64 Chapter 4 19, 1 = during COVID-19) in the sensitivity analyses next to the following potentially confounding baseline variables as stated in the protocol paper (Lensen et al., 2021): gender (coded as 0 = female, 1 = male), age (in years), school weight (coded as 0 = < regional weight average 1 = ≥ regional weight average), teachers’ years of experience (in years), number of work days per week (in days), past or present psychological problems (coded as 0 = no, 1 = yes). Sample size calculation In determining the necessary number of participants, we presumed a significance level (α) of 0.05 and a moderate effect size (δ) of 0.50 (e.g., Verweij et al, 2018). That study gives a good indication as the study population consisted also of professionals in a highly demanding job, was comparable in age and living situation and was not selected on psychological complaints. To reach 80% power, 64 participants had to be included in the intervention as well as the control group. With an estimated dropout rate of 17.5%, comparable to the study from Verweij et al. (2018), we focused on recruiting 155 participants during three consecutive school years. Data analyses All analyses were conducted in R (R Core Team, 2020) using the packages esc for effect size calculation (Lüdecke, 2019) and lme4 (Bates et al., 2018) for linear mixed models and were in accordance with the previously published protocol (Lensen et al, 2021). A probability cut-off of α < .05 was used for all analyses. Intention-to-treat analyses were conducted to examine the effect of the intervention on primary and secondary outcomes and proximal outcomes. Linear mixed models were used for the analyses, which adequately deal with missing data and can account for the multilevel structure of the data (Scott et al., 2013). In this study, observations were nested within participants, and participants were nested within MBSR-training groups and schools. However, since the intraclass-correlation (ICC) of the MBSR-training groups and schools (ICC < .01) was negligible, all models were fitted as two-level models including only random effects for observations nested within teachers (Theobald, 2018). All models were specified including random intercepts, as a more complex random intercept and slope model did not show a significantly better fit for the primary outcome perceived stress. The variance-covariance structure was set to compound symmetry, since a more complex unstructured covariance structure did not show a significantly better fit when compared with a likelihood-ratio test (p = .64). Restricted maximum likelihood was used for estimation in all models. To determine whether the intervention had an effect on the corresponding outcomes, fixed effects for time and group as well as their higher-order interaction were included in the mixed models. Furthermore, the models were repeated using per-protocol data including completers only. In this context, completion was defined as having attended at least 4 of the 8 group sessions (Kuyken et al., 2015). Estimated marginal means and standard errors from the mixed models were used to calculate between-group Cohen’s d effect sizes and corresponding 95% confidence intervals. Effect sizes > 0.80 were considered
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