Following a bench trial, the district court convicted Zia Iqbal on four federal criminal charges: three counts of soliciting or receiving an illegal kickback related to a federal health-care program and one count of making a false statement to federal agents. The district court1 sentenced Iqbal to two years of probation on each count, to be served concurrently. Iqbal appeals, arguing that there was insufficient evidence to support his convictions. We affirm.
I.
In March 2011, Iqbal met Millie Saeger, the administrator' and minority owner' of Patient Care Professionals (POP), a skilled-medical-home-care agency-that provides1 nursing and various therapy services. Iqbal stated that he managed a large group of physicians and that the physicians were looking for home care agencies to refer their patients. He explained that he could refer patients to PCP in return for a share of the profits made from the services to those patients. Saeger said that she was not interested in the arrangement.
Believing Iqbal’s proposal to be unlawful, Saeger contacted the Office of Inspector General of the United States Department of Health and Human Services and spoke with a special agent. The agent commenced an undercover operation at PCP with the hope of obtaining audio or-video evidence of Iqbal proposing an illegal transaction.
On March 16, 2011, Iqbal met with Sae-ger and Special Agent Linda Hanley, who was playing the undercover role of Linda Livesay, financial manager of PCP and the daughter of Cecil Livesay, the principal owner of PCP. Iqbal touted his strong relationship - with physicians through his management company, reiterated the referral relationship, that he had in mind, and said that he desired a fifty-fifty split of all profit PCP obtained from its services to the referred-patients. Iqbal said that the arrangement would be .on strong legal footing because PCP would not compensate the referring physicians. He also stated that he would compensate the physicians indirectly by discounting the services that he provided to -the physicians through his management company.
To mask the profit-splitting scheme, Iqbal suggested that the parties enter into a consulting agreement whereby Iqbal would purport to provide various services to PCP. Iqbal explained to Saeger and Han-ley that he would send invoices to PCP for financial, marketing, and patient education services that he would purportedly perform, but that the invoice amount would always reflect fifty percént of the profits PCP earned from the patients that Iqbal would send to the company. Iqbal made clear that the purpose of these invoices was to ensure that any money exchanged between Iqbal and PCP had a valid paper trail so that the arrangement between the parties appeared legitimate.
The parties eventually signed a consulting agreement with the terms that Iqbal had outlined in his meetings with Saeger and Hanley. At trial, Saeger testified that she understood that the consulting agreement was created to “cover the legalities of *629paying sums of money to Mr. Iqbal,” and that Iqbal would never actually perform any services for PCP. Iqbal never sent invoices to PCP or performed any services for the company.
On April 14, Iqbal e-mailed to Saeger the medical records for a patient of Dr. Siddiqui, a doctor with whom Iqbal had an ongoing consulting relationship. A few days later, Saeger received another e-mail from Iqbal providing a prescription for home-health nursing care for the patient. PCP performed services for the patient and was reimbursed partly through Medicaid.
Iqbal later arranged a meeting with Sae-ger and Hanley at Dr. Siddiqui’s office to introduce them to the doctor. Iqbal said that PCP should communicate with Dr. Siddiqui’s staff about any patient referred from Dr. Siddiqui’s office, but Iqbal said that he would get involved and retrieve patient records if PCP believed that it was not getting the response it desifed.
In May, Iqbal sent Saeger an e-mail that provided the telephone number of a Dr. Bhutto. Iqbal explained. that Dr. Bhutto had a patient in need of PCP’s services and that Saeger should contact Dr. Bhutto regarding a referral. Saeger called Dr. Bhutto, and PCP later received the patient, provided services to her, and billed for reimbursement through Medicare. In an August meeting with Iqbal, Saeger explained that PCP could not provide additional therapy for Dr. Bhutto’s patient because the doctor had not signed two necessary documents. Iqbal told Sae-ger that he and Dr. Bhutto were together every weekend and that he would have the doctor sign the documents.
After both patients received home-health care services, and PCP was reimbursed by Medicaid and Medicare, Saeger provided Iqbal a check for $600, representing fifty percent of the profits that PCP made from the services provided to the two patients. Saeger later -provided Iqbal with a check for $275, which equaled fifty percent of the profits that PCP received from Medicare for additional services provided to Dr. Bhutto’s patient.
The relationship between Iqbal and PCP continued' throughout 2011 and most of 2012. During this time, Iqbal introduced Saeger and Hanley to another doctor with patients who needed home-health care services. In October 2012, the government executed a search warrant at Iqbal’s residence. During the search, federal agents interviewed Iqbal. The agents asked him whether he referred or funneled patients to a health-care provider in exchange for money or something of value, and whether he had promised anyone anything for funneling patients. Iqbal denied having done either. The agents did not find any documents or invoices related to the consulting agreement .that Iqbal entered into with PCP.
