This case involves a putative class of over 16,000 shippers allegedly harmed by a price-fixing conspiracy among the nation's largest freight railroads. The district court denied class certification because the plaintiffs' regression analysis-their evidence for proving causation, injury, and damages on a class-wide basis-measured negative damages for over 2,000 members of the proposed class. Based on that consideration, we affirm.
I
This appeal arises out of eighteen antitrust actions consolidated by the Multidistrict Litigation Panel. The defendants are the four largest freight railroads in the United States: BNSF Railway Company; CSX Transportation, Inc.; Norfolk Southern Railway Company; and Union Pacific Railroad Company. The plaintiffs, who are their customers, allege that the railroads conspired to fix rate-based fuel surcharges. Railroads impose fuel surcharges-additional charges above the base shipping price-when the price of fuel rises above a certain trigger price. Rate-based surcharges are calculated as a percentage of the base shipping price.
Following consolidation, the action was divided into one case involving direct purchasers and another involving indirect purchasers. All plaintiffs alleged that the railroads violated section 1 of the Sherman Act, 15 U.S.C. § 1, by conspiring to fix prices. The direct purchasers sought treble damages under section 4 of the Clayton Act, 15 U.S.C. § 15, and the district court held that they stated a claim, In re Rail Freight Surcharge Antitrust Litig. , 587 F. Supp. 2d 27 (D.D.C. 2008). The indirect purchasers sought injunctive relief under section 16 of the Clayton Act, 15 U.S.C. § 26, and raised various state-law claims. The district court held that the state claims were preempted by federal law, but it declined to dismiss the federal claims.
*621In re Rail Freight Surcharge Antitrust Litig., 593 F. Supp. 2d 29 (D.D.C. 2008), aff'd, Fayus Enters. v. BNSF Ry. Co., 602 F.3d 444 (D.C. Cir. 2010).
The eight named plaintiffs in the direct-purchaser case-Carter Distributing Company; Dakota Granite Company; Donnelly Commodities, Inc.; Dust Pro, Inc.; Nyrstar Taylor Chemicals, Inc.; Olin Corporation; Strates Shows, Inc.; and US Magnesium LLC-moved to certify a class under Federal Rule of Civil Procedure 23(b)(3). The proposed class consisted of all shippers who paid rate-based fuel surcharges for unregulated services purchased from the defendants between July 1, 2003 and December 31, 2008. To show that causation, injury, and damages could be proved on a class-wide basis, the plaintiffs invoked two regression models constructed by their economist, Dr. Gordon Rausser. The "common factor model" identified seven variables said to determine the price of the defendants' services, including fuel surcharges. The "damages model," controlling for those variables, sought to isolate price increases attributable to the alleged conspiracy. The railroads criticized these models on various grounds, including that they measured damages for shipments made under legacy contracts fixed before any conspiracy allegedly began.
The district court initially certified the class. It noted that if individualized proof were necessary to establish causation and injury, then the plaintiffs could not satisfy the Rule 23(b)(3) requirement that common questions predominate. See In re Rail Freight Fuel Surcharge Antitrust Litig., 287 F.R.D. 1, 43 (D.D.C. 2012). But the court found Dr. Rausser's regression analysis to be "plausible" and "workable," so it concluded that causation, injury, and damages were "susceptible to proof at trial through evidence common to the class." Id. at 67. The court rejected many different criticisms of the regression models, but it did not specifically address the question of false positives for legacy contracts.
On interlocutory review, we vacated the certification order and remanded for reconsideration in light of Comcast Corp. v. Behrend, 569 U.S. 27, 133 S.Ct. 1426, 185 L.Ed.2d 515 (2013). In re Rail Freight Surcharge Antitrust Litig.-MDL No. 1869, 725 F.3d 244 (D.C. Cir. 2013) ( Rail Freight I ). We explained that, for an antitrust class action, common questions "cannot predominate where there exists no reliable means of proving classwide injury in fact." Id. at 253. We expressed concern with the district court's failure to address "the damages model's propensity toward false positives," which left us with no way of knowing whether "the overcharges the damages model calculates for class members [are] any more accurate than the obviously false estimates it produces for legacy shippers." Id. at 254. Finally, we stressed that Rule 23, as construed in Comcast, requires a "hard look at the soundness of statistical models that purport to show predominance." Id. at 255.
