OPINION

JULIA SMITH GIBBONS, Circuit Judge.

As a result of a scheme involving doctors writing fraudulent prescriptions and "marketers" filling those fraudulent prescriptions and selling them on the street, Dr. Carl Fowler and Michael Thoran were convicted by a jury of conspiracy to commit healthcare fraud, conspiracy to distribute controlled substances, and conspiracy to pay or receive healthcare kickbacks. Fowler appeals his sentence, and Thoran appeals his convictions and his sentence. During Fowler's sentencing hearing, the district court failed to calculate the Guidelines range and failed to make findings about why the sentence that served as its "starting point" was appropriate. Likewise, at Thoran's sentencing hearing, the district court agreed to the parties' stipulated Guidelines range without making any findings about why it was appropriate. The evidence also indicates that the district court relied on erroneous factual findings in determining the restitution amount for each defendant. Because of these errors, we vacate Fowler and Thoran's sentences and restitution orders and remand to the district court for resentencing and recalculation of the restitution amounts. However, we affirm Thoran's convictions.

I.

In November 2009, Babubhai Patel opened a pharmacy in the building where Fowler's clinic operated and hired Kartik Shah as the manager. Shah paid Fowler to write prescriptions for patients and send those patients to Patel's pharmacy. At some point, Patel introduced Fowler to Toney Taylor, a "marketer"1 who would bring additional patients to Fowler's clinic. Michael Thoran, also known as "Ace," was another marketer. Thoran would visit Highland Park Pharmacy, one of Patel's pharmacies, to pick up prescriptions for five to ten patients from the Visiting Doctors for America about two or three times per week. One witness testified that he once observed Thoran being paid $6,000 for this service.

In 2010, Oxycontin, an opiate pain reliever, was reformulated in a way that discouraged users from snorting or injecting it. At the time Oxycontin was reformulated, a similar drug, Opana, could still be abused as the earlier version of Oxycontin was. Fowler began to prescribe Opana in either October 2010 or sometime in 2011.

At Fowler's sentencing hearing, the district court noted that the jury did not determine the amount of losses. Defense counsel took issue with the $1,752,957 loss amount, arguing that the evidence supported that only 20% of the prescriptions written by Fowler were illegitimate. The Government responded that, in considering the percentage of illegitimate prescriptions coming from both Fowler's regular patients and the marketers' patients, Fowler was responsible for 50% of the value of the medication he billed through the Patel pharmacies, or $1,752,957, which was a conservative estimate, especially because the scheme was based on expensive, rather than cheap generic, drugs.

In looking to the Guidelines, the district court observed that whichever Guidelines range it applied, the displeased party could appeal, so concluded that "in either event, I think that the sentence I impose will comply with the congressional factors in either event being whether I take the higher or the lower guidelines or something in between." Fowler Sentencing Hr'g Tr. 14:13-16, Oct. 28, 2014, ECF No. 1406. Fowler's counsel responded by observing that "the judge has to make some kind of finding about what the advisory guidelines are." Id. at 16:5-6. The court agreed; nevertheless, it recommended starting the inquiry at 108 months, a sentence "substantially lower than the guidelines as computed by the Probation Department."2 Id. at 17:19-20. Fowler's counsel then responded that "if everybody agrees that that's where we start, and if the Court were to depart from that, the comparison for purposes of appeal by the Government would be with 108 months. Then I'm prepared to ... go forward just like that." Id. at 17:22-18:1. "[S]tarting out, as [defense counsel] has agreed, with the Government's request for nine years," id. at 32:8-10, the court went on to discuss the 18 U.S.C. § 3553 factors, then imposed the sentence without calculating the Guidelines range or making any factual findings about why 108 months was an appropriate starting point. When the court asked if there were any objections, defense counsel responded, "I have none other than what has been discussed." Id. at 39:18-19. Ultimately, the district court sentenced Fowler to 72 months' imprisonment followed by two years' supervised release and ordered restitution in the amount of $1,752,957.

At Thoran's sentencing hearing, the Government agreed to stipulate to the 168-210 month range suggested by the defense. The Government discussed how the § 3553 factors led to its sentencing recommendation and the defense presented arguments as to why Thoran should receive a sentence of only 48 months. The defense suggested $455,126 in restitution, while the Government insisted Thoran "be held accountable for the entire loss of $2.6 million." Thoran Sentencing Hr'g Tr. 34:25. The court briefly analyzed the § 3553 factors and imposed a sentence of 108 months with three years of supervised release and ordered restitution of $2,632,854. The defense "object[ed] to the sentence as procedurally and substantively unreasonable." Id. at 44:4-5. Fowler and Thoran filed timely notices of appeal.

