The full statistical analysis plan can be found in the appendix (pp 11–21). There were no previous trials on mental health in pandemics to estimate effects, but effects of brief anxiety-focused interventions in post-disaster settings are between 0·40 and 0·80 standardised mean difference (SMD; see appendix p 12). For an assumed effect size of SMD=0·50, two-tailed α=0·05, and intra-class correlation coefficient of 0·05, n=146 provides at least 80% power; assuming 10% loss to follow-up would require 162 participants; assuming 30% loss would require 195 participants. We targeted at least 162 participants with maximum 195.

All outcome analyses were done in R (R version 3.6.3; R Studio version 1.2.5042). For continuous outcomes, we used an intention-to-treat analysis to estimate score differences between intervention and waitlist participants with a linear mixed-effects model fit, which made use of the lmer function in lme4.24 Score differences and Hedges' g SMD effect size were presented with 95% CIs. To estimate odds ratios for the dichotomous MCID, intention-to-treat analysis was done with a binomial generalised linear mixed-effects models with a log link function, which made use of the glmer function in lme4.24

For all models, to account for clustering in the blocked partially nested-RCT design, we fitted a random intercept and slope for treatment effect by randomisation block and an additional random slope for treatment by intervention group cluster.11 In main analyses, in addition to a fixed effect for assignment to the intervention group, we included a fixed effect for baseline score. In adjusted analyses, we also controlled for age (years), sex (male vs female), systemic sclerosis disease subtype (diffuse vs limited), disease duration (years since diagnosis), and country (Canada, France, other vs USA) as fixed effects.

To minimise the possibility of bias from missing outcome data, we used multiple imputation by chained equations by means of the mice package to generate 20 imputed datasets, using 15 cycles per imputed dataset. Variables in the mice procedure included randomisation block, intervention group, number of intervention sessions attended, measures of all primary and secondary outcomes at baseline and post-intervention, age, sex, systemic sclerosis disease subtype, years since diagnosis, country (Canada, France, UK, Australia, other vs USA), and race–ethnicity (Black and other vs White). Pooled standard errors and associated 95% CIs were estimated by means of Rubin's rules.25

To estimate average intervention effects among compliers (defined as attending ≥6 sessions), we used an instrumental variable approach to inflate intention-to-treat effects from main models by the inverse probability of compliance among intervention group participants (complier-average causal effect analysis); 95% CIs were constructed via a cluster bootstrap approach, resampling at study randomisation block and participant levels. Additionally, for transparency, we presented complete case analyses limited to participants at each timepoint who completed assessments.

Post-hoc analyses included dichotomous analysis of participants with anxiety symptom reduction of at least 1 MCID and analyses of anxiety symptom scores by week of randomisation and by baseline scores of at least 60 versus less than 60. All analyses were two-sided with α=0·05. We did not adjust for multiple analyses since we identified a single primary outcome a priori.

There were several protocol amendments. First, the trial was initiated quickly with finite funding, and the initial protocol12 included outcome assessment only immediately post-intervention. Before collection of any outcome data, we applied for additional funding (Canadian Institutes of Health Research; VR4-172745), which allowed the addition of a 6-week post-intervention assessment. Second, initially specified secondary outcomes included stress and social interaction frequency; both were removed before collecting outcome data owing to concern about assessment length. Third, the COVID-19 Fears Questionnaire was not in the protocol because it was under development. Once validated, it was included as a secondary outcome. Fourth, the CSQ-8, which assessed intervention participant satisfaction, was added subsequent to the initial protocol. Fifth, post-hoc dichotomous and subgroup analyses were done (see appendix pp 11–21).

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