On remand, after permitting supplemental discovery and expert reports, the district court denied class certification. In re Rail Freight Surcharge Antitrust Litig., 292 F. Supp. 3d 14 (D.D.C. 2017) ( Rail Freight II ). The court concluded that Dr. Rausser's expert opinions were reliable enough to be admissible at trial. Id. at 49-63. But in assessing predominance, the court identified three shortcomings in his damages model: first, it measured highly inflated damages for intermodal traffic (i.e. , shipments traveling by rail and another mode of transportation such as trucks or airplanes), id. at 122-26 ; second, as we had noted in the earlier appeal, the model erroneously measured damages for shipments made under legacy contracts, id. at 126-31 ; and third, the model measured negative damages-and hence no injury-for *622over 2,000 members of the proposed class, id. at 132-41. The court concluded that any one of these problems was enough to defeat the plaintiffs' argument for predominance. Id. at 122.
The plaintiffs filed a petition for permission to appeal the class-certification decision under Federal Rule of Civil Procedure 23(f). A motions panel of this Court granted the petition without prejudice to reconsideration at the merits stage. In re Rail Freight Fuel Surcharge Antitrust Litig.-MDL No. 1869, No. 17-8005 (D.C. Cir. Dec. 20, 2017).
II
We begin with the question of our jurisdiction. Orders denying class certification are neither final decisions under 28 U.S.C. § 1291, Coopers & Lybrand v. Livesay, 437 U.S. 463, 98 S.Ct. 2454, 57 L.Ed.2d 351 (1978), nor injunctions immediately appealable under 28 U.S.C. § 1292(a)(1), Gardner v. Westinghouse Broad. Co. , 437 U.S. 478, 98 S.Ct. 2451, 57 L.Ed.2d 364 (1978). However, 28 U.S.C. § 1292(e) permits the Supreme Court to promulgate rules creating new categories of decisions appealable before final judgment. Exercising that authority, the Court has provided that "[a] court of appeals may permit an appeal from an order granting or denying class-action certification," if a "petition for permission to appeal" is timely filed. Fed. R. Civ. P. 23(f).
In this case, the plaintiffs filed a timely petition for permission to appeal, which was enough under Rule 23(f) to secure our jurisdiction. That jurisdiction is "discretionary," Rail Freight I , 725 F.3d at 250, and the railroads contest whether we should exercise it. But their argument on this point is perfunctory-less than one page of briefing, with no case citations-and it almost entirely duplicates their merits arguments. According to the railroads, we should conclude that the denial of class certification was correct. Then, we should dismiss the appeal as raising neither a questionable decision nor an unsettled issue-considerations that bear on whether to permit the appeal in the first place, see id. at 250-54. Because that disposition would make little sense at this juncture, we decline to revisit the motions panel's decision accepting the appeal.
III
Federal Rule of Civil Procedure 23 sets forth various requirements for the certification of class actions. Rule 23(a) provides four "prerequisites" for any class certification, including that there must be "questions of law or fact common to the class." If these prerequisites are met, Rule 23(b)(3) permits certification if, among other things, "questions of law or fact common to class members predominate over any questions affecting only individual members." For purposes of these rules, a "common" question is one that is "capable of classwide resolution-which means that determination of its truth or falsity will resolve an issue that is central to the validity of each one of the claims in one stroke." Wal-Mart Stores, Inc. v. Dukes, 564 U.S. 338, 350, 131 S.Ct. 2541, 180 L.Ed.2d 374 (2011). In contrast, an "individual" question is one for which "members of a proposed class will need to present evidence that varies from member to member." Tyson Foods, Inc. v. Bouaphakeo, --- U.S. ----, 136 S. Ct. 1036, 1045, 194 L.Ed.2d 124 (2016) (quotation marks omitted).
The party seeking class certification "must affirmatively demonstrate" that the commonality and predominance requirements are satisfied. Wal-Mart, 564 U.S. at 350, 131 S.Ct. 2541. This requires a "rigorous analysis" that often will "overlap *623with the merits." Id. at 351, 131 S.Ct. 2541 (quotation marks omitted). Three recent cases address the contours of this analysis. In Wal-Mart, the Supreme Court ordered decertification of a Title VII class where the plaintiffs presented insufficient proof that the defendant had engaged in a general policy of sex discrimination. Id. at 352-55, 131 S.Ct. 2541. In Comcast, the Court ordered decertification where the regression analysis used to show common injury did not track the underlying theory of liability. 569 U.S. at 36-38, 133 S.Ct. 1426. The Court rejected a contention that, at the class-certification stage, "any method of measurement is acceptable so long as it can be applied classwide, no matter how arbitrary the measurements may be." Id. at 36, 133 S.Ct. 1426. But in Tyson Foods , the Court held that concerns about the validity of a statistical sample used to prove class-wide averages-which the Court described as presenting a common objection to the claims of each class member-should be addressed "as a matter of summary judgment, not class certification." 136 S. Ct. at 1047 (quotation marks omitted).
