The employee, Kevin MacDonnell, appeals from a decision by the reviewing board of the Department of *197Industrial Accidents (board) that affirmed a reduction of statutory attorney’s fees under G. L. c. 152, § 13A(2). His employer, the city of Worcester (city), cross-appeals from the same decision, challenging (1) the board’s affirmance of an award of G. L. c. 152, § 34A, permanent and total incapacity compensation; and (2) the board’s reversal of a previous decision allowing the city to recoup disability benefits that were paid to Mac-Donnell while he was participating in a court-ordered alcohol treatment program. We affirm.
Background. On December 2, 2002, while employed as a stonemason with the city, MacDonnell injured his back. As a result, he suffered from low back spasms and radiating pain to his right ankle. Subsequent to his injury, MacDonnell also developed various psychiatric conditions, including depression and anxiety.
After the accident, MacDonnell filed a claim for G. L. c. 152, § 34, temporary total incapacity compensation and was eventually awarded G. L. c. 152, § 35, partial incapacity compensation by an administrative judge. In October, 2005, he filed a new claim for § 34 temporary total incapacity compensation in order to obtain additional compensation and psychiatric treatment. He eventually reached an agreement with the city for the payment of these benefits.
In 2008, MacDonnell filed a claim for G. L. c. 152, § 34A, permanent and total incapacity compensation. After a conference, the administrative judge ordered the city to pay Mac-Donnell § 35 partial incapacity compensation; ordered Mac-Donnell to repay the city $7,846.63 due to the city’s payment of disability benefits while MacDonnell was incarcerated for eighty-two days pending trial for a federal offense; and reduced the statutory attorney’s fee owed to MacDonnell’s attorney.
MacDonnell appealed from the conference order to a full hearing. As a result of this hearing, the administrative judge ordered the payment of § 34A permanent and total incapacity compensation; increased the amount MacDonnell must repay to $15,963.88, to include repayment for both the time that Mac-Donnell was actually incarcerated and the time that he spent in a court-ordered alcohol treatment program; and affirmed the reduction of the statutory attorney’s fee.
*198Both parties appealed the administrative judge’s decision to the board. The board vacated the repayment order relative to the disability benefits paid while MacDonnell was in the alcohol treatment program but otherwise summarily affirmed the administrative judge’s decision. Both parties have now appealed from the board’s decision.
Discussion. 1. Treatment program. The city claims that the board erred in vacating the portion of the administrative judge’s decision requiring MacDonnell to repay benefits received while committed to a court-ordered alcohol treatment program. It argues that such commitment was equivalent to incarceration under G. L. c. 152, § 8(2)(/),1 entitling it to recoup benefits paid during that period. As the board noted in its decision, whether court-ordered commitment in an inpatient treatment program constitutes “incarceration” for the purposes of § 8(2)(/') is an issue of first impression.
“We exercise de nova review of questions of statutory construction . . . and we must overturn agency decisions that are not consistent with governing law.” McDonough’s Case, 448 Mass. 79, 81 (2006). However, “[w]e give substantial deference to a reasonable interpretation of a statute by the administrative agency charged with its administration [and] enforcement.” Bisazza’s Case, 452 Mass. 593, 597 (2008), quoting from Commerce Ins. Co. v. Commissioner of Ins., 447 Mass. 478, 481 (2006). See Arlington Contributory Retirement Bd. v. Contributory Retirement Appeal Bd., 75 Mass. App. Ct. 437, 441 (2009). “When reviewing the board’s decision we give ‘due weight to the experience, technical competence, and specialized knowledge’ of the agency.” McDonough’s Case, 448 Mass. at 81, quoting G. L. c. 30A, § 14(7). Informed by these principles, we will not disturb the board’s conclusion here that MacDonnell’s *199commitment to the treatment program was not incarceration for the purposes of § 8(2)(/).
As a starting point, we consider the structure of the sentence imposed by the United States District Court judge. MacDonnell pleaded guilty to interference with flight crew members. Pursuant to his guilty plea, he was sentenced to “imprisonment of time served” awaiting trial (January 28 through April 18, 2008) and a three-year term of supervised release with various conditions, including the successful completion of a ninety-day inpatient alcohol treatment program. In imposing sentence, the judge made clear that the component of time served reflected that MacDonnell had served “a prison sentence,” even if for a brief period of time. By contrast, with respect to the component of supervised release, the sentencing judge acknowledged it was “for all intents and purposes . . . the same as probation.” Probation is an alternative to incarceration that “allows a criminal offender to remain in the community subject to certain conditions and under the supervision of the court.” Commonwealth v. Durling, 407 Mass. 108, 111 (1990). “[T]he consequence of a disposition of straight probation is the deferment of sentencing ... for a period of time in which the risk of incarceration can be eliminated by successful completion of the probationary period.” Commonwealth v. Rodriguez, 52 Mass. App. Ct. 572, 579 (2001). Here, as the board noted, MacDon-nell’s treatment program was a “specific condition of the employee’s probation which, in turn, was a conditional sentence to be served in lieu of incarceration.”