A grand jury charged Iqbal with two counts of health-care fraud, in violation of 18 U.S.C. §§ 1347(a)(1) and 2, three counts of soliciting or receiving an illegal kickback, in violation of 42 U.S.C. § 1320a-7b(b)(l)(A) and 18 U.S.C. § 2, and one count of making a false statement, in violation of 18 U.S.C. § 1001(a)(2). After the district court granted the government’s motion to dismiss the health-care fraud counts, the case proceeded to a bench trial. The district court found Iqbal guilty on each of the four remaining counts and sentenced him to two years of probation on each count, to be served concurrently. Iqbal appeals, arguing that his convictions are not supported by sufficient evidence. We review the sufficiency of the evidence after a bench trial in the light most favorable to the verdict, upholding the verdict if a reasonable factfinder could *630find the offense proved beyond a reasonable doubt. United States v. Kain, 589 F.3d 945, 948 (8th Cir. 2009).
II.
The district court found Iqbal guilty on three charges under the anti-kickback statute. As to each, the court identified one element of the charge as proof that Iqbal solicited or received a payment that was “paid primarily in order to induce the referral of patients insured by Medicare or Medicaid.” The court then found that the “evidence showed, beyond a reasonable doubt, that defendant solicited kickbacks, represented that he could control the referrals, and actually received money for the few referrals that were made through his efforts.”
On Count Three, concerning solicitation of a kickback on March 16, 2011, the court found that the payments solicited by Iqbal were “for the purpose of inducing PCP to make the referrals.” On Counts Four and Five, concerning the receipt of payments on June 29 and August 9, 2011, the court found that Iqbal “clearly both solicited and received payments in return for his causing patients to be referred to PCP.” The court further found that Iqbal “accepted remuneration for inducing the referrals.” On the false-statement charge, the court found that Iqbal’s statements in response to questions from the federal agents were knowingly and materially false. The court said that “Iqbal knew his denials were untrue because he had in fact received money from PCP for causing the referrals to be made to PCP.”
The statute makes it unlawful to “soli-cite ] or receive[ ] any remuneration ... in return for referring” a person for services that may be paid for under a federal health-care program. 42 U.S.C. § 1320a-7b(b)(1)(A) (emphasis added).2 Iqbal does not dispute the district court’s premise that a person violates the statute by inducing or causing a referral in exchange for a kickback. In his post-trial motion for judgment of acquittal, he expressly acknowledged that one “element” of the anti-kickback statute is “proof that the person receiving remuneration either directly earned or induced the causing of the referral.” R. Doc. 60, at 6 (emphasis added). His brief on appeal asks for review of the sufficiency of the evidence, and argues that “there was no evidence presented that defendant either caused or induced a patient to be referred” to a home health agency. Appellant’s Br. 4 (emphasis added). At oral argument, he argued that a conviction required proof that the defendant was able to “cause” a referral. While Iqbal also argues on appeal that he did not “exercise any level of control over the referral[s],” he has accepted that “causing” or “inducing” a referral is sufficient “control” to satisfy the requirement of taking an act “in return for referring an individual.” Whatever the possible merit of a narrower interpretation of the statute, it was not raised and is not before us. See United States v. Jackson, No. 16-10946, 688 Fed.Appx. 685, 696 n.9, 2017 WL 1969667, at *9 n.9 (11th Cir. May 12, 2017); United States v. Forster, 549 Fed. Appx. 757, 762 n.2 (10th Cir. 2013). We will therefore consider the sufficiency of the evidence on the assumption that Iqbal *631was properly convicted if he solicited or received remuneration in return for causing or inducing the referral of patients to PCP.
