s determination of whether a defendant acted outside the bounds of accepted medical practice or without a legitimate medical purpose. Hurwitz, 459 F.3d at 476 & 480. Accordingly a defendant cannot be convicted “if he merely made an honest effort to prescribe in compliance with an accepted standard of medical practice.” Id. at 476-77 (quoting United States v. Moore, 423 U.S. 122, 142, 96 S.Ct. 335, 46 L.Ed.2d 333 (1975)). Good faith in this context is an objective rather than subjective standard, meaning that “good faith is not merely a doctor’s sincere intention towards the people who come to see him, but, rather, it involves his sincerity in attempting to conduct himself in accordance with a standard of medical practice generally recognized and accepted in the country.” Id. at 478 (quoting United States v. Hayes, 794 F.2d 1348, 1351 (9th Cir.1986)).

Brown contends that he should be subjected to a different standard because, as a nurse practitioner in Virginia, he was authorized to prescribe only under supervision of a licensed physician. Brown fails to articulate, however, the manner in which the elements of the distribution offense should be different for a nurse practitioner as opposed to a physician. Indeed, the district court’s jury instructions set forth the government’s burden of proof in terms which apply equally to physicians and others “licensed and authorized to prescribe controlled substances.” (JA 818). In accordance with the standards set forth above, the district court instructed the jury that the government must prove beyond a reasonable doubt “that the defendant or defendants’ action were not for the legitimate medical purposes in the usual course of professional practice or were beyond the bounds of medical practice.” (JA 817). Under these instructions, Brown, as a nurse practitioner, is held to the same standard of practice as any other licensed medical practitioner, namely the requirement to make an “honest effort to treat his patients in compliance with the accepted standards of medicine.” (JA 818) (emphasis added). Brown did not object to these instructions. Nor does he contend on appeal that the jury instructions were improper.

Brown contends, nonetheless, that the government was required to introduce evidence that his conduct fell below a standard of practice for a nurse practitioner, as opposed to the standard of practice for a physician, and that the government did not do so in this case. We are not persuaded by Brown’s premise that the standard of medical practice should be any different for a nurse practitioner licensed to prescribe medication and a physician licensed to prescribe medication. In both instances the prescription — whether by a physician or a nurse practitioner — must be within the scope of usual medical practice and for a legitimate purpose. A nurse practitioner, like any other medical practitioner, “is not free deliberately to disregard prevailing standards of treatment.” Hurwitz, 459 F.3d at 479 (quoting United States v. Vamos, 797 F.2d 1146, 1151 (2d Cir.1986)); see also United States v. Lawson, 682 F.2d 480 (4th Cir.1982) (in affirming § 841(a)(1) convictions of pharmacist, stating that one element is “whether [the defendant] knew that the purported prescription was not issued for a legitimate medical purpose or in the usual course of medical practice”).

Brown also suggests that if a supervising physician authorizes a nurse practitioner to write prescriptions and does not revoke his ability to prescribe, then there is no basis to convict him absent further evidence that he “endeavored to conceal his prescriptions” or that the nurse and the physician “are deliberately working in concert to issue unlawful prescriptions.” (Brown Br. at 34). According to Brown, in the absence of such evidence of concealment or collusion, a nurse practitioner should be insulated from culpability because a physician has agreed to allow the nurse practitioner to prescribe medication. Such a bright-line rule, however, runs counter to this court’s prior recognition that “there are no specific guidelines concerning what is required to support a conclusion that an accused acted outside the usual course of professional practice,” and the court “must engage in a case-by-case analysis of evidence to determine whether a reasonable inference of guilt may be drawn from specific facts.” Singh, 54 F.3d at 1187 (quotations omitted).

Contrary to Brown’s suggestion, although evidence of concealment or collusion with a physician may be sufficient to convict a nurse practitioner of unlawful distribution of controlled substances, such evidence is not necessary to secure a conviction. A reasonable jury may conclude based upon other facts and circumstances that a nurse practitioner issued prescriptions knowing that they were not for a legitimate purpose or were outside the usual course of professional practice. In this case, for instance, Brown was not merely acting in isolation, solely under direction of a licensed physician. Rather, as we will detail below, this case involved more complex relationships between a non-physician office manager who took an active role in treatment decisions (Boccone), other medical and non-medical employees (including Brown), and supervising physicians who did not maintain a constant presence in the practice (including Drs. Currier and Match).

With these considerations in mind, we now turn to the sufficiency of the evidence supporting the individual counts of distribution of controlled substances, beginning with Brown’s convictions.

a.

Brown was convicted of three counts of unlawful distribution of a controlled substance, oxycodone, corresponding to prescriptions he wrote for three patients: King Dao, on October 23, 2009 (Count Two); Eric Honesty, on June 7, 2010 (Count Seven); and Michael Rogers on April 5, 2010 (Count Nine). Brown concedes that the government proved the first two elements of each of these offenses— that Brown distributed oxycodone, and that he did so knowingly and intentionally to each of these patients. He contends, however, that the government failed to prove the third element — that the prescriptions were illegitimate or outside the course of professional practice. We disagree.

The government introduced several categories of evidence supporting the third element of conviction on each of these charges. First, as to each charged distribution, the government introduced evidence that Boccone directed the treatment prescribed. In particular, with respect to Dao, on October 23, 2009, Boccone entered a treatment note stating:

New regiment [sic] as follows: Opiate Tollerant [sic]. Discontinue all medications. 60mg Oxsycontin [sic] for long acting releif [sic] from chronic intractable pain to be taken with 40mg Oxycontin to establish baseline releif [sic], 40mg to be taken 3 hours after taking a 60mg. 1 lOmg methadone to be taken at bedtime to affect the CYP1A4 Enzyme decreasing metabolising of oxycontin to increase duration. 2ml liquid Oxicodone for immediate releif [sic] in AM when awakening.

(JA 2731). Earlier in the same day, Boc-cone entered further notes regarding Dao’s pain symptoms. (JA 3030). At the same time, Brown is listed as medical provider in the medical records, and Brown issued a prescription for 40 milligram and 60 milligram OxyContin pills that same day. (JA 3030-3033; 2671-2675).

With respect to Honesty, on June 7, 2010, Boccone entered a treatment note stating that he restored an OxyContin prescription:

Restored Oxycontin to 3 tablets every 4 hours while awake from 10:00AM until 10:00PM with one additional at last dosage to total 13 tabs per day; Resored [sic] Roxicodone to 3 tabs q6 with one additional HS, Zanax at lmg ql2, cym-balta 60mg 1 tab q 12, changed neuron-tin to 600 q6.

(JA 2136). That same day, Brown issued four prescriptions for Honesty, including two separate 80 milligram oxycodone prescriptions. (JA 1974-1981).

Finally, with respect to Rogers, in an entry in Rogers’s medical records made by Boccone on February 12, 2009, Boccone increased Rogers’s oxycodone regimen to the level that it remained until Rogers’s death, on April 8, 2010. (JA 1715-1717). He also opined in a treatment note that Rogers “[requires physical therapy,” “has developed a very high tolerance to opiates,” and has a spinal cord injury with “no alternative treatment.” (JA 1781). On April 5, 2010, Brown issued prescriptions in the amount set by Boccone on February 12, 2009. (JA 1700-1702,1715).