IV
The direct-purchaser plaintiffs raise claims under section 4 of the Clayton Act, which provides treble damages to any person "injured in his business or property by reason of anything forbidden in the antitrust laws." 15 U.S.C. § 15(a). To establish liability under section 4, each plaintiff must prove not only an antitrust violation, but also an injury to its business or property and a causal relation between the two. Without common proof of injury and causation, section 4 plaintiffs cannot establish predominance. See, e.g., Comcast, 569 U.S. at 36-38, 133 S.Ct. 1426 ; Rail Freight I, 725 F.3d at 252-53.
The parties dispute the extent to which a court, in conducting the "hard look" required by Rule 23, should assess the reliability of common evidence. Specifically, they contest whether Rule 23 requires reliability above and beyond what is necessary to establish the admissibility of expert testimony under Federal Rule of Evidence 702 and Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). That question arose because the district court found Dr. Rausser's regression models to be reliable for admissibility purposes, Rail Freight II, 292 F. Supp. 3d at 54-63 ; held that "reliability under Rule 23 is a higher standard than reliability under Daubert ," id. at 91 ; and found no predominance based on concerns that "undermine[d] the reliability of Dr. Rausser's damages model," id. at 122. The defendants embrace this reasoning; they argue that Wal-Mart and Comcast rejected certification based on concerns that common evidence was unreliable, even though its admissibility was uncontested. The plaintiffs disagree; they contend that predominance ultimately turns on whether the relevant evidence is common or individualized, and they read Tyson Foods as holding that a court may assess its reliability only in deciding admissibility or summary judgment.
We need not resolve this dispute because Dr. Rausser's damages model, even if sufficiently reliable, does not prove classwide injury. As the district court explained, his model indicates that the proposed class consists of 16,065 shippers. Rail Freight II, 292 F. Supp. 3d at 136. The plaintiffs maintain that the alleged conspiracy injured every one of them. Yet the damages model also indicates that 2,037 members of the proposed class-or 12.7 percent-suffered "only negative overcharges" and thus no injury from any conspiracy. Id. at 137. So even assuming *624the model can reliably show injury and causation for 87.3 percent of the class, that still leaves the plaintiffs with no common proof of those essential elements of liability for the remaining 12.7 percent. The district court held that the need for "individualized inquiries to determine which of at least 2,037 (and possibly more) class members were actually injured by the alleged conspiracy," id. at 140, precluded a finding of predominance. Id. at 122. We review a district court's assessment of predominance only for abuse of discretion. Garcia v. Johanns, 444 F.3d 625, 631 (D.C. Cir. 2006). Here, we find no such abuse.
The plaintiffs argue that their model measures these negative damages only because of normal prediction error. The district court found that prediction error could not "account for all-or even a substantial portion of-the 2,037 shippers that the model shows to be uninjured." Rail Freight II, 292 F. Supp. 3d at 139. The plaintiffs take issue with that finding, but it is not clearly erroneous. In any event, the plaintiffs' argument about prediction error at most suggests that their damages model might falsely have measured no injury for as many as 2,037 shippers. This line of reasoning describes a possible problem with their own evidence; it does not point to affirmative evidence-much less common affirmative evidence-that a conspiracy did in fact injure these shippers.
The plaintiffs further argue that predominance does not require common evidence extending to all class members. That contention appears inconsistent with our statement in Rail Freight I that the plaintiffs, to establish predominance, must "show that they can prove, through common evidence, that all class members were in fact injured by the alleged conspiracy." 725 F.3d at 252 ; see also id. ("we do expect the common evidence to show all class members suffered some injury"). Despite these statements, the district court held that our opinion did not require common evidence of injury to all class members. See Rail Freight II, 292 F. Supp. 3d at 132-34. Instead, it agreed with the plaintiffs that common proof covering "virtually all" members of the proposed class, and leaving only a "de minimis " number of cases requiring individualized proof of injury and causation, would be enough to show predominance. Id. at 135. For the sake of argument, we assume that the district court correctly recognized a de minimis exception to the general rule that, for claims under section 4 of the Clayton Act, causation and injury must be "capable of classwide resolution," Wal-Mart , 564 U.S. at 350, 131 S.Ct. 2541. The court reasonably concluded that such a de minimis exception would not encompass this case.