The partial dissent, post, at 632-33, argues that because Iqbal challenged the sufficiency of the evidence to support his conviction, we must decide whether the district court properly interpreted the statute. The cited authority, United States v. Gentry, 555 F.3d 659 (8th Cir. 2009), does not support the proposition. Neither do the rales of procedure. Gentry was a case in which the appellant did challenge the district court’s interpretation of the relevant statute, so this court unsurprisingly said that “[w]hen a sufficiency argument hinges on the interpretation of a statute, we review the district court’s statutory interpretation de novo.” Id. at 664. Gentry does not say that if an appellant accepts the district court’s interpretation of a statute and challenges only the sufficiency of the evidence under that standard, then this court must sua sponte address the meaning of the statute. We have said over and over that “[i]ssues not raised in a party’s opening brief are waived.” United States v. Rice, 699 F.3d 1043, 1050 (8th Cir. 2012); see Fed. R. App. P. 28(a)(8)(A) (“The appellant’s brief must contain ... appellant’s contentions and the reasons for them.”). The waiver applies with even greater force when the appellant conceded an issue in the district court. Under the circumstances here, we decline to exercise any discretion to raise the issue. Cf. U.S. Nat’l Bank of Or. v. Indep. Ins. Agents of Am., Inc., 508 U.S. 439, 447-48, 113 S.Ct. 2173, 124 L.Ed.2d 402 (1993).
Count Three of the indictment charged Iqbal with soliciting a kickback from PCP in the form of a fifty-fifty profit-sharing arrangement for his referring Medicare and Medicaid patients to PCP. The evidence showed that Iqbal met with Saeger and Hanley on March 16, 2011, and explained that he would refer Medicare and Medicaid patients to PCP if the company agreed to give him fifty percent of any profits made from services provided to those patients. Iqbal represented that given the breadth of his relationships with local physicians, the parties could each make $10,000 per month through the arrangement. Iqbal’s proposal is sufficient to support his conviction on Count Three that he solicited a kickback in return for eventually causing or inducing the referral of patients to PCP.
Count Four of the indictment charged Iqbal with the receipt of $600 in return for referring two patients to PCP, one from Dr. Siddiqui and one from Dr. Bhutto. Count Five of the indictment charged Iqbal with the receipt of $275, which represented fifty percent of the profits from additional services provided to Dr. Bhutto’s patient.
The evidence on Count Four showed that on April 14 and 17, 2011, Iqbal sent two e-mails to Saeger regarding Dr. Siddi-qui’s patient. The first e-mail contained an attachment with the patient’s medical information. In the second e-mail, Iqbal explained that he had an original prescription for home-health nursing care for the patient that he could give to Saeger when they met at Dr. Siddiqui’s office later that week. Iqbal also attached a copy of the prescription. It was signed by Dr. Siddiqui and prescribed “home health nursing care,” but it did not list a specific healthcare provider for the services, so Iqbal’s transmission of the prescription to Saeger allowed PCP to provide services to the patient. After Iqbal sent these e-mails, he set up a meeting at Dr. Siddiqui’s office so that Saeger and Hanley could meet the doctor. At that meeting, the doctor explained that Iqbal told him about PCP and *632that the doctor had more patients for PCP. Iqbal also informed Saeger and Hanley that he had access to Dr. Siddiqui’s patient flies if PCP needed them quickly/ It was therefore reasonable for the district court to infer that Iqbal caused or induced the referral of Dr. Siddiqui’s patient to PCP.
As relevant to Counts Four and Five, the evidence also showed that in May, Iqbal sent another e-mail to Saeger explaining that Dr. Bhutto had a patient for PCP, and that Saeger should call the doctor to set up the services for the patient. After Saeger called Dr. Bhutto, PCP began providing services to the patient. In August, Iqbal told Saeger that he was with Dr. Bhutto every weekend and would have Dr. Bhutto sign necessary documents so that PCP could provide further services to the patient. In light of Iqbal’s statements about his relationship with Dr. Bhutto and Iqbal’s admitted plan to provide reduced-fee consulting services to physicians in return for their referring patients to PCP, a reasonable factfinder could infer that Iqbal induced Dr. Bhutto to refer his patient to PCP on this occasion. Therefore, there was sufficient evidence to support Iqbal’s convictions on Counts Four and Five. ■
Iqbal complains finally that his conviction for making a false statement “rests entirely on the premise that he violated the Anti-Kickback Statute.” He contends that if his convictions for violating § 1320a-7b(b)(l)(A) are overturned, then his conviction for making a false statement should be reversed as well. Because we conclude that sufficient evidence supports Iqbal’s convictions on Counts Three, Four, and Five, his challenge to, the false-statement conviction fails as well.
⅜ ⅜ *
The judgment of the district court is affirmed.
. The Honorable Catherine D. Pérry, United States District Judge for the .Eastern District of Missouri.
. The statute provides:
[WJhoever knowingly and willfully solicits or receives any remuneration (including any kickback, bribe, or rebate) directly or indirectly, overtly or covertly, in cash or in kind — (A) in return for referring an individual to a person for the furnishing or arranging for the furnishing of any item or service for which payment may be made in whole or in part under a Federal health care program ... shall be guilty of a felony ....