Dissenting opinion filed by Chief Judge Prost.
Lourie, Circuit Judge.
West-Ward Pharmaceuticals International Limited and West-Ward Pharmaceuticals Corp. (collectively, "West-Ward") appeal from the decision of the United States District Court for the District of Delaware holding, after a bench trial, claims 1-9, 11-13, and 16 ("the asserted claims") of U.S. Patent 8,586,610 ("the '610 patent") infringed and not invalid. See Vanda Pharm. Inc. v. Roxane Labs., Inc. , 203 F.Supp.3d 412 (D. Del. 2016) (" Opinion "). For the following reasons, we affirm.
BACKGROUND
I.
Aventisub LLC ("Aventisub") owns and Vanda Pharmaceuticals Inc. ("Vanda" and collectively, with Aventisub, "Plaintiffs") holds an exclusive worldwide license to U.S. Reissue Patent 39,198 ("the '198 patent"). The '198 patent expired on November *112115, 2016.1 Vanda also owns the '610 patent, which will expire on November 2, 2027.
The '610 patent relates to a method of treating schizophrenia patients with iloperidone wherein the dosage range is based on the patient's genotype. The cytochrome P450 2D6 gene ("CYP2D6") encodes an enzyme known to metabolize a large number of drugs, including iloperidone. '610 patent col. 1 ll. 29-36. The '610 patent teaches "that treatment of a patient, who has lower CYP2D6 activity than a normal person, with a drug[, such as iloperidone,] that is pre-disposed to cause QT2 prolongation and is metabolized by the CYP2D6 enzyme, can be accomplish[ed] more safely by administering a lower dose of the drug than would be administered to a person who has normal CYP2D6 enzyme activity."Id . col. 2 ll. 15-21. QT prolongation can lead to serious cardiac problems. The '610 patent refers to patients who have lower than normal CYP2D6 activity as CYP2D6 poor metabolizers. It provides examples of dose reductions for poor metabolizers compared to the dose given to someone with a wildtype genotype. Id . col. 9 ll. 34-47, col. 11 ll. 22-28.
Claim 1 of the '610 patent is representative and reads as follows:
A method for treating a patient with iloperidone, wherein the patient is suffering from schizophrenia, the method comprising the steps of:
determining whether the patient is a CYP2D6 poor metabolizer by:
obtaining or having obtained a biological sample from the patient;
and
performing or having performed a genotyping assay on the biological sample to determine if the patient has a CYP2D6 poor metabolizer genotype; and
if the patient has a CYP2D6 poor metabolizer genotype, then internally administering iloperidone to the patient in an amount of 12 mg/day or less, and
if the patient does not have a CYP2D6 poor metabolizer genotype, then internally administering iloperidone to the patient in an amount that is greater than 12 mg/day, up to 24 mg/day,
wherein a risk of QTc prolongation for a patient having a CYP2D6 poor metabolizer genotype is lower following the internal administration of 12 mg/day or less than it would be if the iloperidone were administered in an amount of greater than 12 mg/day, up to 24 mg/day.
Id. col. 17 ll. 2-25.
Vanda owns New Drug Application ("NDA") 22-192 for Fanapt® (iloperidone), an atypical antipsychotic approved by the U.S. Food and Drug Administration ("FDA") in 2009 under 21 U.S.C. § 355(b) for the treatment of patients with schizophrenia. Vanda was able to obtain FDA approval for iloperidone based, at least in part, on the invention disclosed in the '610 patent, which reduces the side effects associated with QTc prolongation, enabling safer treatment of patients with schizophrenia. The '198 patent and the '610 patent are listed in connection with Fanapt® in the FDA's Approved Drug Products with Therapeutic Equivalence Evaluations , commonly known as the "Orange Book."
*1122II.
In 2013, West-Ward3 filed Abbreviated New Drug Application ("ANDA") 20-5480 seeking approval to commercially manufacture, use, offer to sell, and sell a generic version of Fanapt® in 1 mg, 2 mg, 4 mg, 6 mg, 8 mg, 10 mg, and 12 mg strengths for the treatment of schizophrenia pursuant to 21 U.S.C. § 355(j). At that time, the '610 patent had not yet issued and only the '198 patent was listed in the Orange Book. The ANDA contained a certification per 21 U.S.C. § 355(j)(2)(A)(vii)(IV) ("Paragraph IV certification") that the '198 patent was invalid and/or would not be infringed by West-Ward. West-Ward then sent the notice required by 21 U.S.C. § 355(j)(2)(B) ("Paragraph IV notice") of its Paragraph IV certification. On November 25, 2013, Plaintiffs filed Civil Action No. 13-1973 ("2013 suit") in the U.S. District Court for the District of Delaware ("district court") alleging infringement of the '198 patent.
The proposed ANDA label is substantially identical in all material respects to the Fanapt® label. The proposed label states that: iloperidone is "indicated for the treatment of adults with schizophrenia," J.A. 15104 § 1; "[t]he recommended target dosage of iloperidone tablets is 12 to 24 mg/day," J.A. 15103; "[t]he recommended starting dose for iloperidone tablets is 1 mg twice daily," J.A. 15105 § 2.1; and "[i]loperidone must be titrated slowly from a low starting dose," J.A. 15105 § 2.1. The proposed label provides that the "[i]loperidone dose should be reduced by one-half for poor metabolizers of CYP2D6 [see Pharmacokinetics (12.3) ]." J.A. 15105 § 2.2. Section 5.2, entitled "QT Prolongation," explains: "iloperidone was associated with QTc prolongation of 9 msec at an iloperidone dose of 12 mg twice daily" and that "[c]aution is warranted when prescribing iloperidone ... in patients with reduced activity of CYP2D6 [see Clinical Pharmacology (12.3) ]." J.A. 5106-07 § 5.2.
III.
Meanwhile, the '610 patent issued on November 19, 2013, and on June 16, 2014, Vanda filed Civil Action No. 14-757 ("2014 suit") in the district court alleging infringement of the '610 patent. On January 15, 2015, Vanda listed the '610 patent in the Orange Book for Fanapt®. On May 6, 2015, West-Ward sent Vanda a Paragraph IV notice with respect to the '610 patent notifying Vanda that it amended ANDA 20-5480 to contain a Paragraph IV certification that the '610 patent is invalid and/or not infringed. J.A. 19696; see 21 U.S.C. § 355(j)(2)(B)(ii)(II). The district court consolidated the 2013 and 2014 suits.
Following a bench trial, the district court found that West-Ward's proposed products induce infringement of the asserted claims of the '610 patent, but do not contributorily infringe them. Opinion , 203 F.Supp.3d at 435. The court held that West-Ward's "submission of a paragraph IV certification for the '610 [p]atent is an act of infringement" and that Vanda's expert Dr. Alva "practiced the steps of the '610 [p]atent claims" with Fanapt®. Id. at 433. The court found that the proposed ANDA label "recommends": (1) "practitioners use iloperidone to treat patients suffering from schizophrenia"; (2) "oral administration of iloperidone tablets at 12 to 24 mg/day to non-genotypic CYP2D6 poor metabolizers and 12 mg/day or less to genotypic CYP2D6 poor metabolizers"; and (3) "practitioners perform or have performed *1123a genotyping assay to determine whether patients are CYP2D6 poor metabolizers." Id. at 432 (first citing J.A. 15104-05 §§ 1, 2.1, 2.2; then citing J.A. 15120-21 § 12.3).
The district court also held that the asserted claims were not invalid under § 101, § 103, or § 112 for lack of written description. The court did conclude that "the asserted claims depend upon laws of nature," specifically, "the relationship between iloperidone, CYP2D6 metabolism, and QTc prolongation." Id. at 428-29. But the court explained that the '610 patent"addresses natural relationships to which the claims add conducting CYP2D6 genotyping tests to determine the appropriate dose of iloperidone to reduce QTc-related risks." Id. at 429. "The court f[ound] that while it may have been conventional to investigate for side-effects, [West-Ward] has not proven by clear and convincing evidence that the precise test and the discovered results were routine or conventional." Id. The court found that the data disclosed in the patent were "sufficient to support possession of the claimed dosage range, even if not statistically significant." Id. at 431.
