OPINION

ALICE M. BATCHELDER, Chief Judge.

Defendant-Appellant, Lowell E. Amos, a Michigan state prisoner, appeals the district court's order denying his petition for habeas corpus relief under 28 U.S.C. § 2254. Amos claims his trial was unfairly prejudiced by various forms of prosecutorial misconduct, due process violations, and ineffective assistance of trial counsel. We find that each of Amos's claims lacks merit, while some are procedurally defaulted and, therefore, AFFIRM the order of the district court.

I. BACKGROUND

Amos's third wife, Roberta, died of a cocaine overdose while she was in her hotel room alone with Amos. A Michigan jury convicted Amos of first-degree premeditated murder and first-degree murder by poisoning. The court sentenced Amos to two terms of life imprisonment without the possibility of parole.

Amos appealed to the Michigan Court of Appeals, which affirmed the first-degree murder conviction but remanded on double jeopardy grounds to amend the judgment to reflect only one conviction of first-degree murder under two theories. The Michigan Supreme Court denied Amos's application for leave to appeal.

Amos subsequently filed his first petition for a writ of habeas corpus, but the district court ordered that the case be held in abeyance until Amos properly exhausted his claims. Amos returned to the state trial court and moved for relief from judgment raising three claims: (1) ineffective assistance of counsel; (2) jurisdictional defect; and (3) prosecutorial misconduct. The Michigan trial court denied relief on each of these claims. Amos applied for leave to appeal to the Michigan Court of Appeals, which issued a brief order denying the application stating that Amos "fail[ed] to meet the burden of establishing entitlement to relief under M.C.R. 6.508(D)." Michigan v. Amos, No. 243384 (Mich.Ct.App. Apr. 1, 2003). The Michigan Supreme Court denied leave to appeal on the same grounds. Michigan v. Amos, 662 N.W.2d 750 (Mich.2003) (table).

Amos successfully moved the district court to reopen his habeas proceeding and requested relief on six claims of constitutional error in the state court. The district court found that three of the claims were procedurally defaulted, rejected the remaining claims, and denied Amos's request for relief. We granted Amos a certificate of appealability as to three of those claims, and Amos timely filed this appeal.

II. ANALYSIS

We review de novo a district court's denial of a petition for writ of habeas corpus. Tibbetts v. Bradshaw, 633 F.3d 436, 441 (6th Cir.2011). Amos filed his petition on April 7, 2000; therefore, the Antiterrorism and Effective Death Penalty Act (AEDPA) governs his request. Id. Under AEDPA, a federal court may grant a writ of habeas corpus only if the state court's adjudication of the claim "(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States; or (2) resulted in a decision that was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding." 28 U.S.C. § 2254(d)(1)-(2). "AEDPA sets forth a heavy burden for a petitioner to overcome." Tibbetts, 633 F.3d at 442.

We also review de novo a district court's procedural default rulings. Cvijetinovic v. Eberlin, 617 F.3d 833, 836 (6th Cir.2010).

Guilmette v. Howes, 624 F.3d 286, 290 (6th Cir.2010) (en banc) (quoting Tolliver v. Sheets, 594 F.3d 900, 928 n. 11 (6th Cir. 2010)).

To determine whether the state court rejected a petitioner's claim on procedural grounds, we must look to "the last reasoned state court opinion to determine the basis for the state court's rejection of [the petitioner's] claim." Id. at 291. We apply a presumption that a subsequent unexplained order leaves the judgment of the earlier court in place and does not invoke procedural default. Id. at 291-92.

A. Prosecutorial Misconduct

Amos first asserts several claims of prosecutorial misconduct. Specifically, he claims that the prosecution presented false testimony, improperly withheld evidence, and made several improper remarks throughout trial. The district court found that Amos's false-testimony and withholding-of-evidence claims were procedurally defaulted and that Amos did not establish cause and prejudice to overcome the default. Because of this Court's subsequent decision in Guilmette, that determination is no longer correct; nevertheless, we find that all of Amos's claims of prosecutorial misconduct lack merit.

1. Presentation of False Testimony and Improper Withholding of Evidence

Amos's first claim of prosecutorial misconduct alleges that Dr. Kanluen, the Wayne County Medical Examiner and a prosecution witness, overstated the significance of the cocaine level in Roberta's blood to imply that her cause of death was homicide rather than an accident. Amos further argues that the prosecution was aware that the testimony was false and concealed additional evidence indicating its falsity.