In light of the above, we reject Brown’s contention that the record contains no evidence showing that Boccone directed Brown to write any of the three charged prescriptions. While Brown cites lack of testimony by the patients themselves as to who directed the prescriptions, the documentary evidence, combined with testimony regarding the working relationship between Boccone and Brown, amply supports the inference that Boccone directed the prescriptions.

Moreover, we reject Brown’s contention that, even if Boccone directed the prescriptions, the government failed to present any evidence that such conduct rendered the prescriptions illegitimate. The statute itself provides that it is illegal for a non-licensed individual to distribute controlled substances — or to direct or cause distribution thereof. See 21 U.S.C. § 841(a)(1); 18 U.S.C. § 2. In addition, Dr. Hamill-Ruth opined that it is “[absolutely not appropriate” for a non-licensed person to direct, oversee, or guide prescriptions for narcotic pain medications. (JA 530; see JA 3828). Thus, the jury properly could infer that if Boccone directed or caused the prescriptions to be issued, this itself established, or was one factor supporting, the conclusion that the prescriptions were illegitimate. See United States v. Orta-Rosario, 469 Fed.Appx. 140, 144 (4th Cir. 2012) (in affirming convictions of doctor and employee of online prescription service, noting factors relevant to guilt, including “permitting non-medical personnel to write prescriptions with pre-signed bland prescription forms”); United States v. Mahar, 801 F.2d 1477, 1487 (6th Cir.1986) (“[T]hat patients were regularly sold controlled substances ... selected by non-physician lay employees of the Clinic would further support a finding that controlled substances were issued outside the usual course of medical practice and for no legitimate medical purpose.”).

Apart from evidence of Boccone’s involvement in the individual prescriptions underlying the distribution charges, the government also introduced evidence that Boccone influenced the entire course of treatment of each patient, both in the way he managed his office and in his interactions with individual patients. For example, Dao testified that at one point he was arrested at Chantilly Specialists for prescription fraud, and he was unable to take his prescription with him at the time of arrest. After spending 78 days in jail, he returned to Chantilly Specialists to pick up his prescription, and he was provided his prescription without seeing any medical practitioner, in the presence of Boccone, Boccone’s wife, and another individual. (JA 391). Honesty agreed with Brown and Boccone to return 80 mg OxyContin pills to Boccone and Brown. (JA 336-337). And, as noted above, Boccone set the level of medication for Rogers that lasted from 2009 to his death in 2010. (JA 1715-1717).

In addition to evidence of Boccone’s involvement in medical decisions, the government introduced further evidence that the entire course of treatment of patients Dao, Honesty, and Rogers, was illegitimate and outside the usual course of medical practice. This evidence took the form of indicia or red flags of diversion, addiction, and abuse, as highlighted in the report and testimony of Dr. Hamill-Ruth.

In particular, Dao received prescriptions for large volumes of pain medication, continuing without change over an extended period of time, without referrals for alternative treatment or therapy for “underlying medical issues that are very concerning.” (JA 549, 3833). Diagnostic tests were insufficient “to support the diagnosis of intractable pain,” and provided “no good indication to be prescribing this man chronic opiates as far as their documentation is concerned.” (JA 549). Additional red flags included multiple early refills, multiple calls, sporadic visits, and drug screens, all as indicia that prescriptions are fueling a drug addiction. (JA 550-551). A pharmacy called in 2010 to report early refill requests, an incident in which Dao was with another person who attempted to pay with counterfeit money, and Dao’s provision of medication to another person. (JA 2710, 3833). On March 23, 2011, Dao pleaded guilty to prescription fraud based on prescriptions received from Chantilly Specialists. (JA 2659). Dao met with Brown for two appointments after returning from jail following his arrest for prescription fraud. (JA 389, 391, 2700-2705). As noted above, Dao picked up prescriptions that had been filled on the day of his arrest, without any medical examination. (JA 390-391). Dao received prescriptions despite having drug screens on several occasions that were positive for use of cocaine and/or negative for proscribed medications (JA 386, 3205, 3834).

Honesty testified that he never received any physical examination while being seen at Chantilly Specialists. (JA 330). According to Dr. Hamill-Ruth, “there was no good indication in the record for prescribing him significant medication doses,” and “no outside documentation at the initial visit.” (JA 547). Boccone and Brown increased Honesty’s prescriptions over time, up to around 680 to 700 narcotic pain pills per month. (JA 335, 338). Three times when he attempted to take the medications as written in his prescriptions, he overdosed, and he informed Boccone and Brown of the overdoses. (JA 338-339). Further red flags included loss of medications; lack of documentation of injuries and outside medical visits; lack of documentation of prescriptions from other providers; escalating aberrant behavior including threats prompting referrals to psychiatry for “substance abuse, bipolar” disorders; lack of evidence of compliance with referrals; and drug tests negative for prescribed medications. (JA 1990-1991, 2152, 3834-3836). In sum, Dr. Hamill-Ruth opined “his behavior really was very significant for abuse, and it was unconscionable to continue to support his addiction problem without sending him for appropriate referral.” (JA 548).

Indicia of addiction and abuse as to Rogers included that he drove a long distance from Tennessee to receive prescriptions, he was treated with pain medication over an extended period from 2007 to his death in 2010, and additions and adjustments were made without any rationale noted. (JA 3827). Additional red flags include frequent phone calls, requests for early refills, self-escalation of dosing, inconsistencies in reporting thefts, issues with receipt of medication, and needing prescriptions overnighted to his home in Tennessee, positive drug screens and an absence of documentation as to pharmacies used. (JA 3828-3829). Further, Dr. Hamill-Ruth opined that it was inappropriate and “flagrantly dangerous” to prescribe Rogers the combinations of medications he received without adequate documentation. (JA 537). As for the prescriptions issued by Brown days before Rogers’s death, Dr. Hamill-Ruth noted that prescriptions issued for “excessive doses of multiple medications” raise “significant concerns” in light of Rogers’s affliction with pneumonia. (JA 540-541).

Considering all of the above, including the evidence of Boccone’s involvement, in conjunction with indicia of diversion, addiction, and abuse, in the medical record of these patients, the evidence was sufficient for the jury to conclude that Brown knew or had reason to know that prescriptions he issued were for an illegitimate purpose or were not within the scope of usual medical practice.

Brown raises several additional challenges as to the evidence supporting the distribution counts of conviction, which we find unavailing. First, following on his earlier argument regarding the legal standard, Brown suggests that expert testimony by Dr. Hamill-Ruth was not sufficient to convict him because it addressed only a physician’s standard of practice and did not address whether his own treatment fell below the standard of a nurse practitioner. As discussed above, we disagree that the standard of practice for a nurse practitioner differs from that of a physician. Moreover, as to sufficiency of her report and testimony, Dr. Hamill-Ruth did not limit her opinion to the standard of practice for physicians, to the exclusion of other licensed practitioners such as nurse practitioners. Indeed, she testified as to “the practice ... in the field of pain management,” and guidelines that “medical providers who practice in the field of pain management can rely on[.]” (JA 526) (emphasis added). She specifically noted that nurse practitioners, as well as physicians, are authorized to prescribe controlled substances in Virginia. (JA 530). Accordingly, we reject Brown’s contention that Dr. Hamill-Ruth’s testimony was insufficient to prove that Brown’s conduct fell below the standard of medical practice.