The court determined that 35 U.S.C. § 271(e)(4)(A) relief was unavailable for the '610 patent because it did not issue until after the ANDA was filed.4 Id. at 435. The court determined that injunctive relief was appropriate, however, pursuant to its "general equitable power." Id. The court enjoined West-Ward from engaging in the commercial manufacture, use, offer to sell, sale in or importation into the United States of West-Ward's ANDA product prior the expiration of the '610 patent. The court further ordered that "[t]he effective date of any [FDA] approval of [West-Ward's] ANDA No. 20-5480 shall be a date not earlier than the latest of the expiration of the '610 [p]atent or any applicable exclusivities and extensions." J.A. 33
West-Ward timely appealed from the district court's final judgment. We have jurisdiction under 28 U.S.C. § 1295(a)(1).
DISCUSSION
On appeal from a bench trial, we review a district court's conclusions of law de novo and its findings of fact for clear error. Golden Blount, Inc. v. Robert H. Peterson Co. , 365 F.3d 1054, 1058 (Fed. Cir. 2004). A factual finding is only clearly erroneous if, despite some supporting evidence, we are left with the definite and firm conviction that a mistake has been made. United States v. U.S. Gypsum Co. , 333 U.S. 364, 395, 68 S.Ct. 525, 92 L.Ed. 746 (1948) ; see also Polaroid Corp. v. Eastman Kodak Co. , 789 F.2d 1556, 1559 (Fed. Cir. 1986) ("The burden of overcoming the district court's factual findings is, as it should be, a heavy one.").
I. Jurisdiction
We must first address whether the district court properly exercised jurisdiction over the 2014 suit. On November 16, 2017, we directed supplemental briefing on jurisdiction. Both parties responded with supplemental briefing, which, inter alia , addressed whether there is district court jurisdiction under the Drug Price Competition and Patent Term Restoration Act of 1984 ("the Hatch-Waxman Act"), *1124Pub. L. No. 98-417, 98 Stat. 1585 (1984) over an action in which the asserted patent issued after the ANDA was filed and the complaint was filed before the ANDA applicant submitted a Paragraph IV certification for the asserted patent.
Vanda argues that its allegations of infringement under 35 U.S.C. § 271(e)(2) created subject matter jurisdiction in the district court under 28 U.S.C. § 1331 and § 1338(a), and presented a justiciable controversy. Vanda further argues that the Declaratory Judgment Act, 28 U.S.C. § 2201, provides an alternative basis for jurisdiction because it alleged that West-Ward would infringe the '610 patent under 35 U.S.C. § 271(a), (b), or (c) by selling iloperidone.
West-Ward argues that 35 U.S.C. § 271(e)(2) does not create a basis for subject matter jurisdiction over Vanda's infringement claims. West-Ward contends that a claim for § 271(e)(2) infringement can only be based on patents that have issued before an ANDA is filed. Moreover, West-Ward argues, even if the amended Paragraph IV certification could qualify as an act of infringement under § 271(e)(2), jurisdiction would still be lacking because the certification was not made before the 2014 suit was filed. West-Ward further argues that there is declaratory judgment jurisdiction over its claims for relief, but not over Vanda's claims for infringement.
We agree with Vanda that the district court had jurisdiction over this case. We have previously explained that:
By enacting § 271(e)(2), Congress thus established a specialized new cause of action for patent infringement. When patentees pursue this route, their claims necessarily arise under an Act of Congress relating to patents. In short, "[o]nce Congress creates an act of infringement, jurisdiction in the district courts is proper under 28 U.S.C. § 1338(a)."
AstraZeneca Pharm. LP v. Apotex Corp. (AstraZeneca II ), 669 F.3d 1370, 1377 (Fed. Cir. 2012) (alteration in original) (quoting Allergan, Inc. v. Alcon Labs., Inc., 324 F.3d 1322, 1330 (Fed. Cir. 2003) ). The Supreme Court has similarly explained that "the federal courts have jurisdiction over [a suit alleging infringement under § 271(e)(2) ] for a single, simple reason: It 'ar[ose] under a[n] Act of Congress relating to patents.' " Caraco Pharm. Labs., Ltd. v. Novo Nordisk A/S (Caraco II ), 566 U.S. 399, 412 n.5, 132 S.Ct. 1670, 182 L.Ed.2d 678 (2012) (second and third alterations in original) (quoting 28 U.S.C. § 1338(a) ).
Here, Vanda's complaint alleged that West-Ward infringed the '610 patent under 35 U.S.C. § 271(e)(2)(A) by filing the ANDA. J.A. 10002. Nothing more was required to establish the district court's subject matter jurisdiction pursuant to 28 U.S.C. § 1338(a). See AstraZeneca II , 669 F.3d at 1377 (explaining that "the requirements for jurisdiction in the district courts are met once a patent owner alleges that another's filing of an ANDA infringes its patent under § 271(e)(2), and this threshold jurisdictional determination does not depend on the ultimate merits of the claims").
West-Ward's arguments relating to whether there was a qualifying act of infringement raise potential merits problems, not jurisdictional issues. We have previously rejected the argument that a court's jurisdiction "hinged on whether [plaintiff] asserted a 'valid' claim under § 271(e)(2)." Id. The Supreme Court has similarly explained that "[t]he want of an infringing act [under § 271(e)(2) ] is a merits problem, not a jurisdictional one." Caraco II , 566 U.S. at 412 n.5, 132 S.Ct. 1670. Thus, whether Vanda alleged, and subsequently *1125proved, an infringing act is a merits question, not a jurisdictional one.
Moreover, an actual controversy has existed between the parties from the time when the suit was commenced. See Teva Pharm. USA, Inc. v. Novartis Pharm. Corp. , 482 F.3d 1330, 1339-45 (Fed. Cir. 2007) (reversing district court's conclusion that it lacked jurisdiction because there was no justiciable controversy between the ANDA applicant and NDA holder where there was a prior suit between the parties involving a different patent to which the ANDA applicant had submitted a Paragraph IV certification). "To qualify as a case fit for federal-court adjudication, 'an actual controversy must be extant at all stages of review,' " including " 'at the time the complaint is filed.' " Arizonans for Official English v. Arizona , 520 U.S. 43, 67, 117 S.Ct. 1055, 137 L.Ed.2d 170 (1997) (quoting Preiser v. Newkirk , 422 U.S. 395, 401, 95 S.Ct. 2330, 45 L.Ed.2d 272 (1975) ). Here, West-Ward had filed an ANDA and Vanda had sued it. The mere fact that West-Ward had not submitted a Paragraph IV certification for the '610 patent until after Vanda filed suit does not establish that there was not a justiciable controversy over which the court could exercise jurisdiction. See Glaxo, Inc. v. Novopharm, Ltd. , 110 F.3d 1562, 1569 (Fed. Cir. 1997) ("[ Section] 271(e)(2) provide[s] patentees with a defined act of infringement sufficient to create case or controversy jurisdiction to enable a court to promptly resolve any dispute concerning infringement and validity."); DuPont Merck Pharm. Co. v. Bristol-Myers Squibb Co. , 62 F.3d 1397, 1401 (Fed. Cir. 1995) (reversing a district court's determination in declaratory judgment action "that an actual controversy would only occur upon [ANDA applicants'] filing of paragraph IV certifications").5
Thus, the district court properly had jurisdiction over the '610 patent under the Hatch-Waxman Act.
II. Infringement
In a bench trial, infringement is a question of fact that we review for clear error. Alza Corp. v. Mylan Labs., Inc. , 464 F.3d 1286, 1289 (Fed. Cir. 2006). An infringement inquiry pursuant to 35 U.S.C. § 271(e)(2)(A)"is focused on a comparison of the asserted patent [claims] against 'the product that is likely to be sold following ANDA approval.'" Alcon Research Ltd. v. Barr Labs., Inc. , 745 F.3d 1180, 1186 (Fed. Cir. 2014) (quoting Abbott Labs. v. TorPharm, Inc. , 300 F.3d 1367, 1373 (Fed. Cir. 2002) ). The patentee bears the burden of proving infringement by a preponderance of the evidence. Warner-Lambert Co. v. Apotex Corp. , 316 F.3d 1348, 1366 (Fed. Cir. 2003).