The district court found that this claim was procedurally defaulted because the Michigan appellate courts denied leave to appeal by brief orders under M.C.R. 6.508(D). At the time the district court issued its opinion, which was prior to our holding in Guilmette, this finding was correct. However, after Guilmette, brief orders citing generally M.C.R. 6.508(D) are no longer a sufficient basis for a finding of procedural default. Instead, we must look to the last reasoned state court opinion, which in this case is the trial court's denial of Amos's motion for relief from judgment, to determine if the court dismissed Amos's claim on procedural grounds. See Guilmette, 624 F.3d at 291.

The Michigan trial court denied this prosecutorial misconduct claim under M.C.R. 6.508(D)(2), which precludes relief if a court in an earlier appeal has already denied the petitioner's grounds for relief. This Court has previously ruled in an unpublished opinion that this is a collateral estoppel rule that will not procedurally default a claim for habeas relief. Skinner v. McLemore, 425 Fed.Appx. 491, 495 (6th Cir.2011); see also Cone v. Bell, 556 U.S. 449, 466, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009) ("When a state court declines to review the merits of a petitioner's claim on the ground that it has done so already, it creates no bar to federal habeas review."). However, the state court's application of this rule was incorrect because Amos did not raise this claim prior to his motion for relief from judgment.1 See Amos v. Renico, No. 00-10107, 2007 WL 118943, at *6-7, 2007 U.S. Dist. LEXIS 6287, at *17 (E.D.Mich. Jan. 10, 2007). Instead, the court should have applied M.C.R. 6.508(D)(3), which precludes review of a claim that a petitioner could have raised earlier but did not. Had the Michigan court applied the correct rule, Amos's claim would have been procedurally defaulted. See Skinner, 425 Fed.Appx. at 495-96 (analyzing an identical mistake). But, because a procedural rule must be "clearly and expressly invoked" to operate as a bar to habeas review, Amos's first prosecutorial misconduct claim is not procedurally defaulted. See id. Nevertheless, because the state court rejected all of Amos's prosecutorial misconduct claims, Michigan v. Amos, No. 96-1975, at *5 (3d Cir.Ct.Crim.Div. Aug. 1, 2002), we defer to that determination unless it was contrary to or an unreasonable application of clearly established federal law or based on an unreasonable determination of the facts. See Harrington v. Richter, ___ U.S. ___, 131 S.Ct. 770, 783-85, 178 L.Ed.2d 624 (2011).2

To establish that the prosecution presented false testimony, Amos must show that (1) Dr. Kanluen's statements were false, (2) that they were material, and (3) that the prosecution knew they were false. See Brooks v. Tennessee, 626 F.3d 878, 894-95 (6th Cir.2010). To establish that the prosecution improperly withheld evidence, Amos must show (1) that the withheld evidence was favorable to his defense, (2) that the government suppressed it, and (3) that Amos was prejudiced. See Henness v. Bagley, 644 F.3d 308, 324 (6th Cir.2011). Amos's prosecutorial misconduct claims based on these theories lack merit because he has not shown that Dr. Kanluen's testimony was false or that any allegedly withheld evidence was favorable to his defense.

In his testimony, Dr. Kanluen discussed his experiences with cocaine levels in his own lab. His statements were personal observances based on his own recollection. Amos has not presented any evidence that directly contradicts these statements. Instead, he presents several pieces of scientific literature, which he claims establish that the average cocaine level in cocaine-related fatalities is much closer to the level found in Roberta's blood than Dr. Kanluen suggested. His reliance on this literature, however, is misplaced. To the extent that any of this literature presents an "average" level of cocaine found in cocaine-related deaths, it still does not contradict Dr. Kanluen's testimony because his testimony concerned not the average of cocaine levels in fatalities generally, but rather the average level that he has seen in his lab. Amos presents one study that includes the Wayne County Medical Examiner's Office in its data; but the study predates Amos's crime by nearly twenty years and explicitly states that it includes in its data only one cocaine-related death from Wayne County. None of this scientific literature establishes that Dr. Kanluen's testimony was false, nor does it contradict his testimony in any way.3 Accordingly, Amos cannot show that the prosecution presented false testimony or improperly withheld evidence that was favorable to his defense.

2. Improper Remarks

We review Amos's remaining claims of prosecutorial misconduct under a two-part test to determine whether the state court reasonably applied clearly established federal law regarding the influence of prosecutorial misconduct. See Slagle v. Bagley, 457 F.3d 501, 515 (6th Cir. 2006). We first determine whether the prosecutor's conduct was improper. Id. at 516. If it was improper, then we look to four factors to determine whether it was so flagrant as to violate due process: "(1) whether the evidence against the defendant was strong[;] (2) whether the conduct of the prosecution tended to mislead the jury or prejudice the defendant; (3) whether the conduct or remarks were isolated or extensive; and (4) whether the remarks were made deliberately or accidentally." Id.