The fact that the treatment program was a condition of Mac-Donnefl’s supervised release does not end the analysis. We may assume without deciding that with respect to § 8(2)(/), as the city argues, if “the deprivation of liberty to which the defendant was subjected approached incarceration,” then “a condition of probation might be the equivalent of incarceration.” Commonwealth v. Speight, 59 Mass. App. Ct. 28, 32 (2003). Here, any deprivation of liberty experienced by MacDonnell during the treatment program does not approach incarceration due to his relative freedom of movement and his voluntary participation. MacDonnell testified that he was able to leave the treatment program during the daytime to attend Alcoholics Anonymous *200meetings “and stuff.” He may also have received weekend passes to visit home.2 Moreover, he volunteered to attend a treatment program as part of pretrial probation, which he successfully completed prior to sentencing.3 Furthermore, at his sentencing hearing MacDonnell’s counsel requested that participation in a treatment program be included as a condition of probation.
For these reasons, the board’s interpretation of the statute was reasonable, and we defer to its determination, after consideration of judicial decisions noted below, that MacDonnell’s commitment to the treatment program did not amount to incarceration under § 8(2)(/). See Reno v. Koray, 515 U.S. 50, 52-54, 60 n.4 (1995) (defendant not entitled to credit toward his sentence of imprisonment for time spent in a treatment center pretrial); Speight, 59 Mass. App. Ct. at 32 (“at least for the purpose of determining credit for time spent in confinement, an inpatient drug treatment program as a condition of probation does not equal incarceration”); id., quoting Massachusetts Sentencing Commission, Report to the General Court, at 33 (April 10, 1996) (“ ‘residential programming’ and ‘substance abuse treatment’ listed as alternatives to prison” [emphasis in original]). Contrast DuPont v. Commissioner of Correction, 59 Mass. App. Ct. 908, 909-910 (2003), cert, denied, 542 U.S. 943 (2004) (prerelease halfway house is the equivalent of a “correctional facility” because the defendant was specifically assigned to that facility, was not free to come and go, and could not choose to live elsewhere).
Appropriately, MacDonnell does not challenge the denial of workers’ compensation benefits during the eighty-two day period when he was incarcerated and had no freedom of movement or earning capacity. See Connolly’s Case, 418 Mass. 848, 853 (1994). With respect to supervised release, on the facts of this case, where the condition of treatment “was not the equivalent of the involuntary confinement characteristic of a prison sentence,” Speight, 59 Mass. App. Ct. at 32, we cannot say that the board’s determination was inconsistent with the purpose of the workers’ compensation scheme. Moreover, we note that the *201board’s ruling is consistent with the principle that the act “is to be interpreted ‘so far as may be, to promote the accomplishment of its beneficent design. ’ Accordingly, ‘we give this remedial statute a “broad interpretation.” ’ ” Walker’s Case, 453 Mass. 358, 361-362 (2009) (citations omitted).
2. Section 34A benefits. The city further claims that the board’s summary affirmance of the award of § 34A benefits is arbitrary and capricious because MacDonnell failed to meet his burden to establish the required causal relationship between his work-related physical injury and his psychiatric disability.4 Our review on appeal is limited. General Laws c. 152, § 12(2), requires this court to review decisions of the board in accordance with G. L. c. 30A, § 14(7)(a)-(<¿) and (f)-(g). Dalbec’s Case, 69 Mass. App. Ct. 306, 312 (2007). The board’s decision “is not to be reversed unless it is lacking in evidentiary support or a different conclusion is required as a matter of law.” Corraro’s Case, 380 Mass. 357, 359 (1980). In cases like this that involve summary affirmance, “the reviewing court is inspecting the findings and reasoning of the administrative judge.” Dalbec’s Case, 69 Mass. App. Ct. at 313.
“[A]n employee whose emotional disability is the result of a work-related physical injury will be awarded compensation upon a simple demonstration of ‘but for’ causation between the injury and the employee’s condition.” Cornetta’s Case, 68 Mass. App. Ct. 107, 108 (2007). The employee has the burden of establishing causation by a preponderance of the evidence. Patterson v. Liberty Mut. Ins. Co., 48 Mass. App. Ct. 586, 592 (2000).