A. The Applicability of 35 U.S.C. § 271(e)(2)(A)
We first address whether, beyond the jurisdictional question, a claim for infringement of the '610 patent under 35 U.S.C. § 271(e)(2)(A) can lie where the '610 patent issued after the original ANDA was submitted and Vanda sued West-Ward for infringement of the asserted claims prior to West-Ward submitting a Paragraph IV certification. The district court held that West-Ward's submission of the Paragraph IV certification for the '610 patent was an act of infringement. See Opinion , 203 F.Supp.3d at 433. We review the district court's statutory interpretation without deference. Warner-Lambert , 316 F.3d at 1355.
*1126Vanda argues that it proved an act of infringement under 35 U.S.C. § 271(e)(2). According to Vanda, "[w]here a patent issues after an ANDA is filed but before FDA approval, and where-as here-the applicant submits a Paragraph IV certification directed at the new patent, that amendment of the ANDA is an act of infringement under Section 271(e)(2)." Appellee Br. 60.
West-Ward responds that there can be no infringement under § 271(e)(2) because the ANDA was filed before the '610 patent issued. West-Ward contends that the statutorily defined act of infringement excludes amendments to an ANDA and "only reaches ANDAs submitted 'for a drug claimed in a patent or the use of which is claimed in a patent '-not a drug that might or might not later be claimed in a patent or one that has been claimed in a provisional patent application or a patent-pending." Reply Br. 33 (emphases in original) (quoting 35 U.S.C. § 271(e)(2)(A) ) (other internal quotation marks omitted).
The Hatch-Waxman Act amended the Federal Food, Drug, and Cosmetic Act and the patent laws to enable generic drugs to be more easily approved and to respond to loss of effective patent life resulting from the requirement that drug products require premarket testing and then must undergo FDA review, actions that consume significant portions of a patent term. See Eli Lilly & Co. v. Medtronic, Inc. , 496 U.S. 661, 669-70, 110 S.Ct. 2683, 110 L.Ed.2d 605 (1990). The Hatch-Waxman Act "str[ikes] a balance between two competing policy interests: (1) inducing pioneering research and development of new drugs and (2) enabling competitors to bring low-cost, generic copies of those drugs to market." Andrx Pharm., Inc. v. Biovail Corp. , 276 F.3d 1368, 1371 (Fed. Cir. 2002).
Section 202 of the Act, codified at 35 U.S.C. § 271(e)(2)(A), created an "artificial" act of infringement. Eli Lilly , 496 U.S. at 678, 110 S.Ct. 2683. That provision provides in relevant part:
It shall be an act of infringement to submit ... an application under section 505(j) of the Federal Food, Drug, and Cosmetic Act[, codified at 21 U.S.C. § 355(j),] ... for a drug claimed in a patent or the use of which is claimed in a patent , ... if the purpose of such submission is to obtain approval under such Act to engage in the commercial manufacture, use, or sale of a drug ... claimed in a patent or the use of which is claimed in a patent before the expiration of such patent.
35 U.S.C. § 271(e)(2) (emphases added). It "facilitates the early resolution of patent disputes between generic and pioneering drug companies by providing that the mere act of filing a Paragraph IV ANDA constitutes an act of patent infringement." Caraco Pharm. Labs., Ltd. v. Forest Labs., Inc. (Caraco I ), 527 F.3d 1278, 1283 (Fed. Cir. 2008). Litigation does not have to be delayed until actual sale of an accused product.
Although we agree with West-Ward that only an issued patent can give rise to a valid infringement claim under § 271(e)(2)(A), we disagree that that conclusion precludes Vanda's infringement claim in this case. The '610 patent is a patent "for a drug ... the use of which is claimed in a patent," 35 U.S.C. § 271(e)(2)(A), as contemplated in the Act even though it issued after West-Ward filed its ANDA. West-Ward subsequently amended its ANDA to include a Paragraph IV certification for the '610 patent after it issued. The infringement analysis under § 271(e)(2)(A)"require[s] consideration of the amended ANDA."
*1127Ferring B.V. v. Watson Labs., Inc.-Fla. , 764 F.3d 1382, 1390 (Fed. Cir. 2014). "There is no support for the proposition that the question of infringement must be addressed solely based on the initial ANDA filing, given that the statute contemplates that the ANDA will be amended as a matter of course." Id. Thus, amendments to an ANDA, including a Paragraph IV certification for a later-issued patent, can constitute an act of infringement under § 271(e)(2)(A). See Bristol-Myers Squibb Co. v. Royce Labs., Inc. , 69 F.3d 1130, 1135 (Fed. Cir. 1995) (holding that by amending an ANDA to include a Paragraph IV certification, the applicant "committed an act of infringement under the Hatch-Waxman Act because it sought 'to obtain approval ... to engage in the commercial manufacture, use, or sale of a drug ... claimed in a patent ... before the expiration of such patent' " (alternations in original) (quoting 35 U.S.C. § 271(e)(2)(A) ) ).
Here, it is undisputed that West-Ward amended the ANDA by submitting a Paragraph IV certification regarding the '610 patent after that patent issued. J.A. 19696; J.A. 6414-15; Appellant Br. 10; Appellee Br. 59. Such an act is a qualifying act of infringement under § 271(e)(2)(A).6 A filer of an ANDA is therefore subject to a § 271(e)(2)(A) infringement claim on a patent that issues after the filing of the ANDA, but before FDA approval. The resolution of infringement claims under § 271(e)(2)(A) for patents that issue after an ANDA is submitted, but before it is approved, "facilitates the early resolution of patent disputes between generic and pioneering drug companies" in accordance with the purpose of § 271(e)(2)(A). Caraco I , 527 F.3d at 1283.
The FDA regulatory framework and the legislative history further demonstrate that West-Ward is incorrect in asserting that "application" in § 271(e)(2)(A) excludes amendments to the ANDA. Sections 101 and 102 of the Hatch-Waxman Act amended the Federal Food, Drug, and Cosmetics Act to create an abbreviated regulatory pathway for approval of generic drugs, codified at 21 U.S.C. § 355(j), and to require NDA applicants to file certain patent information with the FDA, codified at 21 U.S.C. § 355(b)(1), (c)(2). NDA holders have a continuing obligation to amend the NDA to include the same patent information for patents that issue after the NDA is approved. See 21 U.S.C. § 355(c)(2). The FDA lists this patent information in the Orange Book.
ANDA applications must contain one of four certifications for patents "for which information is required to be filed under [ 21 U.S.C. § 355(b) or (c) ]": (1) "that such patent information has not been filed;" (2) "that such patent has expired;" (3) "the date on which such patent will expire;" and (4) "that such patent is invalid or will not be infringed by the manufacture, use, or sale of the new drug for which the application is submitted." 21 U.S.C. § 355(j)(2)(A)(vii). If the ANDA applicant makes a Paragraph IV certification, it must provide notice to the NDA holder of the certification. Id. § 355(j)(2)(B). Prior to FDA approval, ANDA applicants generally must amend or supplement ANDAs to submit an appropriate patent certification for patents that issue after submission of *1128the ANDA. See id. § 355(j)(2)(B)(ii)(II) ; 21 C.F.R. § 314.94(a)(12)(viii)(C)(ii). Thus, the regulatory framework expressly contemplates certifications for patents that issue after the ANDA is filed.
The type of certification under 21 U.S.C. § 355(j)(2)(A)(vii) impacts when FDA approval may be made effective. 21 U.S.C. § 355(j)(5). If an ANDA applicant submits a Paragraph IV certification, the statute provides for a thirty-month stay of effective FDA approval that may be shortened or lengthened in certain circumstances. Id. § 355(j)(5)(B)(iii). Congressional amendment of the thirty-month stay provision since the enactment of the Hatch-Waxman Act further supports the conclusion that "application" in 35 U.S.C. § 271(e)(2) includes amendments to the ANDA.
As originally enacted, the Hatch-Waxman Act provided for a thirty-month stay as long as the suit was brought within 45 days of receipt of the Paragraph IV notice. See Hatch-Waxman Act, Pub. L. 98-417, § 101, 98 Stat. at 1589. Multiple thirty-month stays could therefore be triggered for the same ANDA as a consequence of the ANDA applicant submitting Paragraph IV certifications and notices for patents listed in the Orange Book that issued both before and after the submission of the original ANDA application. See Andrx , 276 F.3d at 1378 (noting that FDA "treated the listing in the Orange Book of [a patent that issued after the ANDA was submitted] as requiring a new thirty-month stay of its approval of Andrx's ANDA").