II.

We review the reasonableness of a defendant's sentence for abuse of discretion. Gall v. United States, 552 U.S. 38, 46, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007). "A district court abuses its discretion when it applies the incorrect legal standard, misapplies the correct legal standard, or relies upon clearly erroneous findings of fact." United States v. Bridgewater, 606 F.3d 258, 260 (6th Cir.2010) (quoting United States v. Pugh, 405 F.3d 390, 397 (6th Cir.2005)). If the defendant failed to object to the procedural reasonableness of the sentence, we review for plain error. United States v. Wallace, 597 F.3d 794, 802 (6th Cir.2010); United States v. Blackie, 548 F.3d 395, 398 (6th Cir.2008). The amount of restitution ordered is also reviewed for abuse of discretion, United States v. Williams, 612 F.3d 500, 509 (6th Cir.2010), but the findings of fact underlying this calculation are reviewed for clear error, United States v. Triana, 468 F.3d 308, 321 (6th Cir.2006). Such findings are clearly erroneous where "the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed." United States v. Ware, 282 F.3d 902, 907 (6th Cir.2002) (quoting United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948)). Challenges to the sufficiency of evidence are reviewed de novo. United States v. Howard, 621 F.3d 433, 459 (6th Cir.2010).

III.

A.

Fowler asserts that his sentence is procedurally and substantively unreasonable because the district court failed to calculate the Guidelines range or make factual findings in imposing his sentence. The Government does not argue that the district court made adequate factual findings but rather responds that just as other fundamental constitutional rights can be waived, so too can the right to have one's Guidelines range calculated. It asserts that Fowler waived his right to have the district court rule on his objections to the Guidelines range because he agreed that 108 months would be the starting point and did not object before the court imposed a sentence.

We review the district court's sentencing decision for procedural and substantive reasonableness. United States v. Garcia-Robles, 640 F.3d 159, 163 (6th Cir. 2011). A district court commits procedural error by "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." Gall, 552 U.S. at 51, 128 S.Ct. 586 (emphasis added). The reasonableness inquiry is "functional in nature," thus the focus is not on what the district court said, but "on what the transcript reveals that the court did." United States v. Gunter, 620 F.3d 642, 646 (6th Cir.2010).

Although the Guidelines are no longer mandatory after the Supreme Court decision in United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), this circuit has consistently held that the district court must consider the advisory Guidelines range. See, e.g., United States v. Recla, 560 F.3d 539, 548 (6th Cir.2009) ("A district court must consider the advisory Guidelines range...."); Blackie, 548 F.3d at 400 ("The district court must also acknowledge `the defendant's applicable Guideline range.'" (citation omitted)); United States v. McGee, 529 F.3d 691, 699 (6th Cir.2008) ("[T]he sentencing court must still consider the Sentencing Guideline ranges...."); United States v. Moon, 513 F.3d 527, 538 (6th Cir.2008) ("[D]istrict courts are to consider the Guidelines...."). When selecting an appropriate sentence, the district court "must adequately explain the chosen sentence to allow for meaningful appellate review and to promote the perception of fair sentencing." Recla, 560 F.3d at 547 (quoting Gall, 552 U.S. at 50, 128 S.Ct. 586); see also Blackie, 548 F.3d at 401 (noting that this requirement is "more than [a] mere administrative burden[] or meaningless formalit[y]"). In Blackie, the court determined that it could not "meaningfully review [the defendant's] sentence" because the district court failed to state the applicable Guidelines range and provide the specific reasons for imposing a variance. 548 F.3d at 401, 403. Consistent with this holding, we have held that failure to calculate the Guidelines range renders a sentence procedurally unreasonable. For instance, in addressing a procedural reasonableness claim in United States v. Peebles, we concluded:

624 F.3d 344, 347 (6th Cir.2010); see also United States v. Barahona-Montenegro, 565 F.3d 980, 985-86 (6th Cir.2009) (vacating the defendant's sentence because "[t]he district court's failure to calculate clearly the Guidelines range and to explain adequately the chosen sentence are errors that make the sentence procedurally unreasonable").