Brown next contends that his treatment of patients underlying the charged offenses, including Dao, was in good faith because these patients had legitimate medical problems. The existence of legitimate medical problems, however, does not compel a finding that a practitioner prescribed medications in good faith. Indeed, in Singh, the court upheld convictions of a physician for unlawful distribution of controlled substances, even though patients to which medications were prescribed had numerous physical ailments. For example, one patient was diagnosed with “lumbar disc problems and seizures.” Singh, 54 F.3d at 1188. Based on the opinion of an expert witness, the court noted that continued prescriptions of addictive drugs to this patient, in light of indicia of alcohol abuse and recommendations from a psychological evaluation, was “outside the scope of a legitimate medical practice.” Id.

In this case, as in Singh, patients presented with medical problems, including that Rogers had history of a gunshot wound, (JA 3827), Dao suffered from “aching low back pain, intermittent left L5 radiculitis and tension related neck pain,” (JA 3833), and Honesty had hypertension, sleep apnea, asthma, and carpel tunnel syndrome. (JA 3834). Nevertheless, the presence of such legitimate medical problems in many respects supported, rather than undermined, a determination that prescriptions were issued outside the scope of medical practice.

To this end, Dr. Hamill-Ruth identified a disconnect between the problems presented and the course of treatment. For Rogers, she noted a lack of documentation regarding the nature of injuries, and she noted “significant concerns” with prescribing medication to Rogers, in light of his pneumonia. (JA 541, 3827). For Dao, despite many ailments, Dr. Hamill-Ruth noted that he was “not put on an NSAID, sent for PT, or offered interventional pain management, any or all of which could have helped more effectively manage his pain.” (JA 3833). Similarly, for Honesty, “an inadequate exam is documented, and it does not support chronic intractable pain,” and “no exam or other data” is in the record to support some diagnoses. (JA 3834-35). Accordingly, the manner in which legitimate medical problems are addressed, rather than the existence of the problems in the first place, is most probative to whether prescriptions are issued within the usual scope of medical practice. (See JA 527).

Finally, Brown argues that he acted in good faith because supervising doctors and the Virginia Board of Medicine never stated his treatment of any patient was improper. As discussed above, however, the level of supervision Brown received is one factor among many bearing on the issue of whether Brown knew that prescriptions were issued outside the scope of legitimate medical practice. While Brown contends that supervising physicians and the Board never criticized his treatment of any patient, Brown also points to no evidence that they approved specific prescriptions underlying the charged offenses.

The practice agreement between Brown and Dr. Currier does not set forth parameters of supervision or approval of specific prescriptions, nor does it restrict Brown’s prescriptive authority beyond specifying the types of drugs which Brown may prescribe. Rather, it is a form check-box agreement, which states simply that Brown is “authorized by this practice agreement” to prescribe multiple categories of Schedule II drugs. (JA 3763). A jury reasonably could infer based on this practice agreement that Brown maintained responsibility to discern that a given prescription was legitimate or issued in the course of medical practice.

Moreover, Dr. Currier, who was supervising physician during the time of the charged prescriptions, testified that she did not authorize Brown to prescribe medications in the presence of red flags such as inconsistent drug tests, lack of treatment records, and noncompliant or aberrant behavior. (JA 308). She also testified that she was not sufficiently present and informed of clinical information, nor sufficiently involved in treatment decisions, to provide adequate oversight of individual patient treatment. (See JA 264-265, 309).

In addressing this evidence on appeal, Brown draws inferences in favor of the defense rather than the government. For example, Brown opines that “[g]iven [their] practice agreement, the fact that Dr. Currier did not expressly authorize Mr. Brown’s actions — which is all the transcript shows — was tantamount to approval of Mr. Brown’s prescribing practices.” (Brown Reply Br. at 6). Similarly, Brown suggests that the jury was required to infer from Brown’s lack of training and supervision that Brown believed in good faith that the prescriptions he issued were legitimate. But, a contrary inference is also reasonable. In particular, the jury reasonably could infer that, in the absence of adequate supervision and oversight from Dr. Currier, Brown chose to follow directions of Boccone in making the charged prescriptions, including prescribing a high volume of medications for as long as patients were willing to receive them, all with knowledge of or deliberate blindness to the fact that the prescriptions were without grounding in legitimate medical practice.

In sum, substantial evidence supported Brown’s convictions for distribution of controlled substances.

b.

Turning next to Boccone’s convictions for distribution of controlled substances, we conclude that the evidence amply supported the conclusion that Boccone knowingly distributed oxycodone to six patients by entering directions for prescriptions in each patient’s medical file on the dates of the charged distribution.

In particular, as we have already noted, the jury reasonably could infer that Boc-cone directed the charged prescriptions for other patients Dao, Rogers, and Honesty. In a similar manner, the evidence demonstrated that Boccone directed the prescriptions for patients Diane Gisin, Linda Mum-ma, and Bryan Anderson (Counts Three, Four and Five). Specifically, on April 16, 2009, Boccone entered direction in Gisiris medical file stating “[mjaintain current regiment [sic],” and physician’s assistant Joe Frazier signed prescriptions including Roxicodone 30 mg and other opiate drugs. (JA 2576, 2534). In a medical record entry on February 5, 2009, Boccone directed maintenance of an opiate regimen and added prescriptions for Mumma. (JA 3581-3582). Finally, in a medical record entry on August 17, 2009, Boccone entered a detailed treatment note including diagnosis for Anderson, and directed four days of medication, including 80 milligram Oxy-Contin pills. (JA 3933).

This evidence is sufficient to permit the jury to infer that Boccone conducted the patient visits or directed prescriptions for each patient on the date charged, thus causing, as a non-licensed individual, distribution of controlled substances. See 21 U.S.C. § 841(a)(1); 18 U.S.C. § 2; see also United States v. Johnson, 831 F.2d 124, 128 (6th Cir.1987) (“[T]he sale by a non-practitioner of bogus prescriptions which are in fact used to obtain controlled substances is tantamount to the distribution of the substances themselves and hence, is properly punishable as unlawful distribution of drugs in violation of section 841(a)(1).”).

Further, although additional evidence was not required, Boccone’s convictions were also supported by evidence set forth above demonstrating that treatment of patients Dao, Rogers, and Honesty, in concert with Brown, was outside the scope of legitimate medical practice due to indicia of abuse, addiction, and diversion. In addition, with respect to Gisin, Dr. Hamill-Ruth opined that “[prescribing for this patient was substandard,” due to inadequate documentation and evaluations rendering prescriptions outside the bounds of usual medical care. (JA 3838). Mumma also testified that in one instance Boccone attempted to treat her for very high blood pressure by bringing in during an appointment a “blister pack of medication” and directing her to take one. (JA 453). When she refused, he called her cardiologist and introduced himself as “Dr. Paul Boccone.” (JA 454).