In 2003, Congress amended 21 U.S.C. § 355(j) to eliminate the possibility of multiple thirty-month stays for the same ANDA. See Medicare Prescription Drug, Improvement, and Modernization Act of 2003 ("the MMA"), Pub. L. 108-173, § 1101, 117 Stat. 2066, 2449 (2003); H.R. Conf. Rep. No. 108-391, at 835-36 (2003), reprinted in 2003 U.S.C.C.A.N. 1808, 2187. The MMA changed the requirements to obtain a thirty-month stay to add that the patent information for the patent to which the Paragraph IV certification is directed must have been submitted to the FDA "before the date on which the [ANDA] application (excluding an amendment or supplement to the application) ... was submitted." MMA, Pub. L. 108-173, § 1101(a)(2), 117 Stat. at 2449 (emphasis added) (codified at 21 U.S.C. § 355(j)(5)(B)(iii) ). The MMA did not contain a corresponding amendment to 35 U.S.C. § 271(e)(2) to exclude amendments and supplements to the ANDA as cognizable acts of infringement even though it amended § 271(e) in other ways. Id. § 1101(d), 117 Stat. at 2457. This history thus further supports the conclusion that "application" in § 271(e)(2) includes amendments to the ANDA. See Gross v. FBL Fin. Servs., Inc. , 557 U.S. 167, 174, 129 S.Ct. 2343, 174 L.Ed.2d 119 (2009) ("When Congress amends one statutory provision but not another, it is presumed to have acted intentionally."). Thus, the district court properly conducted its infringement analysis for the '610 patent pursuant to 35 U.S.C. § 271(e)(2)(A).
B. Inducement7
We now turn to the merits of the infringement finding. West-Ward argues that the district court clearly erred in finding that it would induce infringement because Vanda failed to prove the requisite direct infringement and specific intent to induce infringement. Vanda responds that the district court correctly found that *1129West-Ward will induce infringement of the asserted claims.
The statute provides that "[w]hoever actively induces infringement of a patent shall be liable as an infringer." 35 U.S.C. § 271(b). However, direct infringement is a necessary predicate for a finding of induced infringement in the usual patent infringement case. Limelight Networks, Inc. v. Akamai Techs., Inc. , --- U.S. ----, 134 S.Ct. 2111, 2117, 189 L.Ed.2d 52 (2014). It also "must be established that the defendant possessed specific intent to encourage another's infringement and not merely that the defendant had knowledge of the acts alleged to constitute inducement." DSU Med. Corp. v. JMS Co. , 471 F.3d 1293, 1306 (Fed. Cir. 2006) (en banc in relevant part) (internal quotation omitted). Circumstantial evidence can support a finding of specific intent to induce infringement. AstraZeneca LP v. Apotex, Inc. (AstraZeneca I ), 633 F.3d 1042, 1060 (Fed. Cir. 2010) (citing Water Techs. Corp. v. Calco, Ltd. , 850 F.2d 660, 668 (Fed. Cir. 1988) ).
We have held that "[i]nducement can be found where there is '[e]vidence of active steps taken to encourage direct infringement,' which can in turn be found in 'advertising an infringing use or instructing how to engage in an infringing use.' " Takeda Pharm. U.S.A., Inc. v. W.-Ward Pharm. Corp. , 785 F.3d 625, 630-31 (Fed. Cir. 2015) (second alteration in original) (quoting Metro-Goldwyn-Mayer Studios Inc. v. Grokster, Ltd. , 545 U.S. 913, 936, 125 S.Ct. 2764, 162 L.Ed.2d 781 (2005) ). Where "the proposed label instructs users to perform the patented method ... the proposed label may provide evidence of [the ANDA applicant's] affirmative intent to induce infringement." AstraZeneca I , 633 F.3d at 1060. When proof of specific intent depends on the label accompanying the marketing of a drug inducing infringement by physicians, "[t]he label must encourage, recommend, or promote infringement." Takeda , 785 F.3d at 631. The contents of the label itself may permit the inference of specific intent to encourage, recommend, or promote infringement. See Sanofi v. Watson Labs. Inc. , 875 F.3d 636, 646 (Fed. Cir. 2017).
West-Ward argues that the district court clearly erred in finding that its proposed label "satisfies" the asserted claims because the language of the label itself cannot constitute direct infringement of the asserted method claims. See Opinion , 203 F.Supp.3d at 432. West-Ward also contends that the court clearly erred in finding that Dr. Alva practiced the asserted claims because he never administered an allegedly infringing dose to a poor metabolizer.
Vanda responds that it did not need to prove instances of direct infringement by physicians because this is a Hatch-Waxman case where infringement is statutorily-defined to be the filing of an ANDA or an amendment thereto, not by selling a product. Even though not required, Vanda contends, it identified a doctor, Dr. Alva, who practiced the steps of the asserted claims with Fanapt®. Vanda argues that the asserted claims do not require that a single physician administer iloperidone to both poor and non-poor CYP2D6 metabolizers, and that West-Ward's argument to the contrary is waived because it was raised for the first time on appeal.
We agree with Vanda that a patentee does not need to prove an actual past instance of direct infringement by a physician to establish infringement under 35 U.S.C. § 271(e)(2)(A). As we have explained, " section 271(e)(2)(A) makes it possible for a patent owner to have the court determine whether, if a particular drug were put on the market, it would infringe the relevant patent."
*1130Bristol-Myers Squibb , 69 F.3d at 1135 (emphases in original). A § 271(e)(2)(A) infringement suit differs from typical infringement suits in that the infringement inquiries "are hypothetical because the allegedly infringing product has not yet been marketed." Warner-Lambert , 316 F.3d at 1365 (emphasis added); see also Glaxo , 110 F.3d at 1570 ("The relevant inquiry is whether patentee has proven by a preponderance of the evidence that the alleged infringer will likely market an infringing product.").
Similarly, patentees in Hatch-Waxman litigations asserting method patents do not have to prove that prior use of the NDA-approved drug satisfies the limitations of the asserted claims. See, e.g. , Sanofi , 875 F.3d at 643 (affirming inducement finding where the district court found "the inducing act will be the marketing by [ANDA applicants] of their generic dronedarone drugs with the label described" and "the induced act will be the administration of dronedarone by medical providers to patients meeting the criteria set forth in the [claims at issue]"); Eli Lilly & Co. v. Teva Parenteral Meds., Inc. , 845 F.3d 1357, 1368 (Fed. Cir. 2017) (explaining "we have not required evidence regarding the general prevalence of the induced activity"); AstraZeneca I , 633 F.3d at 1057 (affirming district court's grant of a preliminary injunction based on claims of induced infringement where the district court found that "the proposed label would cause some users to infringe the asserted method claims"); see also Warner-Lambert , 316 F.3d at 1364 ("The infringement case is therefore limited to an analysis of whether what the generic drug maker is requesting authorization for in the ANDA would be an act of infringement if performed.").
Accordingly, Vanda can satisfy its burden to prove the predicate direct infringement by showing that if the proposed ANDA product were marketed, it would infringe the '610 patent. The district court made factual findings that the proposed label "recommends" that physicians perform the claimed steps, see Opinion , 203 F.Supp.3d at 432-33, and its analysis of the proposed label to assess potential direct infringement by physicians was proper under our precedent. See, e.g. , Ferring B.V. v. Watson Labs., Inc.-Fla. , 764 F.3d 1401, 1408 (Fed. Cir. 2014) ("The infringement determination is thus based on consideration of all the relevant evidence, and because drug manufacturers are bound by strict statutory provisions to sell only those products that comport with the ANDA's description of the drug, the ANDA itself dominates the analysis." (internal quotation marks and alterations omitted) ); AstraZeneca I , 633 F.3d at 1060 (explaining that the district court "correctly determined" that language in the ANDA label "would inevitably lead some consumers to practice the claimed method").