In assessing how many individual adjudications are too many, both the district court and the parties invoke cases addressing the question of when, if ever, a class may include concededly uninjured members. Strictly speaking, this case does not present that question, for the plaintiffs here insist that each member of the proposed class was injured. Nonetheless, the cited cases bear some similarity to this one: Uninjured class members cannot prevail on the merits, so their claims must be winnowed away as part of the liability determination. And that prospect raises the same kind of question at issue here-when does the need for individualized proof of injury and causation destroy predominance? See , e.g ., In re Asacol Antitrust Litig., 907 F.3d 42, 51-58 (1st Cir. 2018) ; In re Nexium Antitrust Litig., 777 F.3d 9, 18-22 (1st Cir. 2015).
The plaintiffs complain that the district court arbitrarily imposed a six-percent upper limit on the percentage of uninjured parties who may be included in a certified *625class. In fact, the court's analysis was more nuanced. As the court explained, the "few reported decisions" involving uninjured class members "suggest that 5% to 6% constitutes the outer limits of a de minimis number." Rail Freight II, 292 F. Supp. 3d at 137. The 12.7 percent figure in this case is more than twice that approximate upper bound reflected in analogous caselaw. Moreover, the district court considered raw numbers as well as percentages: six percent of a "class totaling only fifty-five" members might be de minimis, but 12.7 percent of this class yields "2,037 uninjured class members" (according to the common proof), all of whom would need individualized adjudications of causation and injury. Id. at 137-38. Finally, the district court stressed that the plaintiffs have proposed no "further way"-short of full-blown, individual trials-"to reduce this number and segregate the uninjured from the truly injured." Id. at 138. None of this was an abuse of discretion.
The absence of any winnowing mechanism sharply distinguishes Nexium , the plaintiffs' best case. There, the class included purchasers of a drug allegedly shielded from competition by the unlawful suppression of a generic alternative. 777 F.3d at 13-14. The problem of uninjured class members arose because a small percentage of the class, due to brand loyalty, would have purchased the drug even if a less expensive generic alternative had been available. Id. at 19-20. The First Circuit held that the uninjured class members could manageably be winnowed by having individual consumers file minimal, likely unrebutted affidavit testimony indicating whether, if given the choice, they would have purchased the branded drug or a generic alternative. Id. at 20-21.
Nexium does not support class certification here. For one thing, the First Circuit sharply limited that decision in Asacol. There, the Court explained that any winnowing mechanism must be truncated enough to ensure that the common issues predominate, yet robust enough to preserve the defendants' Seventh Amendment and due process rights to contest every element of liability and to present every colorable defense. 907 F.3d at 51-54. Moreover, the Court held that Nexium's affidavit mechanism could not satisfy both conditions where the defendant seeks to contest the question whether individual class members would have shifted from the branded drug to a less expensive generic alternative. See id. That would require individual trials because genuinely contested affidavits do not support summary judgment and are inadmissible. Id. Here, the defendants intend to contest whether any of the 2,037 shippers suffered injury as a result of any conspiracy. And the question presented in these individual challenges-regarding impacts on shippers of different sizes, shipping different products in different geographic markets, with different transportation options and different degrees of leverage-would be far more complex than the single unitary question (branded or generic?) at issue in Nexium and Asacol.
The plaintiffs also invoke the Supreme Court's discussion of uninjured class members in Tyson Foods . The defendants there sought review of the question whether a certified class may contain any uninjured members. But the Supreme Court reserved that question, 136 S. Ct. at 1049, and the district court here decided it in the plaintiffs' favor, Rail Freight II, 292 F. Supp. 3d at 133-35. So, this aspect of Tyson Foods does not advance the plaintiffs' appeal. The Supreme Court also addressed a further "new argument" raised for the first time in merits briefing-that plaintiffs at the certification stage must prove that all class members were injured or establish a manageable process for culling out *626uninjured class members. 136 S. Ct. at 1049. The Court held that this argument was "premature" because the parties disagreed about what culling mechanisms might be available and the district court had not yet addressed the question. See 136 S. Ct. at 1050. This holding rested on the inappropriateness of raising new issues for the first time in Supreme Court merits briefing. See id. It does not, as the plaintiffs here contend, permit district courts considering class certification to defer questions about the number and nature of any individualized inquiries that might be necessary to establish liability. To the contrary, confronting such questions is part-and-parcel of the "hard look" required by Wal-Mart and Comcast , as recognized even by those courts permitting a class to include some small number of concededly uninjured individuals. See, e.g., In re Asacol , 907 F.3d at 51-54 ; In re Nexium, 777 F.3d at 19-21.