If the district court fails to consider the applicable Guidelines range, but "instead simply selects what the judge deems an appropriate sentence without such required consideration," the sentence may be unreasonable if it does not allow for meaningful appellate review. Moon, 513 F.3d at 539 (quoting United States v. Jones, 489 F.3d 243, 250-51 (6th Cir.2007)); see also United States v. Turner, 536 Fed.Appx. 614, 619-20 (6th Cir.2013) (finding no plain error because although the district court did not acknowledge the Guidelines range, it provided "a sufficient explanation of its reasoning"). In United States v. Johnson for example, the district court, rather than resolve the dispute of the applicable sentencing range, "split the difference" and imposed a sentence in the middle of the range suggested by each side. 446 Fed. Appx. 798, 799-801 (6th Cir.2012) (per curiam). This court concluded that "the selection of a starting Guidelines range in this case can only be described as arbitrary" and that "[b]y arbitrarily selecting a sentencing range that had no direct correlation to facts before the court, the sentencing judge in this case managed to avoid the explanation that would allow us to review the sentence's reasonableness." Id. at 801. Thus, it vacated the defendant's sentence. Id. at 802. Moreover, where one party presents non-frivolous reasons for imposing a different sentence, the district court should usually "go further and explain why [it] has rejected those arguments." Wallace, 597 F.3d at 804 (quoting Rita v. United States, 551 U.S. 338, 357, 127 S.Ct. 2456, 168 L.Ed.2d 203 (2007)). The district court is not permitted "to delegate its obligation to `state in open court the reasons for its imposition of the particular sentence' to the prosecutor and the defendant." Id. at 804-05 (quoting 18 U.S.C. § 3553(c)).

It is difficult to contend, and the Government does not even attempt to argue, that the district court's suggested "starting point" of 108 months was anything other than arbitrary. The district court gave no reason for its selection of 108 months other than to apparently prevent the parties from appealing. Rather than explain the sentencing decision to allow for us to conduct a meaningful review of it, the district court did little more than "split the difference" between Fowler's suggested range of 30-37 months and the 188-235 months suggested in the PSR. See Johnson, 446 Fed.Appx. at 799-801. Based on the transcript, it seems that the district court did not even acknowledge, must less consider, Fowler's arguments that a lower range was appropriate, leaving us no basis to review the sentence on appeal. The district court is not bound by any agreement between the parties and could have found a different Guidelines range was applicable had it made the requisite findings. See United States v. Burchett, 7 F.3d 235, at *2 (6th Cir.1993) (per curiam) (unpublished) (quoting U.S.S.G. § 6B1.4(d)). But it is not this court's duty to supply reasons for the district court's sentencing decision. See United States v. Thomas, 498 F.3d 336, 341 n. 3 (6th Cir. 2007).

We have held numerous times in the past and reiterate now that the district court's failure to calculate or make factual findings about the Guidelines range renders it impossible for us to conduct any meaningful appellate review of the reasonableness of a defendant's sentence. For this reason, the sentence imposed was procedurally unreasonable.

The Government contends, however, that Fowler has waived his right to have the Guidelines range calculated. Waiver is the intentional relinquishment of a known right. United States v. Priddy, 808 F.3d 676, 681 (6th Cir.2015) (citation omitted). The mere failure to object to a sentencing error, even when the party admits there is no objection, does not constitute waiver. Id. However, where one makes "a plain, explicit concession on the record," we will consider that argument waived. United States v. Mabee, 765 F.3d 666, 673 (6th Cir.2014); see also Priddy, 808 F.3d at 681; United States v. Ruiz, 777 F.3d 315, 321 (6th Cir.2015).

Though Fowler may have accepted the 108-month starting point, he made no "plain, explicit concession on the record" that the district court need not carry out its duty to calculate the appropriate Guidelines range. See Mabee, 765 F.3d at 673. Even if we were to construe Fowler's agreement as a waiver, the district court was still under an obligation to make factual findings regarding the applicable Guidelines range. See United States v. Grams, 566 F.3d 683, 686 (6th Cir.2009) (concluding that even though the parties seemed to agree to the Guidelines range and factual findings suggested in the PSR, "the district court should still have stated in open court whether it adopted in part or full the sentencing range and factual findings suggested by the probation office"). Hence, we conclude that the district court abused its discretion by imposing a procedurally unreasonable sentence.

B.

Like Fowler, Thoran asserts that the district court erred in sentencing him because it did not make any findings supporting the Guidelines calculation but rather relied on the PSR's calculation of the number of drugs for which Thoran was responsible, which was an amount much lower than that presented by the Government at the sentencing hearing. Again, the Government does not contend that the district court made adequate factual findings, but rather responds that it stipulated to the Guidelines range of 168 to 210 months, the range advocated by Thoran, and that Thoran did not object to that range.