Turning to specific intent, West-Ward argues that Vanda failed to prove that its proposed label would " 'encourage' or 'recommend' a direct infringer (a psychiatrist or other physician) to perform each step of the claimed methods." Appellant Br. 36 (quoting Takeda , 785 F.3d at 631 ). West-Ward contends that the substantial number of noninfringing uses precludes a finding of specific intent as a matter of law. See Warner-Lambert , 316 F.3d at 1365.
Vanda responds that the district court did not clearly err in finding that the proposed label recommends performance of all the claimed steps. Vanda argues that potential noninfringing uses do not preclude a finding of specific intent to induce infringement in this case.
We agree with Vanda that the district court did not clearly err in finding induced infringement of independent claims 1, 9, *1131and 13.8 Section 2 of the proposed label is entitled "Dosage and Administration." J.A. 15105 § 2. Section 2.1 entitled, "Usual Dose," states:
Iloperidone must be titrated slowly from a low starting dose.... The recommended starting dose for iloperidone tablets is 1 mg twice daily. Dose increases to reach the target range of 6 to 12 mg twice daily (12 to 24 mg/day ) may be made with daily dosage adjustments not to exceed 2 mg twice daily (4 mg/day). The maximum recommended dose is 12 mg twice daily (24 mg/day ).... Prescribers should be mindful of the fact that patients need to be titrated to an effective dose of iloperidone.
Id. § 2.1 (emphases added). Section 2.2, entitled "Dosage in Special Populations," states: "Dosage adjustment for patients taking iloperidone who are poor metabolizers of CYP2D6: Iloperidone dose should be reduced by one-half for poor metabolizers of CYP2D6 [see Pharmacokinetics (12.3) ]." Id. § 2.2 (second emphasis added).
Section 12.3 of the proposed label, entitled "Pharmacokinetics," states:
Approximately 7 to 10% of Caucasians and 3 to 8% of Black/African Americans lack the capacity to metabolize CYP2D6 substrates and are classified as poor metabolizers (PM), whereas the rest are intermediate, extensive or ultrarapid metabolizers. Co-administration of iloperidone with known strong inhibitors of CYP2D6 like fluoxetine results in a 2.3 fold increase in iloperidone plasma exposure, and therefore one-half of the iloperidone dose should be administered.
Similarly, PMs of CYP2D6 have higher exposure to iloperidone compared with [extensive metabolizers] and PMs should have their dose reduced by one-half. Laboratory tests are available to identify CYP2D6 PMs .
J.A. 15121 § 12.3 (emphasis added).
Thus, the district court did not clearly err in finding that § 12.3 "recommends that practitioners perform or have performed a genotyping assay to determine whether patients are CYP2D6 poor metabolizers." Opinion , 203 F.Supp.3d at 432. Experts for both parties testified that the referred-to "laboratory tests" are "genotyping tests." J.A. 6939 (234:8-235:13) (Vanda's expert); J.A. 7103-04 (566:10-568:2) (West-Ward's expert). The district court thus found that "when the label states that 'laboratory tests' are available to identify poor metabolizers, the label is referring to 'genotyping tests.' " Opinion , 203 F.Supp.3d at 433 (citing testimony of both parties' experts). We discern no clear error in this finding.
The label instructs practitioners that "PMs should have their dose reduced by one-half. [Genotyping tests] are available to identify CYP2D6 PMs." J.A. 15121 § 12.3. The court did not clearly err in finding that this constitutes a recommendation to perform genotyping tests on iloperidone patients. That West-Ward introduced other evidence that could have supported a contrary finding does not compel the conclusion that the district court clearly erred. See *1132Anderson v. City of Bessemer City , 470 U.S. 564, 574, 105 S.Ct. 1504, 84 L.Ed.2d 518 (1985) ("Where there are two permissible views of the evidence, the factfinder's choice between them cannot be clearly erroneous."). Moreover, the court's decision to credit the plausible testimony of certain witnesses and reject the testimony of West-Ward's witness as not credible, Opinion , 203 F.Supp.3d at 433, "can virtually never be clear error," Anderson , 470 U.S. at 575, 105 S.Ct. 1504.
We reject West-Ward's contention that the lack of an express finding by the district court that the label recommends obtaining a biological sample requires a remand. The district court found induced infringement of the independent claims, which necessarily required a finding of inducement of the limitation requiring "obtaining or having obtained a biological sample from the patient." '610 patent col. 17 ll. 7-8 (claim 1), col. 18 ll. 9-10 (claim 9), col. 18 ll. 34-35 (claim 13). West-Ward has pointed to no evidence in the record to dispute the testimony of Vanda's witnesses at trial that the genotyping assays the court found were recommended by the label require obtaining a biological sample. J.A. 6928 (190:14-191:1); J.A. 6939 (235:18-23). Given this undisputed evidence and the court's finding that the label recommends genotyping assays, we see no clear error in the court's implicit finding that the proposed label recommends obtaining a biological sample. See, e.g. , Para-Ordnance Mfg., Inc. v. SGS Importers Int'l, Inc. , 73 F.3d 1085, 1090 (Fed. Cir. 1995) (explaining that "[f]rom the decision of the district court, we can, and do, accept the implicit fact-finding").
The district court also did not clearly err in finding that "[t]he label recommends oral administration of iloperidone tablets at 12 to 24 mg/day to non-genotypic CYP2D6 poor metabolizers and 12 mg/day or less to genotypic CYP2D6 poor metabolizers." Opinion , 203 F.Supp.3d at 432 (citing J.A. 15105 §§ 2.1, 2.2). The label recommends a "[u]sual" target dose range (12 to 24 mg/day) and maximum dose (24 mg/day) and then instructs medical providers to "reduce[ ]" the dose for genetic CYP2D6 poor metabolizers (a "[s]pecial population") "by one-half." J.A. 15015 §§ 2.1, 2.2; see also J.A. 15103; J.A. 15121 § 12.3. A one-half reduction of the usual dose amounts yields a target dose range of 6 to 12 mg/day and a maximum dose of 12 mg/day for poor metabolizers. That the label also directs a medical provider to titrate the dosage does not negate its clear recommendations on ultimate dosage range and maximum amount.
Similarly, the fact that the target dose range for genotypic non-poor metabolizers (12 to 24 mg/day) includes 12 mg/day does not compel a finding of noninfringement. The independent claims require administering "greater than 12 mg/day, up to 24 mg/day" of iloperidone to non-poor metabolizers. '610 patent col. 17 ll. 17-20 (claim 1), col. 18 ll. 16-18 (claim 9), col. 18 ll. 44-47 (claim 13). Even if not every practitioner will prescribe an infringing dose, that the target dose range "instructs users to perform the patented method" is sufficient to "provide evidence of [West-Ward's] affirmative intent to induce infringement." AstraZeneca I , 633 F.3d at 1060 ; see also Eli Lilly , 845 F.3d at 1369 (explaining that "evidence that the product labeling that Defendants seek would inevitably lead some physicians to infringe establishes the requisite intent for inducement").
Finally, West-Ward's reliance on Warner-Lambert , an off-label use case, is misplaced. In Warner-Lambert , we explained that "it defies common sense to expect that [ANDA applicant] will actively promote the sale of its approved [ANDA product], in contravention of FDA regulations, for a *1133use that (a) might infringe [NDA holder's] patent and (b) constitutes such a small fraction of total sales." Warner-Lambert , 316 F.3d at 1365. In the context of that off-label use case where there were "substantial noninfringing uses," we declined to "infer" intent to induce infringement. Id. Here, the district court found that the proposed label itself recommends infringing acts.
Accordingly, even if the proposed ANDA product has "substantial noninfringing uses," West-Ward may still be held liable for induced infringement. " Section 271(b), on inducement, does not contain the 'substantial noninfringing use' restriction of section 271(c), on contributory infringement." Sanofi , 875 F.3d at 646. Thus, "a person can be liable for inducing an infringing use of a product even if the product has substantial noninfringing uses...." Id. (citing Grokster , 545 U.S. at 934-37, 125 S.Ct. 2764 ).