First, Amos claims that the prosecution committed constitutional error by referring to the deaths of his mother and his first wife, which the trial court had previously ordered inadmissible. Amos's trial counsel objected to the prosecution's passing reference to their deaths, and the trial court granted a mistrial based on its previous order. On appeal, the Michigan Court of Appeals reversed the mistrial and ordered the trial court to strike the question and give a curative instruction to the jury.

The Michigan trial court adjudicated this claim on the merits during Amos's petition for post-conviction relief. Therefore, we defer to its decision unless it was contrary to clearly established federal law. See Brown v. Bobby, 656 F.3d 325, 329 (6th Cir.2011).

The prosecutor's question on redirect examination was improper. She was aware when she asked the question that evidence regarding the circumstances of the deaths of Amos's first wife and mother were inadmissible, and she admittedly knew that the question would elicit testimony regarding their deaths. Despite the impropriety of the comment, it was not so flagrant as to have denied Amos due process. Although the prosecutor's question was deliberate, the other evidence presented against Amos was strong. Indeed, the trial court excluded evidence regarding Saundra's death because it determined that "the People have a strong case on the intent issue already, without even mention of Saundra Amos' death." Likewise, it is unlikely that these comments misled the jury or prejudiced Amos, because the court struck the comments from the record and instructed the jury to disregard them. See Hill v. Mitchell, 400 F.3d 308, 325 (6th Cir.2005) ("[F]ederal courts generally presume that juries follow their instructions[.]" (internal quotation marks omitted)). More importantly, even if the jury ignored that instruction, neither the prosecutor nor Detective Henahan stated that Amos's first wife and mother were dead. Finally, Amos has not presented another instance of similarly improper remarks regarding their deaths. Accordingly, Amos is not entitled to habeas relief on this claim.

Second, Amos claims that the prosecution purposely misstated facts to the court to boost the credibility of prosecution witness Ruth Loftus, an acquaintance of Amos's who testified that she met with Amos in August of 1991 in Indianapolis and that Amos had confessed to killing his first wife. Later, the prosecution moved to admit business records from September 1991 to establish that Amos was in Indianapolis at the time. Amos's counsel objected on relevance grounds, and the prosecutor responded to the court that Loftus had testified that her second meeting with Amos was in "either August or early September." The court admitted the business records.

Amos first raised this claim in his initial habeas petition and then in his motion for relief from judgment. Because the Michigan trial court rejected all of Amos's prosecutorial misconduct claims, we defer to that decision unless it was contrary to clearly established federal law. See Harrington, 131 S.Ct. at 784-85.

The prosecutor's statement did not rise to the level of prosecutorial misconduct. Although the statement is clearly incorrect, it is not clear that it was improper as an intentional misstatement meant to deliberately mislead the court. Even assuming that it was improper, it was not so flagrant as to rise to a violation of due process. The statement was isolated to the admission of the business records. The dates of Amos's second meeting with Loftus did not arise again as an issue, and nothing in the record suggests that this error expanded beyond the limited context of admitting rebuttal evidence to contradict an impeachment witness. Additionally, it is highly unlikely that these statements prejudiced Amos. The jury heard Loftus's testimony that she met with Amos in August of 1991, and it was free to conclude that the September 1991 business records were irrelevant. Moreover, defense counsel still had the opportunity to argue the records' relevance to the jury because they did not support Loftus's testimony. This claim, therefore, lacks merit.

Third, Amos alleges that the prosecutor's suggestion that Amos smothered his second wife, Carolyn, was constitutional error.4 A prosecutor may argue reasonable inferences from the evidence at closing argument. United States v. Crosgrove, 637 F.3d 646, 663 (6th Cir.2011). Carolyn's autopsy report indicated that her cause of death was not apparent but that the conditions of her body "suggest terminal blockage of the respiratory system." The prosecution's expert witness, Dr. Schmidt, interpreted this statement to mean "smothered," and another witness, Ruth Loftus, testified that Amos had confessed to her that he had killed Carolyn. It was reasonable, therefore, for the prosecutor to argue that Amos had smothered Carolyn. The Michigan Court of Appeals agreed, and its determination was not contrary to or an unreasonable application of Supreme Court precedent.