We have considered Boccone’s arguments challenging his convictions for the distribution counts and find them unavailing. While Boccone focuses on the lack of evidence that he personally signed prescriptions for any of the charged patients, such arguments do not take into account that Boccone’s culpability rests on his conduct in directing or causing the charged prescriptions, which, on the basis set forth above, is supported by substantial evidence. His suggestion that medical providers, and not Boccone, entered the directions in the medical notes as cited above, rests upon drawing inferences from circumstantial evidence in favor of the defense rather than the government. Where Boccone’s name is designated in a timed medical entry in the record, the jury reasonably may infer that he conducted the medical visit, or participated in it, and then entered the text of the entry. Further, Boccone’s contention that other providers entered notes using his name is belied by the fact that those same medical providers entered their own notes in the medical record using their own names. (See, e.g., JA 1715-1717). Finally, Boccone’s contentions that treatment of the patients in the charged offenses was in fact legitimate fail for the same reasons we have rejected Brown’s challenges to the convictions.

In sum, we conclude the evidence was sufficient to support Boccone’s unlawful distribution convictions.

2.

We turn next to appellants’ convictions for conspiracy to distribute controlled substances.

The drug conspiracy statute provides that “[a]ny person who attempts or conspires to commit any offense defined in this subchapter shall be subject to the same penalties as those prescribed for the offense, the commission of which was the object of the attempt or conspiracy.” 21 U.S.C. § 846. To convict a defendant of conspiracy under this statute, the government must establish three essential elements: (1) an agreement to unlawfully distribute controlled substances existed between two or more persons; (2) defendants knew of the conspiracy; and (3) defendants knowingly and voluntarily became a part of this conspiracy. See Bur-gos, 94 F.3d at 857.

“[I]t is not necessary to prove a formal agreement to establish a conspiracy in violation of federal law; a tacit or mutual understanding among or between the parties will suffice.” McIver, 470 F.3d at 563 (quotation omitted). In addition, “[t]he Government is not required to prove that a defendant knew all his co-conspirators or all of the details of the conspiracy.” United States v. Green, 599 F.3d 360, 367 (4th Cir.2010). In the context of unlawful distribution of prescription drugs, conspiracy may be established where the defendant “tacitly agreed with his patients to provide opioid prescriptions without legitimate medical reasons for doing so.” 470 F.3d at 563. “The government can satisfy the knowledge requirement by showing either that Appellant actually knew of the conspiracy, or that he was willfully blind to it by purposely closing his eyes to avoid knowing what was taking place around him.” Id. (internal quotations omitted).

Much of the same evidence supporting the individual distribution convictions also supports the conspiracy conviction in this case. For example, the treatment' of Dao, Rogers, and Honesty, as detailed above, provides sufficient evidence of a conspiracy to unlawfully distribute oxycodone, in light of Boccone’s involvement in treatment decisions, in conjunction with red flags showing that their treatment was outside the scope of medical practice. In addition, the government’s evidence demonstrated a conspiracy extending in scope to treatment of other patients, such as Justin McConnell, whose treatment at the hands of Boccone and Brown was similarly outside the scope of medical practice. From this evidence, a jury reasonably could conclude that appellants agreed with each other and their patients to unlawfully distribute controlled substances, and each knew of the conspiracy or was “purposefully closing his eyes to avoid knowing what was taking place around him.” McIver, 470 F.3d at 563.

Moreover, the government introduced further circumstantial evidence that appellants entered into an agreement to distribute prescriptions outside of medical practice. Such evidence includes time limits placed on examinations by Boccone, scarcity of physical exams, perfunctory visits for prescription refills for' large amounts of drugs, Boccone’s presence in examination rooms during patient exams conducted by Brown and other practitioners, close interaction between Boccone and Brown in the office, Boecone’s processing of prescriptions and forgery of signatures on prescriptions, Boccone’s reference to himself as “doctor,” Brown’s conduct in signing prescriptions filled out by Boccone or prescriptions in stacks while in exams with other patients, and patients’ provision of gifts and services to Boccone and Brown. (JA 128-29, 132-136, 138-39, 142-43, 165, 176, 187-88, 223-25, 257, 365, 368, 412-13).

In sum, considering together the treatment of individual patients with evidence regarding the nature of the practice and defendants’ role in the practice, sufficient evidence supported the conspiracy convictions in this case.

3.

Boccone contends the evidence was insufficient to convict him of health care fraud. The government charged Boccone with violation of 18 U.S.C. § 1347, on the basis that he submitted a claim to Medicare on November 3, 2009, knowing that licensed medical provider had not performed services, particularly in treatment of Dianne Gisin, on April 16, 2009.

The health care fraud statute provides that it is unlawful to “knowingly and willfully execute[ ] ... a scheme or artifice (1) to defraud any health care benefit program; or (2) to obtain by means of false or fraudulent pretenses, representations, or promises, any of the money ... [of] any health benefit program, in connection with the delivery of or payment for health care benefits, items, or services....” 18 U.S.C. § 1347(a). The statute may be violated by a person who obtains reimbursement from Medicare by means of false or fraudulent statements on insurance claims. See McLean, 715 F.3d at 140. “[T]he specific intent to defraud may be inferred from the totality of the circumstances and need not be proven by direct evidence.” Id. at 138.

The government introduced evidence that the person who provided medical services for Gisin on April 16, 2009 was Boccone, (JA 2576), whereas the provider billed to Medicare was physician’s assistant Joe Frazier. (JA 3781-82). Considered in conjunction with Gisin’s testimony that Boccone treated her, this was sufficient for the jury to infer that solely Boccone saw Gisin on that date and Frazier did not provide any medical services. Because Boccone caused claims to be submitted to Medicare falsely representing the provider who performed services on the date charged, Boccone’s health care fraud conviction is supported by substantial evidence.

Boccone argues that Medicare allows submission of a bill for a visit with a member of a medical provider’s staff, noting for example that Medicare billing code 99211 provides for an office visit “not requiring] the presence of a physician,” where “[u]sually, the presenting problem^) are minimal.” (Boccone Br. at 51-52). Notably, however, the billing code submitted to Medicare in this case was 99215, not 99211. (JA 3781). In contrast to code 99211, code 99215 is reserved for office visits requiring either a “comprehensive examination” or “[m]edical decision making of a high complexity,” where “the presenting problem(s) are of moderate to high severity,” typically requiring 40 minutes spent face-to-face with the patient. See American Medical Assoc., Current Procedural Terminology (CPT), 10 (2009 Standard Ed.). Here the evidence suggests the opposite — that no legitimate medical decisions were made on April 16, 2009, much less decisions of high complexity or following a comprehensive examination. This further supports a determination that the bill which Boccone submitted in this case included false and misleading information regarding the nature of the provider and the services performed.

In sum, Boccone’s health care fraud conviction was supported by substantial evidence.

4.

Boccone argues that the evidence was insufficient to support his convictions for failure to pay over employment taxes.

Under 26 U.S.C. § 7202,
Any person required under this title to collect, account for, and pay over any tax imposed by this title who willfully fails to collect or truthfully account for and pay over such tax, shall, in addition to other penalties provided by law, be guilty of a felony and, upon conviction thereof, shall be fined not more than $10,000, or imprisoned not more than 5 years, or both, together with the costs of prosecution.