III. Patent Subject Matter Eligibility
We next address whether the asserted claims are directed to patent-eligible subject matter. West-Ward argues that the asserted claims are ineligible under § 101 because they are directed to a natural relationship between iloperidone, CYP2D6 metabolism, and QT prolongation, and add nothing inventive to those natural laws and phenomena. West-Ward contends that the asserted claims are indistinguishable from those held invalid in Association for Molecular Pathology v. Myriad Genetics, Inc. , 569 U.S. 576, 133 S.Ct. 2107, 186 L.Ed.2d 124 (2013) and Mayo Collaborative Services v. Prometheus Laboratories, Inc. , 566 U.S. 66, 132 S.Ct. 1289, 182 L.Ed.2d 321 (2012).
Vanda responds that the asserted claims are patent-eligible under § 101 at both steps of Mayo / Alice . Vanda contends that the district court erred in holding that the asserted claims are directed to a law of nature. According to Vanda, the court's "conclusions that the asserted claims 'depend upon,' 'touch[ ] upon,' and 'address' laws of nature and natural phenomena do not, as a matter of law, establish that the asserted claims are directed to a patent-ineligible concept under Step 1 of the Alice / Mayo analysis." Appellee Br. 45 (alteration and emphasis in original).
Section 101 of the Patent Act states that "[w]hoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title." 35 U.S.C. § 101. However, § 101"contains an important implicit exception": " 'laws of nature, natural phenomena, and abstract ideas' are not patentable." Mayo , 566 U.S. at 70, 132 S.Ct. 1289 (alteration omitted) (quoting Diamond v. Diehr , 450 U.S. 175, 185, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981) ).
The Supreme Court has established a two-step framework to determine patent subject matter eligibility under 35 U.S.C. § 101 :
First, we determine whether the claims at issue are directed to one of those patent-ineligible concepts. If so, we then ask, "[w]hat else is there in the claims before us?" To answer that question, we consider the elements of each claim both individually and "as an ordered combination" to determine whether the additional elements "transform the nature of the claim" into a patent-eligible application. We have described step two of this analysis as a search for an " 'inventive concept' "-i.e., an element or combination of elements that is "sufficient to ensure that the patent in practice amounts to significantly more than a patent upon the [ineligible concept] itself."
*1134Alice Corp. Pty. v. CLS Bank Int'l , --- U.S. ----, 134 S.Ct. 2347, 2355, 189 L.Ed.2d 296 (2014) (citations omitted) (alteration in original) (quoting Mayo , 566 U.S. at 72-73, 75-79, 132 S.Ct. 1289 ).
Step one requires determining "whether the claims at issue are directed to one of those patent-ineligible concepts." Id. (emphasis added); see also Enfish, LLC v. Microsoft Corp. , 822 F.3d 1327, 1335 (Fed. Cir. 2016). The Supreme Court has cautioned that "too broad an interpretation of" ineligible subject matter "could eviscerate patent law" because "all inventions at some level embody, use, reflect, rest upon, or apply laws of nature, natural phenomena, or abstract ideas." Mayo , 566 U.S. at 71, 132 S.Ct. 1289. Accordingly, at step one, "it is not enough to merely identify a patent-ineligible concept underlying the claim; we must determine whether that patent-ineligible concept is what the claim is 'directed to.' " Rapid Litig. Mgmt. Ltd. v. CellzDirect, Inc. , 827 F.3d 1042, 1050 (Fed. Cir. 2016). If the claims are not directed to a patent ineligible concept at step one, we need not address step two of the inquiry. See Enfish, 822 F.3d at 1339. That is the case here.
Consistent with Supreme Court precedent, we agree with Vanda that the asserted claims are not directed to patent-ineligible subject matter.9 Claim 1 recites "[a] method for treating a patient with iloperidone, wherein the patient is suffering from schizophrenia." '610 patent col. 17 ll. 2-3. Claim 1 requires specific steps: (1) determining the patient's CYP2D6 metabolizer genotype by (a) obtaining a biological sample and (b) performing a genotyping assay; and (2) administering specific dose ranges of iloperidone depending on the patient's CYP2D6 genotype. Id. col. 17 ll. 2-25.
West-Ward contends that the Supreme Court held that similar claims were patent ineligible in Mayo and Myriad . The patent in Mayo claimed a method for "optimizing" the dosage of thiopurine drugs by administering thiopurine drugs to a patient and measuring the level of certain metabolites in the blood, wherein the level of metabolites indicates whether to adjust the dosage. Mayo , 566 U.S. at 74-75, 132 S.Ct. 1289. The Supreme Court held that the claims recited a natural law, and did not include any "additional features that provide practical assurance that the process is more than a drafting effort designed to monopolize the law of nature itself." Id. at 77, 132 S.Ct. 1289.
This case, however, is not Mayo . First, the claims in Mayo were not directed to a novel method of treating a disease. Instead, the claims were directed to a diagnostic method based on the "relationships between concentrations of certain metabolites in the blood and the likelihood that a dosage of a thiopurine drug will prove ineffective or cause harm." Id. This "relation is a consequence of the ways in which thiopurine compounds are metabolized by the body-entirely natural processes. And so a patent that simply describes that relation sets forth a natural law." Id.
Although the representative claim in Mayo recited administering a thiopurine drug to a patient, the claim as a whole was not directed to the application of a drug to treat a particular disease. See id. at 74, 87, 132 S.Ct. 1289. Importantly, the Supreme Court explained that the administering step was akin to a limitation that tells engineers to apply a known natural relationship or to apply an abstract idea with computers. See id. at 78, 132 S.Ct. 1289 *1135(comparing the claim in Mayo to "Einstein telling linear accelerator operators about his basic law and then trusting them to use it where relevant"). To further underscore the distinction between method of treatment claims and those in Mayo , the Supreme Court noted that "[u]nlike, say, a typical patent on a new drug or a new way of using an existing drug, the patent claims do not confine their reach to particular applications of those laws." Id. at 87, 132 S.Ct. 1289.
In this case, the '610 patent claims are directed to a method of using iloperidone to treat schizophrenia. The inventors recognized the relationships between iloperidone, CYP2D6 metabolism, and QTc prolongation, but that is not what they claimed. They claimed an application of that relationship. Unlike the claim at issue in Mayo , the claims here require a treating doctor to administer iloperidone in the amount of either (1) 12 mg/day or less or (2) between 12 mg/day to 24 mg/day, depending on the result of a genotyping assay. The specification further highlights the significance of the specific dosages by explaining how certain ranges of administered iloperidone correlate with the risk of QTc prolongation. See, e.g. , '610 patent at col. 4 ll. 1-15. Thus, the '610 patent claims are "a new way of using an existing drug" that is safer for patients because it reduces the risk of QTc prolongation. Mayo , 566 U.S. at 87, 132 S.Ct. 1289.
Moreover, unlike the claim in Mayo , to the extent that preemption is a concern, the '610 patent claims do not "tie up the doctor's subsequent treatment decision." Id. at 86, 132 S.Ct. 1289. The claim in Mayo did not go beyond recognizing (i.e. , "indicates") a need to increase or decrease a dose. Id. at 75, 132 S.Ct. 1289. In Mayo , "a doctor ... could violate the patent even if he did not actually alter his treatment decision in the light of the test." Id. The claim was not a treatment claim. It was "not limited to instances in which the doctor actually decreases (or increases) the dosage level where the test results suggest that such an adjustment is advisable." Id. at 76, 132 S.Ct. 1289. Thus, the claim in Mayo did not involve doctors using the natural relationship between the metabolite level and lessening "the likelihood that a dosage of a thiopurine drug will prove ineffective or cause harm." Id. at 77, 132 S.Ct. 1289. The claims in Mayo therefore "tie up the doctor's subsequent treatment decision whether that treatment does, or does not, change in light of the inference he has drawn using the correlations. And they threaten to inhibit the development of more refined treatment recommendations...." Id. at 86-87, 132 S.Ct. 1289.
Here, the '610 patent claims recite the steps of carrying out a dosage regimen based on the results of genetic testing. The claims require doctors to "internally administer[ ] iloperidone to the patient in an amount of 12 mg/day or less" if the patient has a CYP2D6 poor metabolizer genotype; and "internally administer[ ] iloperidone to the patient in an amount that is greater than 12 mg/day, up to 24 mg/day" if the patient does not have a CYP2D6 poor metabolizer genotype. '610 patent col. 17 ll. 13-20. These are treatment steps. In contrast, as shown above, the claim in Mayo stated that the metabolite level in blood simply "indicates" a need to increase or decrease dosage, without prescribing a specific dosage regimen or other added steps to take as a result of that indication. Mayo , 566 U.S. at 75, 132 S.Ct. 1289. Here, the claims do not broadly "tie up the doctor's subsequent treatment decision." Id. at 86, 132 S.Ct. 1289.
