Opinion for the Court filed by Circuit Judge HENDERSON.
KAREN LeCRAFT HENDERSON, Circuit Judge:
After signing a plea agreement, the appellant pleaded guilty to four counts of sex trafficking of children, see 18 U.S.C. § 1591(a)(1). At sentencing the district court imposed a term of imprisonment and also ordered the appellant to pay a total of $3,892,055 in restitution to the four victims. The appellant challenges the restitution order; the government argues, however, that he waived his right to appeal the restitution order. While we conclude the appellant did not waive his right to appeal the restitution order, we reject his merits argument and affirm the district court.
I.
From 2006 through 2009, the appellant prostituted four underage females: S.H., T.S., M.S. and A.L. He prostituted S.H. from approximately March 1, 2008 through August 2008; T.S. from approximately March 18, 2006 through May 15, 2009; M.S. from approximately May 17, 2009 through May 30, 2009; and A.L. from approximately May 27, 2009 through May 30, 2009. He did so by transporting each victim from his residence in Temple Hills, Maryland into the District of Columbia, where the four exchanged sex for money.
The government indicted the appellant on September 1, 2009. On December 11, 2009, he signed a ten-page plea agreement. The agreement provides that the appellant "agrees to admit guilt and enter a plea of guilty to . four counts of violating 18 U.S.C. § 1591 (Sex Trafficking of Children)." Appendix (A) 24. Section Eleven of the plea agreement provides that "pursuant to 18 U.S.C. § 1593 and 3664, it is mandatory that the Court order [the appellant] to make restitution for the full amount of any victims' compensable losses" and that any contested restitution issue may be litigated at sentencing or at a subsequent hearing. A 28. Section Twelve of the plea agreement includes the following appeal waiver:
[The appellant] is aware that federal law, specifically 18 U.S.C. § 3742, affords [him] the right to appeal the sentence in this case. [He] is aware that in the event that sentence is imposed upon consideration of the Sentencing Guidelines rather than in accordance with Section Two [ie. if the Court rejects the plea agreement], the Government's factual stipulations and predictions about the calculation of the sentencing guidelines are not binding on the sentencing judge. Knowing that, [the appellant] waives the right to appeal his sentence or the manner in which it was determined pursuant to 18 U.S.C. § 3742, except to the extent that (a) the Court sentences [him] to a period of imprisonment longer than the statutory maximum, or (b) the Court departs upward from the applicable Sentencing Guideline range pursuant to the provisions of U.S.S.G. § 5K.2 or based on a consideration of the sentencing factors set forth in 18 U.S.C. § 3553(a). Further, [he] reserves the right to make a collateral attack upon [his] sentence pursuant to 28 U.S.C. § 2255, if new and currently unavailable information becomes known to him. In agreeing to this waiver, [the appellant] is aware that [his] sentence has yet to be determined by the Court. Realizing the uncertainty in estimating what sentence the Court ultimately will impose, [the appellant] knowingly and willingly waives [his] right to appeal the sentence, to the extent noted above, in exchange for the concessions made by the Government in this Agreement.
A 29.
On December 31, 2009, the appellant pleaded guilty before a magistrate judge, who accepted the plea agreement. On November 1, 2010, the district court sentenced the appellant to 240 months' imprisonment.
The district court also held separate evidentiary hearings on January 21 and February 3, 2011 to calculate the amount of restitution the appellant owed the four minors. Before the hearings, the court received (1) mental health assessments (MHAs) prepared by psychologist C. David Missar (Missar) for each of the four; and (2) a report from the four minors' guardian ad litem.
Missar's MHAs were based on his reviews of each victim's mental health records and other relevant records, as well as his interviews of A.L. and S.H. Missar did not interview M.S. or T.S. because M.S. had disappeared and T.S.'s family did not respond to Missar's attempts to contact them. Based on this information, Missar diagnosed each victim with various mental health and substance abuse problems, including Post-Traumatic Stress Disorder (PTSD). Missar recognized that some of the victims' mental health and substance abuse problems predated their association with the appellant but he concluded there was "little doubt" that the appellant had "exacerbated" any preexisting mental health problems. A 222, 226, 230, 242. Additionally, the fact that each victim was a minor prostitute working for the appellant created "tremendous additional emotional traumas" for each. A 222, 226, 230, 242. Missar concluded that each victim required "significant mental health services, in different stages and to differing degrees, for the rest of her life," including therapy, psychiatric care and educational tutoring. A 222, 226, 230, 242. Missar created a "mid-range" estimate of the total cost of services each victim would need over her lifetime: $679,800 for A.L., $849,400 for T.S., $839,700 for M.S. and $849,400 for S.H.