To secure a conviction under this statute for failure to pay employment taxes, the government must prove that (1) defendant has a duty to withhold and pay over employment taxes for the employer, and (2) defendant willfully failed to perform one of these tax-related duties. See United States v. Lord, 404 Fed.Appx. 778, 775 (4th Cir.2010); United States v. Gilbert, 266 F.3d 1180, 1185 (9th Cir.2001).

Here, the government introduced substantial evidence to satisfy both elements of the offense. Concerning Boccone’s duties, Boccone admitted to a government special agent that he was responsible for withholding employment taxes from his employees and for paying over such withholdings to the Internal Revenue Service. (JA 478). He also had prior experience with filing payroll tax forms and remitting employment taxes with his former company, Berwyn Mortgage. (JA 3958-3968). Concerning Boccone’s failure to pay, Boccone admitted at trial that he was aware of the obligation to pay employment taxes withheld, and there was no dispute that Boccone failed to pay the taxes due. (JA 623, 759).

Boccone suggests, nonetheless, that his failure to pay was not willful because there was no money available to pay them when due. Contrary to Boccone’s suggestion, the government introduced evidence that Chantilly Specialists had sufficient funds to satisfy the tax obligations or there would have been sufficient funds had other expenditures not been paid. (JA 4006-4336). “The intentional preference of other creditors over the United States is sufficient to establish the element of willfulness.” Turpin v. United States, 970 F.2d 1344, 1347 (4th Cir.1992) (internal quotations omitted). Even if other expenditures were necessary for operation of the business, this does not undermine a finding of willfulness. Indeed, “paying wages and ... satisfying debts to creditors in lieu of remitting employment taxes to the IRS, constitute circumstantial evidence of a voluntary and deliberate violation of § 7202.” Lord, 404 Fed.Appx. at 779.

In sum, the government introduced substantial evidence to support the tax law convictions.

C.

Boccone argues that the prosecutor improperly commented on his veracity during closing argument. Boccone did not object to the prosecutor’s closing argument at trial. Accordingly our analysis is “confined to plain error review.” United States v. Woods, 710 F.3d 195, 202 (4th Cir.2013). “Under this standard, [appellant] must show not only that the district court committed an error that was plain, but also that the error affected [appellant’s] substantial rights thereby impacting the outcome of his trial.” Id. (internal quotations omitted).

The prosecutor’s argument arose out of testimony by Boccone at trial regarding his provision of a handwriting exemplar during the investigation of the case. In relevant part, Boccone testified as follows on re-direct examination:

Q. Did you go in voluntarily on your own to give [Special Agent Walker] handwriting exemplars ?
A. Yes, I did.
Q. Have you gotten any results?
A. No.

(JA 659-60) (emphasis added). During defense counsel’s closing argument, counsel reminded the jury of this testimony, stating as follows:

Mr. Boccone took the stand. Told you that he went voluntarily on his own to Special Agent Walker, and then for two to three hours give them handwriting samples. Apparently they were thinking he forged prescriptions. Now think about it.... Who wakes up and walks off to the police station to give a handwriting sample if they know that they’ve been forging prescriptions? He goes in there to give a handwriting sample.

(JA 781) (emphasis added).

After this argument concluded, the government asked to correct the record in rebuttal to reflect that the handwriting exemplar in fact “was done pursuant to a grand jury subpoena.” (JA 792). Counsel for Boccone thereupon requested an opportunity to clarify himself “in respect to the handwriting exemplar, it was pursuant to a grand jury subpoena,” which request the court allowed. (Id.). At that point, counsel for Boccone concluded his argument by stating to the jury: “[W]ith respect to the handwriting exemplars, the grand jury issued a subpoena for Mr. Boc-cone to give his handwriting exemplars, and he went and gave the handwriting exemplars pursuant to the grand jury subpoena to Special Agent Walker. ” (JA 793) (emphasis added).

Subsequently, upon rebuttal, the prosecution stated as follows to the jury:

Ladies and gentlemen, we now know that Paul Boccone gave a handwriting exemplar pursuant to a grand jury subpoena when he told you during his sworn testimony that it was voluntarily. What else in Paul Boccone’s testimony under oath is false, ladies and gentlemen?

(JA 811).

Boccone suggests that this argument was improper because (1) Boccone in fact testified truthfully that he voluntarily gave a handwriting exemplar, and (2) the prosecutor’s statement constitutes an improper expression by the prosecutor as to the veracity of a defense witness.

With respect to the first challenged statement by the prosecutor, there was no impropriety in reminding the jury that Boccone gave the exemplar “pursuant to a grand jury subpoena” whereas in his testimony he stated that “it was voluntarily.” (JA 811). This is consistent with the correction made by Boccone’s own counsel. (JA 793). It is also consistent with the evidence. In particular, Boccone gave the exemplar after the investigating attorney informed Boccone’s counsel that the grand jury had issued a subpoena for the defendant’s handwriting. (JA 988). Boccone was in fact served with the subpoena. (JA 940). While Boccone points out on appeal that the subpoena was not served on Boccone until he arrived at the police station, it is nonetheless accurate to state that the exemplar was given “pursuant to a grand jury subpoena.” (JA 811). Accordingly, the first challenged statement in the prosecutor’s argument was not improper.

The second challenged statement in the prosecutor’s argument, by contrast, may have exceeded the bounds of fair advocacy. This court has “recognized that it is highly improper for the government to refer to a defense witness as a liar.” United States v. Moore, 11 F.3d 475, 481 (4th Cir.1993); see, e.g., Woods, 710 F.3d at 202 (prosecutor improperly stated that defendant “lied ... under oath when he testified this morning”). Although the prosecutor did not expressly call the defendant a “liar,” the prosecutor’s argument clearly communicated to the jury the prosecutor’s view that defendant lied under oath.

We need not decide, however, whether the prosecutor’s argument constituted error. Even assuming that it did, and the error was plain, we conclude the error did not affect Boccone’s “substantial rights.” Id. “When the evidence of guilt is overwhelming and a perfect trial would reach the same result, a substantial right is not affected” by a particular error. Id. (internal quotations omitted). In undertaking this analysis, we have considered the following well-established factors:

(1) the degree to which the prosecutor’s remarks have a tendency to mislead the jury and to prejudice the accused; (2) whether the remarks were isolated or extensive; (3) absent the remarks, the strength of competent proof introduced to establish the guilt of the accused; and (4) whether the comments were deliberately placed before the jury to divert attention to extraneous matters.

Id. (quotations omitted).

Here, accepting that the challenged argument by the prosecution had a tendency to mislead the jury and prejudice Boccone, the remarks nonetheless were made in conjunction with an express correction by Boccone’s own counsel regarding Boc-cone’s testimony. Thus, even if the prosecution had not made the challenged argument, the jury had an independent basis to question whether Boccone had been fully truthful in his testimony. In addition, while the remarks came at a prominent point at the culmination of the closing argument, they were brief relative to the length of the argument as a whole.

Further, the government’s evidence against Boccone was overwhelming and was supported by multiple categories of evidence, each independently supporting the convictions, including medical records demonstrating Boccone’s involvement in treatment of patients and the nature of the prescriptions he directed, testimony from patients, and testimony and records regarding Boccone’s office practices. Even assuming that Boccone had not forged prescriptions, sufficient evidence demonstrated that Boccone conspired to and directed distribution of controlled substances outside the bounds of medical practice.