Our decision in CellzDirect supports concluding that these claims are patent eligible. In that case, we held that "a method of producing a desired preparation of *1136multi-cryopreserved hepatocytes cells" was patent eligible. CellzDirect , 827 F.3d at 1047. We explained that "[t]he end result of the ... claims is not simply an observation or detection of the ability of hepatocytes to survive multiple freeze-thaw cycles. Rather, the claims [were] directed to a new and useful method of preserving hepatocyte cells." Id. at 1048. We further emphasized that "the natural ability of the subject matter to undergo the process does not make the claim 'directed to' that natural ability." Id. at 1049 (emphasis in original). Otherwise, claims directed to actually "treating cancer with chemotherapy" or "treating headaches with aspirin" would be patent ineligible. Id.
Nor does Myriad compel a different outcome. The Supreme Court in Myriad held "that a naturally occurring DNA segment is a product of nature and not patent eligible merely because it has been isolated, but that cDNA is patent eligible because it is not naturally occurring." Myriad , 569 U.S. at 580, 133 S.Ct. 2107. The Court was careful to note that "method claims" and "patents on new applications of knowledge about [particular] genes" were "not implicated by [its] decision." Id. 595-96, 133 S.Ct. 2107 (emphasis in original). The '610 patent does not claim naturally occurring DNA segments. Rather, the asserted claims fall squarely within categories of claims that the Court stated were not implicated by its decision.
At bottom, the claims here are directed to a specific method of treatment for specific patients using a specific compound at specific doses to achieve a specific outcome. They are different from Mayo . They recite more than the natural relationship between CYP2D6 metabolizer genotype and the risk of QTc prolongation. Instead, they recite a method of treating patients based on this relationship that makes iloperidone safer by lowering the risk of QTc prolongation. Accordingly, the claims are patent eligible.
IV. Written Description
We next consider West-Ward's argument that the district court erred in finding that the claims are not invalid for lack of adequate written description. To satisfy the written description requirement the patent disclosure must "reasonably convey[ ] to those skilled in the art that the inventor had possession of the claimed subject matter as of the filing date." Ariad Pharm., Inc. v. Eli Lilly & Co. , 598 F.3d 1336, 1351 (Fed. Cir. 2010) (en banc). Whether a claim satisfies the written description requirement is a question of fact that we review for clear error following a bench trial. Alcon Research , 745 F.3d at 1190.
West-Ward argues that the asserted claims are invalid for lack of written description because nothing in the '610 patent demonstrates possession of the claimed dosage ranges for poor and non-poor CYP2D6 metabolizer genotypes. West-Ward contends that the description does not contain experiments with doses of 12 mg/day or less given to poor metabolizers, and reports data that does not support the claimed poor-metabolizer dose range.
Vanda responds that the district court did not clearly err in finding that the '610 patent adequately describes the claimed dosages for poor metabolizers. Vanda contends that West-Ward waived any written description challenge to the dosages for non-poor metabolizers, and that West-Ward's argument is, in any event, meritless.
We agree with Vanda that the district court did not clearly err in finding that the '610 patent contains adequate written description for the claimed "12 mg/day or less" dosage range for poor metabolizers. The patent reports the results of tests *1137comparing the concentrations of P88 and P95, iloperidone's two main metabolites, and changes in QTc interval upon administration of doses of iloperidone, both with and without the addition of a CYP2D6 inhibitor, to individuals with wildtype or a poor metabolizer genotype associated with two common CYP2D6 polymorphisms. '610 patent col. 4 l. 62-col. 10 l. 56. The patent reports that "QTc prolongation is correlated to the ratios of P88/P95 and (iloperidone+P88)/P95." Id. col. 9 ll. 57-58.
The '610 patent further explains that the reported results "show that patients can be more safely treated with iloperidone if the dose of iloperidone is adjusted based on the CYP2D6 genotype of each patient," id . col. 9 ll. 31-34; accord id. col. 2 ll. 15-24, and provides examples of such doses, id. col. 9 ll. 34-47, col. 11 ll. 22-28. For a poor metabolizer, those examples include reducing the dose of iloperidone administered by "75% or less, 50% or less, or 25% or less of the dose typically administered to a patient having a CYP2D6 genotype that results in a CYP2D6 protein" with wildtype activity. Id. col. 9 ll. 34-43. The patent then provides a specific example of a dose for non-poor metabolizers, "24 mg per day," and the appropriate reduction for a poor metabolizer "reduced dosage of 18, 12, or 6 mg per day." Id . col. 9 ll. 43-47. The disclosure of a dose outside of the claimed range does not compel a finding that the asserted claims lack adequate written description. See Scriptpro, LLC v. Innovation Assocs., Inc. , 762 F.3d 1355, 1359 (Fed. Cir. 2014) ("It is common, and often permissible, for particular claims to pick out a subset of the full range of described features, omitting others.").
The district court heard testimony that the data reported in the '610 patent show a trend for higher QTc prolongation among genotypic CYP2D6 poor metabolizers given a 24 mg/day dose, and support a reduction in dose for CYP2D6 poor metabolizers by a factor of 1.5 to 3.5. West-Ward introduced some testimony challenging the sufficiency of the data and the lack of statistical analysis, but that does not render the court's reliance on testimony supporting validity impermissible. See Anderson , 470 U.S. at 574-75, 105 S.Ct. 1504. On this record, we cannot say that the district court clearly erred in finding that the '610 patent sufficiently discloses the claimed range for poor metabolizers.
Moreover, West-Ward waived its written description challenge with respect to non-poor metabolizers by failing to properly present it to the trial court. The Supreme Court has observed that as a "general rule ... a federal appellate court does not consider an issue not passed upon below." Singleton v. Wulff , 428 U.S. 106, 120, 96 S.Ct. 2868, 49 L.Ed.2d 826 (1976). Although appellate courts have discretion to decide when to deviate from this general waiver rule, see id. at 121, 96 S.Ct. 2868, West-Ward has not articulated a basis for us to reach this issue for the first time on appeal and we discern none, see HTC Corp. v. IPCom GmbH & Co., KG , 667 F.3d 1270, 1282-83 (Fed. Cir. 2012).
West-Ward points only to a single page in each of its opening and reply post-trial briefs to support its claim that this issue is not waived. Those pages make passing reference to the dosage range for non-poor metabolizers in the context of the written description arguments West-Ward advanced for poor metabolizers. West-Ward does not point us to any argument or evidence that it advanced before the district court specifically with respect to non-poor metabolizers. Indeed, West-Ward did not identify lack of written description with respect to non-poor metabolizer dose range in its pretrial submissions identifying the issues to be tried. West-Ward has thus waived any further argument that the *1138non-poor metabolizer dosage range was not adequately supported by the written description.
V. Injunctive Relief
We finally address the propriety of the injunctive relief awarded by the district court. West-Ward argues that the injunctions were not supported by the courts "general equitable power," and the lack of jurisdiction or an infringing act under 35 U.S.C. § 271(e)(2) precludes upholding the injunctions under 35 U.S.C. § 271(e)(4). West-Ward contends that "the FDA has independently determined that litigation over the '610 patent should not delay approval of iloperidone ANDAs filed before the patent issued and was submitted to the agency." Appellant Br. 62 (citing https://www.accessdata.fda.gov/drugsatfda_docs/appletter/2016/207231Orig1s000ltr.pdf). West-Ward further argues that because Vanda did not cross-appeal the denial of an injunction under 35 U.S.C. § 271(e)(4) that provision cannot be an alternative ground to uphold the FDA injunction.
Vanda responds that the district court's injunctions can be affirmed under 35 U.S.C. § 271(e)(4) and that the court erred in not granting relief pursuant to that provision. In any event, Vanda contends that the district court did not err in granting injunctive relief pursuant to its equitable powers against West-Ward.