The guardian ad litem submitted a restitution report on January 4, 2011. The report relied on Missar's recommendations, calculations of the money the appellant received due to each victim's prostitution (estimating each victim made $500 per day while prostituting) and sixty-eight hours of attorney's fees for each victim at $125 per hour. The total recommended restitution was $1,122,925 for T.S., $871,825 for M.S., $1,398,525 for S.H. and $632,525 for A.L.
Missar was the only witness at the district court's two restitution hearings, during which he explained the reasoning he used in preparing the MHAs. First, Missar acknowledged that the estimated amount for needed mental health services was similar for each victim despite the fact that the length of time each had worked for the appellant varied. Missar explained that PTSD can develop in a matter of days but can cause lifetime damage. While Missar acknowledged that each victim had health/ drug problems, he nonetheless believed that his treatment recommendations were necessary and appropriate because even if a victim had had no pre-existing mental health problem, the appellant's abuse of her would have made necessary the treatment he recommended. Missar further explained that, while he had been unable to interview M.S. and T.S., he could render an expert opinion on their eonditions/treatment based on his review of each victim's grand jury testimony, his extrapolation from the two victims he did interview and his previous experience in evaluating individuals without interviewing them.
On March 30, 2011, the district court granted, inter alia, the following restitution: (1) to S.H., $849,400 for treatment and $365,600 for ill-gotten gains; (2) to T.S., $573,800 for treatment and $577,500 for ill-gotten gains; (3) to M.S. $839,700 for treatment and $5,465 for ill-gotten gains; and (4) to A.L., $679,800 for treatment and $790 in ill-gotten gains. In determining the necessary treatment, the district court adopted all of Missar's recommendations but corrected the total amount in the guardian ad litem's report for T.S.'s treatment because of a mathematical error. In calculating ill-gotten gains, the district court relied primarily on each victim's grand jury testimony. The appellant timely appealed.
II.
A.
The appellant challenges the district court's restitution order only. The government first maintains that the appellant waived his right to appeal the restitution order. We disagree.
A waiver of the right to appeal a sentence is presumptively valid and is enforceable if the defendant's decision to waive is "knowing, intelligent, and voluntary." United States v. Guillen, 561 F.Sd 527, 529 (D.C.Cir.2009); see also Brady v. United States, 397 U.S. 742, 748, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970) ('Waivers of constitutional rights not only must be voluntary but must be knowing, intelligent acts done with sufficient awareness of the relevant circumstances and likely consequences."). Moreover, "[a]n anticipatory waiver—that is, one made before the defendant knows what the sentence will be— is nonetheless a knowing waiver if the defendant is aware of and understands the risks involved in his decision." Guillen, 561 F.3d at 529; see also United States v. Cunningham, 145 F.3d 1385, 1391 (D.C.Cir.1998) (in waiving right to counsel, record must show defendant "knows what he is doing and his choice is made with eyes open") (quotation marks omitted). "In the context of a plea bargain, . a determination [of whether a waiver is knowing and intelligent] is usually made at the plea hearing, at which the court can fully explain the consequences of the waiver by informing the defendant of exactly what rights he is giving up and what rights he retains." United States v. Accardi, 669 F.3d 340, 344 (D.C.Cir.2012) (citing Guillen, 561 F.3d at 528). A waiver, however, does not prevent an appeal if the district court commits an error of law during sentencing. See Guillen, 561 F.3d at 530. For example, a waiver is not "enforced if the sentencing court's failure in some material way to follow a prescribed sentencing procedure results in a miscarriage of justice"—for instance, an "utter[ ] fail[ure] to advert to the factors in 18 U.S.C. § 3553(a)," or if the sentence "is unlawful because it exceeds the statutory maximum." Id. at 531.
We conclude that the appellant did not waive his right to appeal the restitution order by signing the plea agreement. The ten-page plea agreement contains eighteen separate sections. Section Twelve of the plea agreement provides for waiver of appeal and recites, in pertinent part: "You [are] aware that federal law, specifically 18 U.S.C. § 3742, affords [you] the right to appeal the sentence in this case . [and that you] waive[ ] the right to appeal [your] sentence or the manner in which it was determined pursuant to 18 U.S.C. § 3742.... " A 29 (emphasis added). But the remainder of Section Twelve refers only to "a period of imprisonment" and "the applicable Sentencing Guidelines range" (providing for a range for imprisonment, supervised release and fines but not for restitution). See A 29. Section Twelve also references Section Two of the plea agreement (entitled "Recommendation as to Appropriate Sentence"), which defines "sentence" as simply the period of incarceration, stating "[you] and the Government agree that a sentence of 180 to 240 months incarceration is the appropriate sentence." A 25 (emphases added). Section Two also mentions "other sentencing incidents" such as "fines and terms of supervised release," but does not include restitution. A 25.