Finally, in light of the correction by defense counsel, there is no indication that the comments were deliberately placed before the jury to divert attention from the evidence in this case.

In sum, although part of the challenged prosecution argument may have been improper, any error resulting therefrom does not warrant reversal of Boccone’s conviction.

D.

Boccone and Brown challenge the district court’s sentencing determination. We address first their contention that the district court failed to adequately explain the sentence given.

“We review a sentence for abuse of discretion.” United States v. Bell, 667 F.3d 431, 440 (4th Cir.2011). As part of this review, we must

“ensur[e] that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence — including an explanation for any deviation from the Guidelines range.”

United States v. Lynn, 592 F.3d 572, 575 (4th Cir.2010) (quoting Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)).

With respect to the explanation provided by the district court, “[rjegardless of whether the district court imposes an above, below, or within-Guidelines sentence, it must place on the record an individualized assessment based on the particular facts of the case before it.” Bell, 667 F.3d at 442 (quotations omitted). “The explanation must be sufficient to allow for meaningful appellate review, such that the appellate court need not guess at the district court’s rationale.” Id. (internal quotations omitted). This court previously has observed that “[w]ithout an affirmative showing the information [in the presen-tence report] is inaccurate, the court is free to adopt the findings of the [presen-tence report] without more specific inquiry or explanation.” United States v. Terry, 916 F.2d 157, 162 (4th Cir.1990) (internal quotations omitted).

In setting forth the reasons for the sentence in this case, the district court stated as follows with respect to Boccone:

All right. Well, Mr. Boccone, I find the guideline factors in this case to be properly assessed at a range of 360 months to life. That because of your financial condition, the imposition of any fine or cost is not warranted. But considering your age and prior record and the nature of this offense, I find that a sentence somewhat below the guideline range would be appropriate. It will be the sentence of the Court that as to Counts, 1 to 5, 7, and 9, you be committed to the custody of the Attorney General to serve a term of 180 months....

(JA 1124). The court imposed lesser concurrent terms of imprisonment for the remaining counts of conviction. For Brown, the district court stated only:

All right. Well, I find the guideline factors in this case to be properly assessed at a range of 188 to 235 months. I also find because of your financial condition, Mr. Brown, that the imposition of any fine or cost is not warranted. And in considering the factors under Section 3553, which I must, considering your— the facts of this case and the extent of your involvement, I find that a sentence below the low end of the guideline range would be appropriate. It will be the sentence of the Court, as to Counts, 1, 2, 7, and 9, you be committed to the custody of the Attorney General to serve a term of 60 months....

(JA 1103-04).

The district court’s explanation for the sentence was lacking in several respects. In particular, the district court failed to explain adequately the application of each of the statutory sentencing factors, and to provide “an ‘individualized assessment’ based on the particular facts of the case before it” of the basis for the substantial downward variance imposed. Bell, 667 F.3d at 442. The district court’s cursory reference to statutory factors, with mention of “age and prior record and the nature of this offense” for Boccone, and “the facts of this case and the extent of ... involvement” for Brown, (JA 1103, 1124), does not explain how these factors for each defendant apply to warrant a downward variance, leaving us to “guess at the district court’s rationale.” Bell, 667 F.3d at 442.

In addition, while we can glean from the court’s explanation that the district court adopted in toto the findings and conclusions in the presentence report, the district court’s failure to explain why it did so is procedurally unreasonable. The district court did not discuss the objections and arguments raised by appellants prior to and during the sentencing hearing, including their specific contentions that the drug quantity calculations and corresponding offense level determinations contained in the presentence reports were not correct, and Boccone’s objection to application of a sentencing enhancement. (See JA 1057, 1096, 1117, 4434, 4384).

This court has not previously decided how much “more specific inquiry or explanation” is required, as suggested by Terry, 916 F.2d at 162, when a district court adopts findings in a presentence report over objections and arguments by a defendant. See United States v. Montes-Pineda, 445 F.3d 375, 380 (4th Cir.2006) (“[A] district court’s explanation should provide some indication ... that the court considered ... the potentially meritorious arguments raised by both parties about sentencing.”). We need not decide this question here, however. As set forth below, assuming the district court did not sufficiently explain the sentence imposed, this error is harmless under the circumstances of this case.

“[Procedural errors at sentencing are routinely subject to harmlessness review.” Lynn, 592 F.3d at 576 (quotations omitted). When the court commits a procedural error in failing to explain a sentence given, the government may avoid reversal if the error “did not have a substantial and injurious effect or influence on the” result and the court can “say with ... fair assurance that the district court’s explicit consideration of [the defendant’s] arguments would not have affected the sentence imposed.” Id. at 585 (quotations and citations omitted).

In applying this harmless error review, we find persuasive the court’s treatment of a procedural error in United States v. Cox, 460 Fed.Appx. 248, 250 (4th Cir.2012). There, the court reasoned:

In this case, the district court erred by providing no explanation for the length of the active prison term it imposed upon Cox. We conclude, however, that the Government met its burden to show that this error was harmless. Because Cox received a substantial downward variance, we conclude the district court’s inadequate explanation ‘did not have a substantial and injurious effect or influence on the result’ of the sentencing proceeding. Furthermore, Cox’s arguments in support of a 120-month sentence were without legal merit, allowing us to conclude with ‘fair assurance that the district court’s explicit consideration of those arguments would not have affected the sentence imposed.’

Id. (quoting Lynn, 592 F.3d at 585).

In this case, as in Cox, because appellants received significant downward variances, the district court’s failure to adequately explain application of the sentencing factors “did not have a substantial and injurious effect or influence on the result” of the sentencing proceeding. Lynn, 592 F.3d at 585 (internal quotations omitted). In addition, the district court’s failure to set forth reasons for adopting the guidelines range set forth in the presentence report, including failure to address appellants’ arguments as to the calculation of the guidelines range, was harmless because these arguments are without merit, as we set forth below. As such, we may conclude with “fair assurance that the district court’s explicit consideration of those arguments would not have affected the sentence imposed.” Lynn, 592 F.3d at 585 (internal quotations omitted).

Accordingly, we turn next to address appellants’ arguments as to the guidelines range calculation.

1.

Appellants first argue, as they did before the district court, that the court incorrectly calculated the drug quantity used to determine their base offense level under the sentencing guidelines.

We review “the district court’s calculation of the quantity of drugs attributable to a defendant for sentencing purposes for clear error.” United States v. Slade, 631 F.3d 185, 188 (4th Cir.2011). In other words, the court must be “left with the definite and firm conviction that a mistake has been committed.” United States v. Stevenson, 396 F.3d 538, 542 (4th Cir.2005).

“The Government must prove by a preponderance of the evidence the amount of controlled substances attributable to a defendant.” United States v. Carter, 300 F.3d 415, 425 (4th Cir.2002). In calculating drug quantity, “a sentencing court may give weight to any relevant information before it, including uncorroborated hearsay, provided that the information has sufficient indicia of reliability to support its accuracy.” United States v. Crawford, 734 F.3d 339, 342 (4th Cir.2013) (quoting Unit ed States v. Wilkinson, 590 F.3d 259, 269 (4th Cir.2010)).