Finally, Amos claims that the prosecutor made constitutionally improper comments regarding Amos's extramarital relationships, gender-based appeals to the largely female jury, and the credibility of a defense witness. As part of his direct appeal, Amos challenged the prosecutor's comments regarding his extramarital relationships. The Michigan Court of Appeals refused to review his claim regarding these comments because Amos did not object to them at trial. We will not review them either because "the contemporaneous-objection rule is an adequate and independent state ground barring federal habeas review." See Awkal v. Mitchell, 613 F.3d 629, 648 (6th Cir.2010) (en banc). Amos does not present any cause or prejudice to overcome this default; therefore, this claim is not properly before us for consideration. Id. at 649. The Michigan courts rejected his remaining claims on the merits, and we defer to that decision unless it was contrary to clearly established federal law.

Even if we assume that any of these comments were improper, it is not clear that they misled the jury or prejudiced Amos. As the Michigan Court of Appeals noted on direct appeal, the trial court instructed the jury that the attorneys' questions and remarks were not evidence and that the jury could not convict Amos on account of his infidelities. Amos, 1998 WL 1990424, at *2-3, 1998 Mich.App. LEXIS 2091, at *7. Moreover, the comments were isolated and side comments and questions from the prosecutor would not have been more influential than the significant evidence establishing Amos's guilt, particularly because the comments were limited to closing argument and questions posed to two witnesses. Accordingly, the decisions of the Michigan courts were not contrary to or an unreasonable application of federal law.

B. Due Process Violations

Amos's second claim for habeas relief is that the Michigan Supreme Court denied him due process of law and rendered his trial fundamentally unfair when it ruled on the government's interlocutory appeal regarding the admission of Loftus's testimony. Prior to Amos's trial, the prosecution filed a motion in limine seeking to present to the jury Loftus's testimony that Amos told her that he had killed his last wife and that he would "probably" kill is next wife. The trial court ruled that Loftus's testimony was inadmissible, and the Michigan Court of Appeals affirmed.

On September 20, 1996, the prosecution filed for leave to appeal to the Michigan Supreme Court. Amos contends that the prosecution did not serve notice of this appeal on his trial counsel. The record, however, indicates that the prosecution's leave for appeal contains a proof of service that states that the prosecution served the appeal on defense counsel by personal service on September 20. On September 24, 1996, the Michigan Supreme Court ruled on the appeal, apparently without a response from Amos, and reversed the trial court's decision, finding that Loftus's testimony was relevant and not unfairly prejudicial. Amos, 552 N.W.2d at 917. Based on this ruling, Amos presents two specific due process claims: (1) the Michigan Supreme Court denied him due process by failing to give him notice or an opportunity to be heard on the appeal; and in the alternative, (2) Loftus's testimony was highly prejudicial and rendered the trial fundamentally unfair.

Amos's first due process claim of lack of notice and an opportunity to be heard is not procedurally barred because he raised this issue in his direct appeal, and his motion for reconsideration. The Michigan courts, however, never ruled on the merits of this claim. Instead, they analyzed only the second aspect of Amos's due process claim — that Loftus's testimony rendered the trial unfairly prejudicial. We therefore review this claim de novo. See Maples v. Stegall, 340 F.3d 433, 436 (6th Cir.2003).

Amos argues that the lack of notice and opportunity to be heard deprived him of the effective assistance of counsel as that right is articulated in United States v. Cronic, 466 U.S. 648, 104 S.Ct. 2039, 80 L.Ed.2d 657 (1984), and the right to present his own defense as articulated in Crane v. Kentucky, 476 U.S. 683, 106 S.Ct. 2142, 90 L.Ed.2d 636 (1986), and Chambers v. Mississippi, 410 U.S. 284, 93 S.Ct. 1038, 35 L.Ed.2d 297 (1973). However, the record and counsels' admissions at oral argument indicate that the Michigan courts did not deny Amos an opportunity to be heard.

First, the state's emergency application for leave to appeal contained a proof of service indicating that the application was personally served on Amos's trial counsel on the same day that the state filed it with the court. Amos's only attempt to contradict the proof of service is his counsel's statement in the record that he was out of the office the day that the state filed the motion, and he received it only the day before the court ruled. However, even if his trial counsel did not receive notice of the application in time to file a response, the record indicates, and counsel admits, that the Michigan Supreme Court had before it the record from the Michigan Court of Appeals, which included Amos's response in that court. The Michigan Supreme Court, therefore, would have been aware of Amos's arguments against the admission of Loftus's testimony, and Amos has not indicated what additional arguments he was unable to present. The right to a meaningful opportunity to present a defense does not afford a defendant the absolute right to make any and every argument that he wishes in his defense. Wynne v. Renico, 606 F.3d 867, 871 (6th Cir.2010). Amos was given a meaningful opportunity to challenge the admittance of Loftus's testimony, especially considering that he had the opportunity to file a motion for rehearing of the Michigan Supreme Court's ruling but failed to do so. Accordingly, his due process claim for lack of notice and opportunity to be heard is without merit.