While Section Eleven of the plea agreement explains that the appellant must pay restitution, the fact that the appellant acknowledges the obligation to pay restitution does not mean that he forfeits the right to appeal the amount thereof. Moreover, a comparison of the plea agreement's restitution provision—Section Eleven— with its forfeiture provision—Section Thirteen—indicates that the appeal waiver does not apply to restitution. Like Section Eleven, Section Thirteen provides that forfeiture is mandatory. Unlike Section Eleven, however, Section Thirteen contains its own appeal waiver: "[You] further agree[ ] to waive all constitutional and statutory challenges in any manner (including direct appeal .) to any forfeiture carried out . as it relates to the non-contested items...." A 30. The fact that the plea agreement expressly eliminates an appeal right for forfeiture but not for restitution suggests that appeal of restitution has not been waived. Cf. Posters 'N' Things, Ltd. v. United States, 511 U.S. 513, 517-22, 114 S.Ct. 1747, 128 L.Ed.2d 539 (1994) (language omitted from one statutory provision but included in parallel provision indicates former provision does not include language); Clinchfield Coal Co. v. Fed. Mine Safety & Health Review Comm'n, 895 F.2d 773, 779 (D.C.Cir.1990) ("explicit direction for something in one provision, and its absence in a parallel provision, implies an intent to negate it in the second context").
The government nonetheless contends that waiver of the right to appeal the "sentence" waives the right to appeal restitution because "restitution" is necessarily part of a "sentence." As noted above, Section Twelve of the plea agreement cites to the defendant's right to appeal a sentence under 18 U.S.C. § 3742. Section 3742 does not address restitution. Resti tution is instead treated in sections 3663 and 3664 of Title 18. Significantly, section 3664(o)(l)(B) provides that a defendant appeals a restitution order pursuant to section 3742: "[a] sentence that imposes an order of restitution is a final judgment notwithstanding the fact that such a sentence can be subsequently appealed and modified under section 3742." 18 U.S.C. § 3664(o)(l)(B) (emphases added). But the appellant's plea agreement defines sentence without reference to restitution—at the very least, it is ambiguous as to whether "sentence" includes restitution. Cf United States v. Anderson, 545 F.3d 1072, 1078 (D.C.Cir.2008) (" 'In determining whether any particular plea agreement has been breached, we look to the reasonable understanding of the parties and resolve any ambiguities in the agreement against the government.' ") (quoting United States v. Rodgers, 101 F.3d 247, 253 (2d Cir.1996)). Because the plea agreement cites only section 3742, which, as noted, does not mention restitution, we believe the appellant did not knowingly waive his right to appeal the restitution award.
The government also points to out-of-circuit authority that, it contends, establishes that waiver of the right to appeal a sentence waives the right to appeal restitution as well. See, e.g., United States v. Cohen, 459 F.3d 490, 497 (4th Cir.2006) ("[A]s a general rule, a defendant who has agreed '[t]o waive knowingly and expressly all rights, conferred by 18 U.S.C. § 3742, to appeal whatever sentence is imposed,' . has waived his right to appeal a restitution order."). But other out-of-circuit cases have held that waiver of the right to appeal a "sentence" does not apply to "restitution" under the language of the plea agreement. United States v. Oladimeji, 463 F.3d 152, 157 (2d Cir.2006) (no waiver because plea agreement indicated "sentence" referred to imprisonment only); United States v. Sistrunk, 432 F.3d 917, 918 (8th Cir.2006) (no waiver under plea agreement stating: "the defendant hereby waives all rights conferred by [18 U.S.C. § 3742] to appeal his sentence, unless the Court sentences the defendant above offense level 10"); United States v. Zink, 107 F.3d 716, 718 (9th Cir.1997) (plea agreement indicated reference to "any sentence" was to sentence calculated under Sentencing Guidelines). In one of the cases cited by the government, the Seventh Circuit emphasized that, while it found the waiver in that case included restitution, its "analysis [was] guided foremost by the facts before [it]." United States v. Worden, 646 F.3d 499, 504 (7th Cir .2011).
