Statistical analysis

Data analysis was completed based on intention-to-treat and data collected from all participants enrolled in the study was included in the analysis. For dichotomous outcomes, missing values from post-intervention assessments of individuals who discontinued the study were handled according to the baseline-observation-carry-forward approach as we assumed no change for those where the outcome was unobserved. For continuous outcomes (e.g. treatment log), intention-to-treat meant that we only retained data from participants for whom the information was available to avoid multiple imputations.

Statistical analyses were performed using SPSS 22.0 (IBM Corp., Armonk, NY, USA). Independent sample t-tests were used to assess group differences in demographic and clinical-related parameters at baseline. We analyzed the effects of the intervention on the outcome measures using a 2×2 factor repeated measures analysis of variance with time (baseline and post-intervention) and group (continuous 40 Hz stimulation vs. intermittent gamma-frequency stimulation) as factors. Significant interactions and within-group comparisons were further explored with paired t-tests. Analysis of daily pain levels before and after each treatment session (self-reported in treatment logs) was performed by averaging the daily ratings to reflect changes on a weekly basis. Changes of average pain ratings over the course of the study were analyzed with a repeated measures ANOVA with time (weeks 1-5) and pain ratings (before/after a session) as within-subject factors, and group (40 Hz continuous vs. intermittent stimulation) and treatment response (responders vs. non-responders) as between-subject factors. For all ANOVAs, data were continuous and normally distributed, with no significant outliers and no evidence of sphericity from the Mauchly’s test or violation of homogeneity of variance from the Levene’s test. We also conducted logistic regression analyses to examine the possible influence of baseline clinical outcome variables on treatment response. The independent variables (i.e., fibromyalgia symptoms, pain severity and interference, depression, quality of life, and sleep quality at baseline) were each entered separately on to the model to probe for indices evaluating prediction of response. The alpha level was set at 5% for all tests. Based on previous studies [38], to determine effect size required (r = .95) to obtain sufficient statistical power (80%) with the significance level of α = 0.05, the minimum sample size for each group is 20 patients.