Effects of treatment on the signal-averaged LPP response and subjective responses were examined using RM-ANOVA. To ensure the success of our randomization procedure, we first tested whether there were group differences at pretreatment in LPP response. No significant between-groups differences in pretreatment LPP response were observed in experiment 1 (F1,38 = 0.02, P = 0.89, ηpartial2 < 0.01), experiment 2 (F1,22 = 0.06, P = 0.81, ηpartial2 < 0.01), or experiment 3 (F1,27 = 1.29, P = 0.27, ηpartial2 = 0.05).

We performed a power analysis under a range of possible effect sizes and RM correlations. For instance, assuming a small-medium effect size (Cohen’s f = .25) and a medium RM correlation (r = 0.35), power for the signal-averaged LPP analysis is 0.80 with n = 43. With a Cohen’s f = 0.30 and a large RM correlation (r = 0.50), statistical power is 0.83 with n = 26. In contrast, assuming a medium-large effect size (Cohen’s f = 0.35) and a medium RM correlation (r = 0.35), statistical power is 0.82 with n = 24. This latter effect size estimate was based on effect sizes observed in three published studies of the effects of MORE on cardiac autonomic reactivity (ηpartial2 = 0.18) (28), LPP responses (ηpartial2 = 0.17), and BOLD responses in striatal reward circuitry (Cohen’s d = 2.13) (29) to natural reward cues. Our actual observed effect size in experiment 1 (Cohen’s f = 0.37) was close to the latter assumption, yielding an achieved power of 0.95. For hypothesis testing, in experiment 1, we assessed the interaction of Group (MORE versus SG) with Time (Pretreatment versus Posttreatment) and Stimulus Type (Opioid versus Neutral) on LPP response. In experiments 2 and 3, we assessed the interaction of Group (MORE versus SG) with Time (Pretreatment versus Posttreatment) and Condition (View versus Regulate) on LPP response. When appropriate, Greenhouse-Geisser corrected values were used, and significant (P < 0.05) main effects and interactions were interrogated with Bonferroni-adjusted planned post hoc tests. RM-ANOVA models of LPP response included posttreatment opioid dose (in average daily morphine equivalents) to control for the pharmacological impact of opioid exposure on electrocortical responses. In a separate series of sensitivity analyses, we controlled for pain severity, and effects of MORE on LPP responses in experiments 1 to 3 remained statistically significant.

Because of the small sample size in experiments 2 and 3, we used multilevel modeling (MLM) of trial-level LPP data as an additional sensitivity analysis for these two experiments. Given its capacity to partition sources of variance from the error term, MLM increases power to detect fixed effects without averaging across trials to minimize noise, and thus, this analytic technique is seen as well suited for application to ERP research (40). MLM models included random intercepts and no random slopes. Change in model fit statistics (i.e., −2LL) was used to select the optimal covariance structure for repeated effects (e.g., AR1 versus diagonal) as well as for our overall model building approach. We began parsimoniously by first examining an unconditional growth model and then adding fixed effects and evaluating model fit with likelihood ratio tests. Satterthwaite approximations estimated degrees of freedom. In experiment 2, the significant likelihood ratio test (χ2diff = 17.87, dfdiff = 6, P = 0.006) indicated that the fully parameterized model should be retained over the unconditional growth model, and the Group × Time × Condition interaction was significant in trial-level MLM analyses (F1,1473.29 = 5.49, P = 0.019). In experiment 3, the significant likelihood ratio test (χ2diff = 22.04, dfdiff = 6, P = 0.001) indicated that the fully parameterized model should be retained over the unconditional growth model, and the significant likelihood ratio and the Group × Time × Condition interaction were also significant in trial-level MLM analyses (F1,1034.53 = 6.25, P = 0.013).

We then computed a measure of relative responsiveness to natural reward versus drug reward by subtracting LPP regulatory response to opioid cues from LPP regulatory response to natural reward cues (regulate − view difference scores) and assessed the Group × Time interaction on this relative responsiveness measure. This analytic approach has been used in previous LPP studies of individuals with substance use disorders (17). Our statistical plan for this approach was modeled from a previous study of MORE in which we identified a significant Group × Time interaction on an autonomic measure of relative responsiveness to natural reward versus drug reward (35).

In experiment 4, we assessed the interaction of Group (MORE versus SG) with Time (Pretreatment versus Posttreatment) and Condition (View versus Regulate) on log-transformed positive affect and craving reactivity scores (task block ratings − baseline ratings). Last, in experiment 4, we conducted a path analysis with bootstrapping in PROCESS 2.16.1 software to evaluate pre-post changes in subjective natural reward responsiveness as a mediator of treatment effects (MORE versus SG) on changes in opioid misuse (as measured by the COMM) from pretreatment to 3-month follow-up, with significant mediation indicated by the 95% bias-corrected confidence intervals not spanning zero.

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