We agree with Vanda that 35 U.S.C. § 271(e)(4) supports the injunctive relief granted by the district court. As discussed above, the district court properly held that Vanda had established infringement of the '610 patent under § 271(e)(2). Section 271(e)(4) provides in relevant part:
For an act of infringement described in paragraph (2)-
(A) the court shall order the effective date of any approval of the drug or veterinary biological product involved in the infringement to be a date which is not earlier than the date of the expiration of the patent which has been infringed,
(B) injunctive relief may be granted against an infringer to prevent the commercial manufacture, use, offer to sell, or sale within the United States or importation into the United States of an approved drug, veterinary biological product, or biological product,
...
The remedies prescribed by subparagraphs (A), (B), (C), and (D) are the only remedies which may be granted by a court for an act of infringement described in paragraph (2), except that a court may award attorney fees under section 285.
35 U.S.C. § 271(e)(4). Section 271(e)(4) contains no carve-out for patents that issue after the date of submission of the original ANDA. Moreover, the statute explicitly states that "the only remedies" a court may grant following an infringement finding under § 271(e)(2) are pursuant to § 271(e)(4)(A)-(D) and attorney fees pursuant to § 285. Accordingly, upon a finding of patent infringement under § 271(e)(2), the district court must order remedies in accordance with § 271(e)(4).
West-Ward's reliance on the FDA's letter approving a different company's ANDA 20-7231 for iloperidone tablets is misplaced. The letter indicates that because the '610 patent was "submitted to the [FDA] after submission of [that] ANDA," litigation with respect to the '610 patent"would not create a statutory stay of approval." https://www.accessdata.fda.gov/drugsatfda_docs/appletter/2016/207231Orig1s000ltr.pdf. The FDA letter merely recognizes that the issuance of the '610 patent after submission of that ANDA
*1139renders the thirty-month statutory stay inapplicable. See 21 U.S.C. § 355(j)(5)(B)(iii) (providing that triggering of thirty-month stay requires, inter alia , that the NDA holder submit necessary "patent information before the date on which the application (excluding an amendment or supplement to the application ) ... was submitted" (emphasis added) ). It says nothing about whether the FDA would or would not change the effective approval date of the ANDA pursuant to a 35 U.S.C. § 271(e)(4)(A) court order if the '610 patent were found valid and infringed. West-Ward's argument thus improperly conflates the requirements to obtain a thirty-month stay under § 355(j)(5)(B)(iii) with the relief available pursuant to § 271(e)(4) following a finding of patent infringement under § 271(e)(2).
In fact, where "the FDA has already approved the ANDA, the district court's [ § 271(e)(4)(A) ] order would [only] alter the effective date of the application, thereby converting a final approval into a tentative approval." In re Omeprazole Patent Litig. , 536 F.3d 1361, 1367-68 (Fed. Cir. 2008) ; see also Mylan Labs., Inc. v. Thompson , 389 F.3d 1272, 1281-84 (D.C. Cir. 2004) (affirming revocation of final FDA approval of an ANDA and resetting of the effective approval date following a judgment of patent infringement pursuant to the district court's § 271(e)(4)(A) order where the infringement suit was filed too late to trigger the 30-month stay). And the FDA is entitled not to set an approval date prior to the expiration of a patent that has been found to be infringed under § 271(e)(4)(A) and not invalid in a Hatch-Waxman case. The district court's authority to grant the remedies provided in 35 U.S.C. § 271(e)(4) following a judgment of patent infringement under § 271(e)(2) is not limited to those circumstances expressly listed in 21 U.S.C. § 355(j)(5)(B)(iii). See Ortho-McNeil Pharm., Inc. v. Mylan Labs., Inc. , 520 F.3d 1358, 1366 (Fed. Cir. 2008) ("The district court was correct to reset the effective date of an ANDA directly under 35 U.S.C. § 271 without going through 21 U.S.C. § 355.").
Because we sustain the district court's infringement finding under § 271(e)(2), we also affirm the court's grant of injunctive relief. Although the district court erred in concluding that the remedies pursuant to § 271(e)(4) were unavailable, the court granted Vanda injunctive relief consistent with those remedies. We may thus affirm the district court's grant of injunctive relief pursuant to § 271(e)(4).
Additionally, Vanda did not need to file a cross-appeal to allow us to affirm the district court's grant of injunctive relief with respect to the FDA. Without filing a cross-appeal, "an appellee may 'urge in support of a decree any matter appearing in the record, although his argument may involve an attack upon the reasoning of the lower court,' but may not 'attack the decree with a view either to enlarging his own rights thereunder or of lessening the rights of his adversary.' " El Paso Nat. Gas Co. v. Neztsosie , 526 U.S. 473, 479, 119 S.Ct. 1430, 143 L.Ed.2d 635 (1999) (quoting United States v. Am. Ry. Exp. Co. , 265 U.S. 425, 435, 44 S.Ct. 560, 68 L.Ed. 1087 (1924) ); see also Radio Steel & Mfg. Co. v. MTD Prods., Inc. , 731 F.2d 840, 844 (Fed. Cir. 1984) (holding that "a party will not be permitted to argue before us an issue on which it has lost and on which it has not appealed, where the result of acceptance of its argument would be a reversal or modification of the judgment rather than an affirmance").
The district court expressly ordered relief that Vanda argues may be affirmed on the basis of § 271(e)(4). See J.A. 33. Thus, our affirmance does not enlarge Vanda's rights under the judgment *1140or require its amendment. Indeed, Vanda could not have filed a cross-appeal in this case because "[a] party that is not adversely affected by a judgment lacks standing to [cross-appeal]." TypeRight Keyboard Corp. v. Microsoft Corp. , 374 F.3d 1151, 1156 (Fed. Cir. 2004).
We have considered West-Ward's remaining arguments but find them to be unpersuasive.
CONCLUSION
For the foregoing reasons, we affirm the district court's decision.
AFFIRMED
The parties have not appealed any determinations with respect to the '198 patent. The parties stipulated to the infringement of claim 3 of the '198 patent and the court concluded that claim 3 would not have been obvious.
The QT interval is the time between the Q and T waves of the heart rhythm. When corrected for the patient's heart rate it is abbreviated QTc.
During the pendency of this appeal, ownership of ANDA 20-5480 transferred from Roxane Laboratories Inc. to West-Ward. For simplicity, we refer to the ANDA applicant throughout as West-Ward.
The court specifically stated that Vanda was "not entitled to relief pursuant to 35 U.S.C. § 271(e)(4)(A) for the '610 [p]atent because the '610 [p]atent did not issue until after the effective date of any FDA approval of [West-Ward's] ANDA...." Opinion , 203 F.Supp.3d at 435. But the parties have treated the district court's reference to "the effective date of any FDA approval" as a typographical error, and the district court's rationale as being based on the '610 patent not having issued until after the filing date of the ANDA. See Appellant Br. 28; Appellee Br. 60 & n.6. We do the same.
Because we determine that 28 U.S.C. § 1338(a) provides a proper basis for jurisdiction, we do not reach the parties' declaratory judgment jurisdiction arguments.
We note that West-Ward did not argue to the district court at the pleadings stage that the complaint should be dismissed for failure to state a claim upon which relief could be granted on this basis. Cf. AstraZeneca II , 669 F.3d at 1381 (concluding that "the district court erred in part by concluding that [patentee's] failure to state a cognizable § 271(e)(2) claim defeated its jurisdiction" and affirming the dismissal for "fail[ure] to state a § 271(e)(2) claim" where applicant moved to dismiss both for lack of jurisdiction and failure to state a claim).
Because we conclude that the district court did not clearly err in finding induced infringement, we need not and do not reach Vanda's arguments in the alternative on contributory infringement.
Because we affirm the district court's infringement findings with respect to these independent claims, we need not reach this issue regarding the dependent claims because any error in the district court's analysis of the dependent claims is harmless. See TiVo, Inc. v. EchoStar Commc'ns Corp. , 516 F.3d 1290, 1312 (Fed. Cir. 2008) (affirming infringement finding as to some but not all claims and explaining that "[b]ecause the damages calculation at trial was not predicated on the infringement of particular claims, and because we have upheld the jury's verdict that all of the accused devices infringe the software claims, we affirm the damages award entered by the district court").
For purposes of validity, the parties did not argue the claims separately, so they rise or fall together.