As with Fowler's case, at Thoran's sentencing hearing, the district court failed to make findings about the applicable Guidelines range. Instead, it simply agreed to the range stipulated by the parties without any explanation that would allow us to meaningfully review that range. Furthermore, like Fowler, Thoran made no "plain, explicit concession" that the district court need not calculate his Guidelines range. See Mabee, 765 F.3d at 673. Thus, the district court abused its discretion by failing to calculate the appropriate Guidelines range.

We underscore the necessity of the district court's obligation to calculate the Guidelines range and make factual findings with respect to that range. The failure to do so deprives defendants of a substantial right, namely, the right to meaningful appellate review of their sentences, see Wallace, 597 F.3d at 806-07, and forecloses us entirely from reviewing their sentences for reasonableness. We, therefore, hold that for a sentence to be procedurally reasonable, the district court must calculate the Guidelines range and make factual findings regarding that range. We need not involve ourselves in the minutiae of how specifically to carry out that duty but simply hold that district courts must do so in a manner that will allow this court to meaningfully review the imposition of a defendant's sentence.

IV.

A.

As for the loss calculation underlying the restitution amount, Fowler asserts that it is problematic in several ways: First, the testimony supports that only 20% of the prescriptions were illegitimate. Next, the calculation was based on the prescriptions written by Dr. Clark, who was not part of the conspiracy and about whom there is no evidence regarding the amount of illegitimate prescriptions written. Third, the calculation was based on a conspiracy lasting from November 2009 until August 2011, but the Government's witness testified that Fowler's participation in the scheme did not begin until the middle of 2010. Finally, the Government did not know how much of the losses came from marketers, and the testimony revealed that some of the prescriptions were only partially fraudulent. The Government, while not explaining the propriety of its restitution calculation, responds that Fowler intentionally abandoned any challenge to the amount of loss, so we should review for plain error.

In determining the amount of restitution, the Government must prove the losses by a preponderance of the evidence and the court must find that the defendant's criminal conduct directly and proximately caused the actual or intended loss to the victim. United States v. Church, 731 F.3d 530, 538 (6th Cir.2013). While the district court need not make specific findings in calculating restitution, the information relied upon by the district court in reaching the final calculation must have "sufficient indicia of reliability to support its probable accuracy." United States v. Jackson-Randolph, 282 F.3d 369, 386 (6th Cir.2002) (citation omitted).

As an initial matter, Fowler plainly did object to the restitution amount during the sentencing hearing and nothing in the record indicates, as the Government insists, that he abandoned this challenge, so we will review for abuse of discretion.

At trial, Shah first testified that of Fowler's "regular patients," only 20% of the prescriptions were illegitimate, but 80% of those from the marketers' patients were illegitimate. Trial Tr. 420:5-16, Feb. 14, 2014, ECF No. 1241. He later stated that "out of [Fowler's] 100 percent pool of the patients, like 80 percent was legitimate and 20 percent was illegitimate, but for the times like when the patients come from the marketer's point of view, the 80 percent, like that was, again, an estimation that that was for [an] illegitimate purpose." Trial Tr. 602:19-603:7, Feb. 18, 2014, ECF No. 1242. Fowler interprets the latter language to mean that only 20% of his total number of patients was illegitimate. The evidence favors Fowler's interpretation that only 20% of the prescriptions he wrote, including those from marketers' patients, were illegitimate. This is particularly true in light of the fact that Shah's later interpretation is in clarification of his earlier one. For this reason, the Government's decision to base its restitution calculation on 50% of the total value of the medication billed by Fowler is erroneous, as the testimony indicates that Fowler was responsible for only a fraction of that loss.

Moreover, though the Government's loss calculation was apparently based on the conspiracy beginning in 2009, witnesses testified that Fowler's participation in the conspiracy did not begin until sometime in 2010. Shah testified that Fowler first received money for referring patients to Patel's pharmacy in mid-2010, and Taylor testified that he began bringing patients to Fowler sometime in 2010, but that he could not remember exactly when. Thus, the evidence also indicates that Fowler was held responsible for prescriptions written before he became involved in the conspiracy.

Based on the record, these two issues alone lead us to conclude that the district court's restitution order was based on clearly erroneous findings. The evidence supporting the restitution calculation is not sufficiently reliable, so we conclude that the district court abused its discretion.

B.