Similarly, we are guided by the facts before us. We conclude that based on the language of the appellant's plea agreement, his Rule 11 colloquy and the rule of construction that ambiguity in a contract is construed against the drafter, the appellant did not knowingly waive his right to appeal the restitution order.
B.
Having established that the challenge to the restitution order has not been waived, we proceed to determine the merits of that challenge. We review a restitution order for abuse of discretion, United States v. Fair, 699 F.3d 508, 511-12 (D.C.Cir.2012), and we examine the factual findings underpinning the order for clear error, United States v. Bryson, 485 F.3d 1205, 1208 (D.C.Cir.2007).
Because the appellant pleaded guilty to 18 U.S.C. § 1591, the district court was required to impose restitution under 18 U.S.C. § 1593. See 18 U.S.C. § 1593(a). Under section 1593, the order of restitution "shall be issued and enforced in accordance with [18 U.S.C. § ] 3664 in the same manner as an order under section 3663A." 18 U.S.C. § 1593(b)(2). Section 3663A is part of the Mandatory Victims Restitution Act (MVRA). Under the MVRA, "[a]ny dispute as to the proper amount or type of restitution shall be resolved by the court by the preponderance of the evidence" with the government bearing the burden to establish the amount of loss suffered by the victim. 18 U.S.C. § 3664(e).
Section 1593 requires that the defendant pay the victim "the full amount of the victim's losses," id. § 1593(b)(1), defined as the sum of two components: (1) ill-gotten gains plus (2) the "full amount of the victim's losses," defined as "(A) medical services relating to physical, psychiatric, or psychological care; (B) physical and occupational therapy or rehabilitation; (C) necessary transportation, temporary housing, and child care expenses; (D) lost income; (E) attorneys' fees, as well as other costs incurred; and (F) any other losses suffered by the victim as a proximate result of the offense." 18 U.S.C. § 2259(b)(3) (incorporated by reference in 18 U.S.C. § 1593(b)(3)).
The losses set forth in the second component of the definition—the "full amount of the victim's losses"—must be proximately caused by the defendant's conduct. United States v. Monzel, 641 F.3d 528, 535, 538 (D.C.Cir.2011) (defendant who possessed single image of victim was not proximate cause of victim's loss which was "due in large part to her knowledge that each day, untold numbers of people across the world are viewing and distributing images of her sexual abuse" and "she would have suffered tremendously from her sexual abuse regardless of what Monzel did"); see also 18 U.S.C. § 3663A(a)(2) (defining "victim" as "a person directly and proximately harmed"). In other words, the defendant should not be required to pay restitution for harm he did not cause. This does not mean, however, that the defendant must be the sole cause of the harm. See Monzel, 641 F.3d at 538 (suggesting entire liability for harm may be imposed on defendant if two or more causes produce single result and either one cause would be sufficient alone to produce result or each cause is essential to harm).
Nor must the amount of restitution be proven with exactitude. As we have explained, "determining the dollar amount of a victim's losses attributable to the defendant will often be difficult" and "such a determination will inevitably involve some degree of approximation," which is "not fatal." Id. at 540. "Rather, the district court's charge is 'to estimate, based upon facts in the record, the amount of [the] victim's loss with some reasonable certainty.' " Id. (quoting United States v. Doe, 488 F.3d 1154, 1160 (9th Cir.2007) (section 2259 does not require "mathematical precision")).
Finally, the appellant makes several arguments that the district court abused its discretion. First, he argues that the district court did not properly take into account the fact that the four minors had been involved in prostitution or other trau matic events before their contact with him. We disagree. Missar testified that he attempted to determine "what would somebody who had just that experience with [appellant] need." A 461-62. And he acknowledged that, while the victims had suffered trauma before being prostituted by the appellant, his abuse was the "proximate" or "most significant cause" and the treatment he recommended would be necessary even if the victims had had no previous trauma. A 880-84.
Second, the appellant contends that the court erred by failing to find that the victims were in fact interested in seeking Missar's recommended treatment. Not so. We compensate a victim with restitution, that is, money—whether she chooses to use the money in a particular way is up to her. See United States v. Frazier, 651 F.3d 899, 904 (8th Cir.2011) (purpose of restitution under MVRA is to "make victims of crime whole" by "fully compensating]" them for their losses) (quotation marks omitted).