Amos's second due process claim is likewise without merit. Although Amos challenged the admissibility of Loftus's testimony on direct appeal, he never articulated this challenge as implicating a federal due process claim.5 Instead, his challenge focused more on the court's application of the state rules of evidence, which is not cognizable as a federal constitutional claim on habeas review. Broom v. Mitchell, 441 F.3d 392, 406 (6th Cir.2006). Amos alleged that Loftus's testimony denied him a fair trial and due process, but "general allegations of the denial of a `fair trial' or `due process' have been held insufficient to `fairly present' federal constitutional claims" for federal habeas review. Newton v. Million, 349 F.3d 873, 877 (6th Cir.2003). Because Amos did not articulate this evidentiary challenge as a federal due process claim at any time during his direct or collateral appeals,6 it is procedurally defaulted, and we review it only if he has shown cause and prejudice. See Williams v. Anderson, 460 F.3d 789, 806 (6th Cir. 2006).

Amos does not assert any cause for his failure to raise this due process claim to the state courts, and his claim lacks any merit that would support a finding that he was prejudiced by the failure to raise it. Significant evidence pointed to Amos's guilt, including forensic evidence that showed that the condition of Roberta's body was consistent with homicide, and evidence that Amos was the last person to see Roberta alive and the only person in the room with her when she died. As the Michigan Court of Appeals noted on direct appeal, Amos "admittedly orchestrated the removal of two potentially important pieces of evidence." Amos, 1998 WL 1990424, at *10, 1998 Mich.App. LEXIS, at *27. And as the Michigan Supreme Court correctly determined, Loftus's testimony was relevant to the issue of intent. Amos challenged Loftus's testimony in several respects, alleging that he had never met with her in Indianapolis and making generic attacks on her character. In light of the other evidence of Amos's guilt, and the challenges that he asserted to Loftus's testimony, it does not appear that Loftus's testimony was such a highly significant factor that its admission, even if improper, rendered the trial fundamentally unfair.

C. Ineffective Assistance of Trial Counsel

Finally, Amos claims that his trial counsel was ineffective for failing to investigate and call expert witnesses to refute Dr. Kanluen's testimony. The district court found that these claims were procedurally defaulted because the Michigan trial court rejected them under M.C.R. 6.508(D)(3), which is an independent and adequate state ground sufficient for procedural default that required Amos to raise these claims during his direct appeal. See Ivory v. Jackson, 509 F.3d 284, 292 (6th Cir.2007). We may not review a procedurally defaulted claim unless the petitioner can demonstrate cause for his failure to comply with the state rule and that he suffered actual prejudice. Haliym v. Mitchell, 492 F.3d 680, 690 (6th Cir.2007).

Amos asserts ineffective assistance of appellate counsel as the cause for his failure to raise these claims on direct appeal. However, even if this is sufficient to show cause, Amos has failed to establish that he suffered actual prejudice. "Prejudice requires a showing that the errors at trial worked to the petitioner's actual and substantial disadvantage, infecting his entire trial with error of constitutional dimensions." Id. at 691 (internal alteration and quotation marks omitted); see also Strickler v. Greene, 527 U.S. 263, 296, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (affirming denial of habeas relief where petitioner showed cause but failed to establish prejudice). Amos cannot establish such prejudice because his trial counsel's failure to investigate and call expert witnesses did not work to Amos's actual and substantial disadvantage. The scientific articles that he claims counsel should have discovered would not have contradicted Dr. Kanluen's testimony as he argues they would have because Dr. Kanluen testified as to the cocaine levels he experienced in his lab, not the average amount of cocaine found in cocaine-related fatalities. Likewise, the only experts Amos claims his counsel should have called were the authors of these irrelevant scientific studies. Amos also fails to articulate what additional information counsel would have gleaned from Dr. Kanluen's employees, who claimed that Dr. Kanluen destroyed an earlier version of Roberta's death certificate. These employees refused to identify themselves, and counsel informed the jury about the original death certificate during his cross-examination of Dr. Kanluen. Therefore, because counsel's failures did not affect the outcome of Amos's trial, he cannot establish prejudice to overcome the procedural default of his claims of ineffective assistance of trial counsel.

III

For the foregoing reasons, we AFFIRM the decision of the district court.