Finally, the plaintiffs argue that the 2,037 class members for whom their damages model shows no injury are a de minimis portion of the class because their shipments make up less than one percent of the railroads' overall revenue from the alleged conspiracy. But revenue is irrelevant to predominance, which looks to whether elements such as causation and injury may be proved through common evidence, not how much the defendants benefited from any wrongdoing.
V
Looking beyond Dr. Rausser's regression analysis, the plaintiffs point to other evidence that they say can prove injury and causation on a class-wide basis. In Rail Freight I , we concluded that Dr. Rausser's analysis was "essential" to the plaintiffs' case for certification: "No damages model, no predominance, no class certification." 725 F.3d at 253. The district court reached the same conclusion on remand, after careful review of all the documentary and expert evidence. This was not an abuse of discretion.
The plaintiffs invoke documentary evidence that the defendants enforced fuel surcharges "uniformly and with few exceptions." Rail Freight II, 292 F. Supp. 3d at 122 ; see id. at 103-07. But imposing fuel surcharges does not show injury caused by a conspiracy. The parties vigorously dispute whether higher overall prices during the class period were attributable to causes besides any conspiracy-such as the marked increase in fuel prices that occurred around the beginning of the class period, see J.A. 6592-93. As the district court explained, Dr. Rausser designed his regression models precisely to control for these kinds of potential alternative causes, see Rail Freight II, 292 F. Supp. 3d at 101, yet his damages model showed that 2,037 shippers were uninjured despite paying fuel surcharges. The plaintiffs' evidence of widespread fuel surcharges helps explain why the proposed class is a large one, but it neither proves that the 2,037 shippers were injured by the alleged conspiracy nor otherwise compels a finding of predominance.
Next, the plaintiffs invoke the expert testimony of Dr. James McClave, who argued that the 2,037 shippers must have been harmed by the conspiracy. Dr. McClave reasoned that because these shippers made fewer purchases on average, and thus had less bargaining power than the rest of the class, they must have been more susceptible to injury. Moreover, Dr. McClave's own study concluded that the defendants' smallest customers-roughly 10,000 shippers who made only one purchase either before or during the class period-collectively paid higher prices than did larger shippers.
*627This analysis is not common proof of injury to the 2,037 shippers. For one thing, of the 10,000 shippers studied by Dr. McClave, only 3,700 were in the class, and Dr. McClave did not indicate how many of them were included among the 2,037 class members for whom Dr. Rausser's model showed no injury. Moreover, evidence that a group of one-time shippers may have paid higher prices collectively does not prove that all (or almost all) of them were injured individually. And, as the district court explained, Dr. McClave did not attempt to identify how many of the one-time shippers did in fact pay more, let alone which of them were among the 2,037. See Rail Freight II, 292 F. Supp. 3d at 139.
The plaintiffs respond that Dr. McClave's analysis, even if inconclusive, at least suggests that reduced bargaining power made the 2,037 shippers more vulnerable to any conspiracy. This line of reasoning parallels one rejected by the Supreme Court in Wal-Mart . There, an expert opined that Wal-Mart's "strong corporate culture" made it "vulnerable to gender bias." 564 U.S. at 354, 131 S.Ct. 2541 (quotation marks omitted). The Court found this evidence insufficient to prove that injury could be established on a class-wide basis, because the expert could not say what percentage of adverse employment decisions were in fact caused by bias. Id. The McClave study is similarly incomplete because, as explained above, it does not attempt to identify which of the small shippers, or what percentage of them, were in fact harmed by the alleged conspiracy.
VI
In Asacol , the First Circuit noted the absence of even a single case "allowing, under Rule 23, a trial in which thousands of class members testify." 907 F.3d at 57-58. That Court declined to create "the first such case." Id. So do we. Given the need in this case for at least 2,037 individual determinations of injury and causation, the district court did not abuse its discretion in denying class certification on the ground that common issues do not predominate.
Affirmed.