Third, the appellant complains that the district court improperly calculated similar damages amounts for each victim despite the fact that each victim prostituted for significantly different lengths of time; specifically, S.H. for approximately 914 days, T.S. for approximately 1159 days, M.S. for approximately fourteen days and A.L. for four days. Missar explicitly addressed this point, however, by explaining that the psychological harm from PTSD takes only a short time to occur. See, e.g., A 360 ("[T]he psychological impact and trauma that each of the girls sustained within the first few days . really set the stage for a traumatic reaction in their brain that is likely to carry on for, in my opinion, the rest of their lives."); A 420 ("[C]ertainly the longer that the trauma went on, the more significant the trauma is, but in terms of meeting a particular threshold of being traumatic, if you will, they are equivalent, in my opinion."). The district court did not abuse its discretion in accepting Missar's explanation.
Fourth, the appellant contends that the district court's calculation of his ill-gotten gains is improper because (1) the court relied primarily on grand jury testimony; (2) according to various studies, the testimony of child sexual abuse victims is inherently unreliable; and (3) the victims' testimony regarding the amount of ill-gotten gains was "frankly unbelievable," particularly because he has little money today. Appellant Br. 12-18. We disagree. There is no per se rule prohibiting a district court from relying on grand jury testimony at sentencing; in fact, the court may rely on such testimony so long as it has "sufficient indicia of reliability." See In re Sealed Case, 246 F.3d 696, 699-700 (D.C.Cir.2001) (quotation marks omitted). Nor do we agree that the victims' testimony was unbelievable. The victims gave detailed grand jury testimony and each victim's testimony was consistent with the others'. Thus, the district court did not abuse its discretion in relying on their grand jury testimony.
For the foregoing reasons, we affirm the judgment of the district court.
So ordered.
. For S.H., the district court multiplied $400 (the average daily amount S.H. testified she earned for the appellant) by 914 days (the length of time the appellant admitted he had prostituted S.H.). For T.S., the court multiplied $500 (the daily amount T.S. testified she was required to earn for the appellant) by 1155 (the total number of days the appellant admitted that he prostituted T.S., minus four days T.S. testified she failed to meet the $500 daily minimum). For M.S., the court added $200 (the amount M.S. made on the first night she worked for the appellant) to $5,265, the product of the remaining number of days M.S. worked for the appellant and $405 (the average amount M.S. earned each day). For A.L., the district court added the average of the amounts A.L. testified that she charged for each of the four sexual contacts she had on her first night working for the appellant ($280) to the amount she charged for each of the three contacts on the second night.
. Intetpretation of a plea agreement relies on contract law. In re Sealed Case, 686 F.3d 799, 802 (D.C.Cir.2012), and ambiguity in a plea agreement is construed against the drafting party; in this case, the government. See Segar v. Mukasey, 508 F.3d 16, 25 (D.C.Cir.2007).
. Section Eleven provides, in pertinent part: "[You] understand[] that in addition to the other penalties provided by law . it is mandatory that the Court order [you] to make restitution for the full amount of any victims' compensable losses." A 28.
. Moreover, at the Rule 11 hearing during which the appellant entered his guilty plea, the magistrate judge did not discuss restitution or the right to appeal restitution but did discuss imprisonment, fines, forfeiture and supervised release. See Accardi, 669 F.3d at 344 (finding appeal waiver not knowing and intelligent when no colloquy regarding appeal waiver occurred at Rule 11 hearing).
.Section 3742(a) provides that a defendant may appeal a sentence if it
(1) was imposed in violation of law;
(2) was imposed as a result of an incorrect application of the sentencing guidelines; or
(3) is greater than the sentence specified in the applicable guideline range to the extent that the sentence includes a greater fine or term of imprisonment, probation, or supervised release than the maximum established in the guideline range, or includes a more limiting condition of probation or supervised release under section 3563(b)(6) or (b)(ll) than the maximum established in the guideline range; or
(4) was imposed for an offense for which there is no sentencing guideline and is plainly unreasonable.
. The government cites United States v. Monzel, in which we stated (in part relying on 18 U.S.C. § 3664(o)(l)(B)) that a restitution order is part of a sentence. 641 F.3d 528, 541 (D.C.Cir.2011) ("Amy is asking the court to revisit her restitution award, which is part of Monzel's sentence.") (emphasis in original). We recognize that, due to section 3664(o)(l)(B)'s reference to section 3742, "sentence" as used in section 3742 includes restitution. To avoid this type of problem in the future, the government should consider including, in the appeal waiver section of the plea agreement, express waiver of the right to appeal restitution.