Data collection was completed November 28, 2018, and data analyses were conducted from December 10, 2018, to November 5, 2019. Sample size was determined using Stata, version 15 (StataCorp LLC) using the SSI module for noninferiority trials.42 For CAPS-5 severity scores, a noninferiority margin of 5 points, SD of 10, a 1-sided α of 0.025,36 power of 0.80, and equal allocation of participants between treatments indicated that 63 patients per randomization arm were needed. To protect against an anticipated attrition rate of 26%, the sample was inflated to 170 patients. Characteristics of veterans who completed half or more of the treatment sessions were compared with those who did not using χ2 analysis and t tests for categorical and continuous data, respectively.

Noninferiority was assessed using linear mixed models that included treatment condition, time (baseline, posttreatment, 3 months, and 6 months), and time by treatment interaction as fixed effects. Because outcomes were highly correlated for both the loving-kindness meditation (intraclass correlation coefficient [ICC], 0.55; 95% CI, 0.41-0.68) and CPT-C (ICC, 0.58; 95% CI, 0.46-0.70) at the individual level, a patient identifier was included as a random effect to account for correlated outcomes over time. Correlation at the group cohort level was found to be minimal and not included in the final models. Age, sex, trauma type, and baseline PROMIS depression and CAPS-5 scores for the PTSD and depression noninferiority models, respectively, were included as covariates. A patient identifier was included as a random effect to account for correlated outcomes over time (ICC, 0.44; 95% CI, 0.22-0.68 and 0.45; 95% CI, 0.28-0.62 in the loving-kindness meditation and CPT-C arms, respectively). The noninferiority of loving-kindness meditation with respect to CPT-C was analyzed using the 95% CI for the group × time interaction term, with noninferiority of loving-kindness meditation to CPT-C claimed if the lower limit of the 95% CI was greater than –δ. Analyses were performed using both intention-to-treat (ITT) and completer (those attending ≥6 sessions of loving-kindness meditation or CPT-C) samples given that ITT analyses may bias results toward noninferiority,43 with noninferiority claimed if both completer and ITT analyses demonstrated noninferiority36,43 at the 6-month time point. If noninferiority was shown, as part of the analytic plan for the primary aim, we assessed superiority using the group × time interaction term from the linear mixed models described previously, with a 2-sided α of .05 considered significant.44,45

Between- and within-group effect sizes based on the previously mentioned models were calculated as Cohen d. Proportions with clinically meaningful change, full remission, and no longer meeting DSM-5 criteria were compared using χ2 tests. Veterans with missing data were coded as not demonstrating clinically meaningful change and as retaining diagnostic status. All analyses were completed in Stata, version 15 (StataCorp LLC).

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