In the context of a drug conspiracy, a “defendant is responsible not only for his own acts, but also for ‘all reasonably foreseeable acts’ of his co-conspirators in furtherance of the joint criminal activity.” Slade, 631 F.3d at 188. A defendant is “accountable for all quantities of contraband with which he was directly involved and all reasonably foreseeable quantities of contraband that were within the scope of the criminal activity that he jointly undertook.” Bell, 667 F.3d at 441 (quoting U.S.S.G. § 1B1.3 cmt. n. 2).

According to the presentence report adopted by the district court, Brown was responsible for the equivalent of 12,453 kilograms of marijuana, based upon 100% of the prescription amount provided to patients Honesty, Dao, Rogers, and McConnell after he commenced work at Chantilly Specialists in July, 2009. (JA 4438). Boc-cone was responsible for the equivalent of 18,155 kilograms of marijuana, representing the medications prescribed to Honesty, Dao, and Rogers for the entirety of their care, under the direction of Boccone. Where these drug weights exceeded an equivalent of 10,000 kilograms of marijuana, both Boccone and Brown were subjected to a base offense level of 36. See U.S.S.G. § 2D1.1.

The evidence presented by the government at trial was sufficient to establish that Boccone and Brown conspired to unlawfully distribute controlled substances to Honesty, Dao, and Rogers, outside the bounds of medical practice and not for a legitimate medical purpose during the time that they were involved with treatment of these patients. Whether or not Boccone or Brown individually saw these patients during each visit to Chantilly Specialists is not dispositive of the drug quantity calculation where they each knew, or reasonably should have known, that the entire course of treatment was beyond the scope of legitimate medical practice. See McIver, 470 F.3d at 563. The illegitimacy of the entire course of treatment is supported not only by the report and testimony by Dr. Hamill-Ruth, but also by Boccone’s role in directing the treatment as a non-medical professional.

In addition, although McConnell’s treatment was not addressed in the report of Dr. Hamill-Ruth, the government offered sufficient evidence at trial that Brown treated McConnell outside the scope of legitimate medical practice, in disregarding many of the same indicia of abuse and diversion present with Honesty, Dao, and Rogers. For example, McConnell did not provide prior treatment records upon beginning treatment at Chantilly (JA 184), Brown treated McConnell without ever having given him a physical exam (JA 189), and his prescriptions increased significantly over time leading to an addiction. (JA 190, 193). In addition, Brown made untoward physical contact and personal calls to McConnell that impacted the treating relationship. (JA 192-93). Boccone also was involved in directing prescriptions. (JA 197-98). The presentence report noted all these facts, in addition to others obtained based upon an investigative interview report, regarding adjustments made by Brown in prescriptions and Brown’s promise to keep prescribing him 30 milligram oxycodone pills. (JA 4410).

In sum, the drug weight calculation by the district court properly was supported by an aggregation of quantities of controlled substances distributed to Honesty, Dao, Rogers, and McConnell, where treatment of these patients was outside the scope of legitimate medical practice.

Appellants argue on appeal that the district court’s drug calculations were erroneous because the court did not follow the calculation methods set forth by the Fourth Circuit in Bell. There, defendants pleaded guilty to offenses including conspiracy to possess with intent to distribute oxycodone, which they obtained through prescriptions while patients at a pain management center. Bell, 667 F.3d at 434 & 435. This court held that the district court did not adequately explain the basis for the sentence, particularly drug quantity, where the district court based drug quantity on the amount of prescriptions received by each patient. Id. at 439-441. The court noted that, generally, “[w]here there is no evidence that any of the drugs obtained by members of a conspiracy were obtained or possessed legally, all reasonably foreseeable quantities possessed ... may be considered ‘relevant conduct’ attributable to that defendant.” Id. at 442. But, in “a case involving a valid prescription, ” the court noted,

if ... the government wishes to use the total quantity prescribed to one or more conspiracy members as evidence of the quantity of ‘contraband ... within the scope of the [conspiracy],’ it must also provide evidence, and the district court must make a finding, of something more — for example ... that the conspiracy actually distributed a particular amount[,] [or] that the person who was prescribed the drug lawfully kept and consumed only a portion (or none) of the prescribed amount....”

Id. at 443 (quoting U.S.S.G. § 1B1.3 cmt. n. 2). Appellants contend the district court erred by failing to make any such findings in this case. We disagree.

Bell is inapposite for several reasons. First, in Bell, “there [was] no dispute that [defendant] received her pills using a valid prescription issued to her by physicians at a single institution.” Id. at 444 (emphasis added). Just the opposite was true in the present case, where the government introduced evidence demonstrating that the prescriptions issued to Dao, Honesty, Rogers, and McConnell were not valid prescriptions. While appellants contend that these patients made use of some or most of their prescriptions to provide relief for their medical conditions, this fact does not transform an otherwise unlawful prescription issued outside the scope of medical practice into a valid one.

Second, the defendants in Bell pleaded guilty on the basis that they, as patients, distributed oxycodone that they had already received from a pain management center. By contrast, appellants here were convicted of issuing prescriptions outside the scope of medical practice. Whether patients in Bell actually ingested the medication could be determinative to whether they in fact distributed the medication to others. See id. at 443. Here, by contrast, whether the patients actually consumed the prescription drugs in question is not itself determinative of whether the prescriptions were made outside the scope of medical practice. Indeed, evidence that the patients in this case ingested excessive quantities of pain medication over an extended time period was itself an indicia of addiction further demonstrating illegitimacy of the prescriptions.

Finally, unlike in Bell, the district court in this case adopted the guidelines range in the presentenee report that was based on a detailed drug quantity calculation as set forth in the presentence report. In contrast, the district court in Bell picked a round number below that calculated in the presentence report, without offering any specific explanation for why that number was chosen. Id. at 444. Accordingly, the presentence report in Bell provided no basis, as it did in this case, for the drug quantity calculation by the district court.

Based on the foregoing, we reject appellants’ argument that we must vacate the sentence for further fact finding and explanation regarding the calculation of drug quantity. Although the district court erred in failing to adequately explain its reasons for the sentence given, this error was harmless where we can determine based on the presentence report adopted by the court that there was no clear error in the calculation of drug quantity.

2.

Boccone challenges the four-point enhancement under § 3Bl.l(a), for his role as a leader in the conspiracy. The court “review[s] a district court’s decision to apply a sentencing adjustment based on a defendant’s role in the offense for clear error.” United States v. Sayles, 296 F.3d 219, 224 (4th Cir.2002).

To qualify for a four-level increase under § 3Bl.l(a) of the Sentencing Guidelines, a defendant must have been “an organizer or leader of a criminal activity that involved five or more participants or was otherwise extensive.” § 3Bl.l(a). “Factors the court should consider include the exercise of decision making authority, the nature of participation in the commission of the offense, the recruitment of accomplices, the claimed right to a larger share of the fruits of the crime, the degree of participation in planning or organizing the offense, the nature and scope of the illegal activity, and the degree of control and authority exercised over others.” Id. Application Note 4.

In applying this enhancement, we look to “whether the defendant’s role was that of an organizer or leader of people, as opposed to that of a manager over the property, assets, or activities of a criminal organization.” United States v. Llamas, 599 F.3d 381, 390 (4th Cir.2010) (internal quotations omitted). The enhancement “is appropriate where the evidence demonstrates that the defendant controlled the activities of other participants or exercised management responsibility.” Id. (internal quotations omitted).