The Government concedes that the district court erred in failing to make specific findings regarding why Thoran should be held accountable for the entire loss of $2.6 million, rather than just the loss resulting from the patients Thoran recruited and agrees to remand. As this calculation was based on the clearly erroneous assumption that Thoran was responsible for the entire loss, and because the Government is in agreement, we conclude the district court abused its discretion. See United States v. White, 492 F.3d 380, 418 (6th Cir.2007).3

V.

Finally, Thoran challenges the sufficiency of the evidence to support two of his convictions. With respect to the conviction for conspiracy to distribute controlled substances, he merely states that the Government "presented no evidence that he willingly joined the conspiracy to distribute narcotics" and that there was no proof that he knew the prescriptions were not legitimate or distributed them to someone other than a patient. R. at 23, Thoran Br. at 12-13. Regarding his conviction for conspiracy to pay or receive healthcare kickbacks, he states, again without developed argumentation, that "the Government failed to meet each element of this conspiracy."4 Id. at 14.

In analyzing this claim, "we review the evidence in the light most favorable to the prosecution and determine whether `any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.'" United States v. Soto, 794 F.3d 635, 657 (6th Cir.2015) (quoting United States v. Lutz, 154 F.3d 581, 587 (6th Cir.1998)). The verdict can be upheld based solely on circumstantial evidence, and this evidence need not "remove every reasonable hypothesis except that of guilt." United States v. Williams, 195 F.3d 823, 826 (6th Cir.1999). But we must take care not to weigh the evidence or judge the credibility of witnesses who testified at trial. Howard, 621 F.3d at 460.

Thoran makes no effort to develop his argument that the evidence is insufficient to support his convictions but essentially states that there was no proof the elements were met. "Issues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived. It is not sufficient for a party to mention a possible argument in [a] skeletal way, leaving the court to put flesh on its bones." El-Moussa v. Holder, 569 F.3d 250, 257 (6th Cir. 2009) (alteration in original) (quoting McPherson v. Kelsey, 125 F.3d 989, 995-96 (6th Cir.1997)). Though we need not address Thoran's skeletal arguments, we nevertheless conclude they fail on the merits.

To establish a claim for conspiracy to distribute controlled substances, the jury must have found, beyond a reasonable doubt, that Thoran (1) entered into an agreement with two or more persons to violate drug laws, (2) knowingly and intentionally joined the conspiracy, and (3) participated in the conspiracy. United States v. Paige, 470 F.3d 603, 608 (6th Cir.2006). The evidence indicates that Thoran entered into an agreement with several co-conspirators, including Patel and several pharmacists, to bring in patients to the pharmacies in exchange for cash. Thoran was actively involved in this conspiracy. The witnesses' testimony also revealed that Thoran would often have prescriptions filled for several patients without them being present, and when the patients were present, they would receive the drugs and immediately give them to Thoran. Further, several patients complained that Thoran never gave them their medications after filling the prescriptions at the pharmacy. It is reasonable to conclude based on this circumstantial evidence that Thoran was not helping patients receive legitimate prescriptions, but rather selling their controlled substances for profit in violation of drug laws. This is further evinced by the fact that he was paid several thousand dollars for this arrangement. This evidence is more than sufficient for a rational jury to have convicted Thoran of this crime.

To convict Thoran for conspiracy to pay or receive healthcare kickbacks, the Government must have produced sufficient evidence for the jury to conclude beyond a reasonable doubt that (1) Thoran agreed with two or more persons to commit an offense against the United States, in this case, receiving kickbacks in return for goods or services paid for by a federal healthcare program, (2) Thoran knew of the unlawful objective and voluntarily joined the conspiracy, and (3) one or more persons committed an overt act to effect the object of the conspiracy. 18 U.S.C. § 371; 42 U.S.C. § 1320a-7b(b); Njoku, 737 F.3d at 64 (citation omitted). As discussed above, the evidence is sufficient to establish that Thoran was involved in an agreement with several people to receive payment (kickbacks) in exchange for bringing patients to the pharmacy. The high monetary payment he accepted for his service and the evidence that he personally received many of the prescriptions written for the patients is sufficient to infer that he knew the object of the conspiracy was illegal but joined in anyhow. This was more than a mere agreement; the conspirators acted in furtherance of the agreement by carrying out the scheme. Therefore, the evidence is sufficient for a rational jury to have convicted him on this charge as well.

VI.

We vacate Fowler and Thoran's sentences and remand for resentencing consistent with this opinion. We also affirm Thoran's convictions for conspiracy to distribute controlled substances and conspiracy to pay or receive healthcare kickbacks.