The administrative judge adopted the opinion of Dr. Nestel-baum, an impartial medical examiner. G. L. c. 152, § 11 A. In his report, Dr. Nestelbaum stated, “It seems that most of [MacDonnell’s] disability is likely related to his chronic back pain .... [I]f [MacDonnell’s] pain symptoms should resolve it is more likely that his psychiatric disorders should not be of sufficient intensity most of the time to cause total[] disability. . . . [A]t the present time Mr. MacDonnell is in my *202view totally disabled from his psychiatric disorders in large part due to his complaints of severe pain.” While Dr. Nestelbaum in his discussion of causation did identify a number of “significant and stressful life events”5 since MacDonnell’s 2002 work injury, he opined that some of these events were “downstream affects” of the injury and ultimately concluded that MacDonnell’s work-related injuries were “a major factor” in his current psychiatric condition.
Based on Dr. Nestelbaum’s report, the administrative judge did not err in concluding by a preponderance of the evidence that there was a causal relationship between MacDonnell’s work-related physical injury and his subsequent psychiatric disability. See Dube’s Case, 70 Mass. App. Ct. 121, 128 (2007). MacDonnell was not required to present any additional evidence to meet his burden with respect to causation. See G. L. c. 152, § 11A(2). Moreover, the city had the opportunity to depose Dr. Nestelbaum to raise further questions regarding the issue of causation but chose not to do so. G. L. c. 152, § 11A(2) (“Either party shall have the right to engage the impartial medical examiner to be deposed for purposes of cross examination”).
3. Attorney’s fees. MacDonnell claims that the board erred in summarily affirming the administrative judge’s order to reduce MacDonnell’s statutory attorney’s fees because it was beyond the scope of the administrative judge’s authority, arbitrary and capricious, or contrary to law to reduce those fees for a purely punitive reason. As noted above, in cases of summary affirmance, “the reviewing court is inspecting the findings and reasoning of the administrative judge.” Dalbec’s Case, 69 Mass. App. Ct. at 313.
MacDonnell’s claim that the administrative judge exceeded his authority is without merit. General Laws c. 152, § 13A(2), clearly provides that an administrative judge may reduce a prevailing party’s attorney’s fees in light of “the complexity of the dispute or the effort expended by the attorney.” Here, the administrative judge affirmed the conference order reducing *203MacDonnell’s attorney’s fees to one hundred dollars and noted that the reduction was a result of the “lack of precision and attention to detail on the part of the employee’s attorney in his presentation of this case.” In other words, the administrative judge reduced the statutory award of attorney’s fees based on the lack of effort on the part of the attorney, a permissible reason under § 13A(2).
MacDonnell’s claim that the administrative judge’s application of § 13A(2) was arbitrary or capricious is similarly without merit. See Scheffler’s Case, 419 Mass. 251, 258 (1994) (decision is not arbitrary and capricious if it “is factually warranted and . . . [has] adequate evidentiary and factual support and disclos[es] reasoned decision making”). Here, MacDonnell’s counsel made inaccurate representations to the administrative judge concerning MacDonnell’s incarceration and MacDonnell’s average weekly wage. The administrative judge reasoned that these inaccurate representations were indicative of a lack of precision and attention to detail and, thus, a lack of effort. Because there was sufficient evidence to support his clearly reasoned decision, the administrative judge’s application of § 13A(2) was not arbitrary or capricious. There is no evidence to support MacDonnell’s argument that the reduction in attorney’s fees was motivated by an impermissible punitive motive.6
The decision of the reviewing board is affirmed.
So ordered.
General Laws c. 152, § 8(2), provides:
“An insurer paying weekly compensation benefits shall not modify or discontinue such payments except in the following situations:
“(/) the employee has been incarcerated pursuant to conviction for a felony or misdemeanor and has thereby forfeited any right to compensation during such period . . . .”
The sentencing judge left the question of MacDonnell’s eligibility for weekend passes to the discretion of the treatment program and the probation department.
MacDonnell received credit for the time spent in pretrial treatment against the court-ordered ninety days in treatment.
On appeal, the city does not raise any defenses involving G. L. c. 152, § 1(7A), as it did at the hearing below. As such, the city has waived this issue on appeal. Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975).
Specifically, “[MacDonnell’s] mother died, his long term relationship ended, he lost his house. He exchanged roles with his children so that now he lives downstairs and they live upstairs and he is dependent on them. He was in jail for several months.”
MacDonnell also argues that the administrative judge unfairly penalized only MacDonnell’s counsel even though the city’s counsel also reviewed and signed the document erroneously reporting MacDonnell’s weekly wage. General Laws c. 152, § 13A(2), does not authorize the administrative judge to reduce the city’s counsel’s fees.