For example, in United States v. Ellis, 951 F.2d 580 (4th Cir.1991), the court examined application of the enhancement to a scheme to corruptly secure the passage of legislation in West Virginia. Although the corrupt scheme involved only four participants, the court upheld the application of the § 3Bl.l(a) enhancement because the unknowing services of lobbyists, legislators, and their staffs advanced the criminal activity. Ellis, 951 F.2d at 585. The court observed that “[i]n considering whether an activity is ‘otherwise extensive,’ a court may consider, as it did here, ‘all persons involved during the course of the entire offense,’ even the ‘unknowing services of many outsiders.’ ” Id. (quoting § 3B1.1, cmt. n. 2).

In this case, the evidence at trial strongly supported a determination that Boccone was both the organizer and the leader of the charged conspiracy to distribute controlled substances. Although the presentence report does not identify five or more participants in the conspiracy, there is ample evidence that the criminal activity was extensive. As noted in the presentence report:

The defendant was the president of Chantilly Specialists and the owner from December 2005 until March 2010. He ran Chantilly Specialists’ day-to-day operations, hired and directed employees, approved payments by the company, signed payroll checks, and made financial decisions on behalf of the company. Additionally, the evidence revealed Boc-cone, despite having no medical training or knowledge, saw patients and made decisions regarding the prescription of Schedule II controlled substances.

(JA 4362). In addition, although many employees of Chantilly Specialists may not be culpable enough to be considered “participants” in the conspiracy, they were still involved as unwitting providers of support to the conspiracy in allowing prescription of medications to patients over an extended period of time without a legitimate medical purpose and outside the usual scope of medical practice. Likewise, the number of patients involved, whether those patients were aware of their abuse or unwittingly receiving illegitimate prescriptions, also augmented the scope and significance of the illegal activity under leadership of Boccone. Accordingly, because Boccone exhibited authority and control over both office employees and patients in furtherance of his criminal activity, the district court correctly applied the four-level enhancement for Boccone’s role as a leader in the conspiracy.

In sum, where appellants have not raised any meritorious arguments impacting the guidelines calculation, and where the district court awarded a substantial downward departure from the guidelines range, we find harmless the district court’s error in failing to explain adequately the sentence given.

III.

Based on the foregoing, appellants’ convictions and sentences are

AFFIRMED. 
      
      . "Oxycodone is a potent and addictive opioid that is classified as a Schedule II drug under the Controlled Substances Act." United States v. McIver, 470 F.3d 550, 553 n. 3 (4th Cir.2006) (citing 21 U.S.C. § 812 (2000); 21 C.F.R. § 1308.12(b)(1) (2004)). “It is marketed in instant-release form under trade names such as Roxicodone, Roxicet, OxylR, and Ox-yFAST, and in a controlled release form as OxyContin.” Id.
      
     
      
      . Boccone also urges the court to consider a report prepared by Jason Brajer, MD, approximately two months following the jury verdicts in this case. Dr. Brajer comments upon and provides a counter-point to conclusions reached by Dr. Hamill-Ruth in her expert report. In the same vein as the criticisms noted above, the points raised by Dr. Brajer more properly go to the weight of the testimony rather than its admissibility.
     
      
      . Brown contends the evidence is insufficient to link him to the agreement with Honesty, because in some of his testimony Honesty references Brown and Boccone together, without identifying specific activity by Brown. He also contends this agreement is irrelevant to the charged prescriptions. Viewing the testimony in this manner, however, neglects to draw inferences in favor of the government and impermissibly invites the court to weigh the evidence. Honesty's testimony provides a basis upon which to infer an unlawful agreement between Honesty, Brown, and Boccone, which is one factor among several showing that treatment of Honesty was outside the scope of medical practice, and that Brown knew that the specific charged prescription, as part of that course of treatment, was illegitimate.
     
      
      . Because of the limited nature of the agreement in this case, we need not address whether conceivably a practice agreement could include such restrictions on authority of a nurse practitioner, and a physician could exercise such oversight over individual prescriptions, to foreclose as a matter of law culpability of a nurse practitioner. In this manner, we find only theoretical significance in the fact that, as Brown notes, Virginia law authorizes a practice agreement to "restrict such prescriptive authority as deemed appropriate by the physician providing direction and supervision.” (Brown Br. at 33, quoting Va.Code Ann. § 54.I-2957.01(A)). It suffices in this case that no such restrictions were embodied in Brown’s practice agreement.
     
      
      . The court is in receipt of a letter submitted by Boccone’s counsel post-argument, pursuant to Federal Rule of Appellate Procedure 28(j). Under this subsection of the rule, titled "Citation of Supplemental Authorities,” a party may submit such a letter only "[i]f pertinent and significant authorities come to a party's attention after the party's brief has been filed.” Fed. R.App. P. 28(j). The submission here, however, does not contain pertinent and significant authorities that came to Boccone’s attention after his briefs were filed. Rather, it contains citations to the record in reference to points made at oral argument. We are thus not obligated to consider this letter. In any event, the information provided in Boccone’s letter does not alter the conclusions we reach above.
     
      
      . Boccone also argues that the government failed to charge him within a three-year statute of limitations period. Boccone, however, waived this argument by not raising it before or during trial. See United States v. Williams, 684 F.2d 296, 300 (4th Cir.1982). Boccone counters that the government itself has waived any reliance on waiver by addressing the merits of his argument in opposition to Boccone’s post-trial motion for acquittal. But, to the extent this court has recognized such a “waiver of waiver” argument, it has been in instances of government "acquiescence” to the issue being raised on appeal. United States v. Metzger, 3 F.3d 756, 757-58 (4th Cir.1993). The government did not so acquiesce in this case, because it raised Boc-cone’s waiver in opposition to the motion for acquittal and raised it again on appeal.
     
      
      . We And inapposite prior cases, including those cited by appellants, in which the court has remanded for resentencing despite the district court’s award of a downward variance. In those cases, unlike here, the court remanded after finding clear error in the calculation of a guidelines range. See, e.g., United States v. Gomez, 690 F.3d 194, 203 (4th Cir.2012) (remanding where district court failed to properly calculate guidelines range); United States v. Napan, 484 Fed.Appx. 780, 781-82 (4th Cir.2012) (remanding where the district court misapplied an enhancement, despite award of downward variance). Nor does this case involve a variance without explanation in the direction opposite to that requested by the appellant. See, e.g., Lynn, 592 F.3d at 582 (remanding where district court provided "no explanation at all for a substantially above-Guidelines sentence”); United States v. Engle, 592 F.3d 495, 503 (4th Cir.2010) (remanding where the government appealed downward variance imposed without sufficient explanation).
     
      
      . The presentence report identifies only three other participants in the criminal conspiracy, Brown, Dr. Anthony Fasano, and physician's assistant Joe Frazier. Although the government suggests that patients such as Honesty and Dao also were participants, the presen-tence report concludes that Boccone did not direct or manage their activities. In light of our conclusion above that the criminal activity was “otherwise extensive,” we need not address here whether the criminal activity "involved five or more participants.” § 3Bl.l(a).
     