Sample size calculation
An a-priori power calculation in G*Power on the basis of the F-test family, choosing ANOVA (repeated measures within-between interaction) as the statistical test, setting the number of measurements at 4 (pre-treatment, post-treatment, 6 months follow-up, 12 months follow-up), with a correlation of .35 between repeated measures, nonsphericity set at .80, the significance level at .05 (two-sided), a power of .80 and an expected effect of medium size (f = .25) resulted in a required total sample size of 42. Accounting for attrition, we were able to assess a larger number of participants (n = 52) at 12 months follow-up.
Interventions
Treatment in both conditions consisted of a maximum of 20 sessions over 30 weeks. The amount of treatment sessions could be adjusted to the patient’s needs, with a minimum of 9 and a maximum of 20 sessions. In the ACT condition, the mean of treatment sessions was 15.02 with a standard deviation of 5.75. For the CBT condition this was 14.89 and 5.60 respectively, with no significant difference between the two conditions (
p = .92). CBT was provided in a manner consistent with standard CBT for depression [
14] and included both behavioral and cognitive aspects in an integrated fashion [
24]. The first eight sessions (phase one) addressed BA and social skill development. The next eight sessions (phase two) addressed cognitive dispute and changing the content of thinking.
ACT was provided through the treatment manual for depression developed for this study by the first author [
25], based on Hayes et al. [
17], Zettle [
26] and Robinson and Strosahl [
27]. The manual consists of 16 sessions addressing acceptance, defusion, an observing perspective and present moment awareness in the first eight sessions. The subsequent part of the treatment addressed behavioral change through values clarification and shaping committed action.
In short, we found that at post-treatment, remission rates from depression were 75 and 80% for the ACT and CBT conditions, respectively. Patients in both conditions further reported significant and large reductions of depressive symptoms and improvement on quality of life from pre- to post-treatment as well as at the 6-month follow-up. Our findings indicated no significant differences between the two intervention groups at post-treatment and at 6-month follow-up. More information on pre- vs. post-treatment and 6-month follow-up efficacy related results of the trial can be found elsewhere [
7].
Data analytic approach
Consistent with the initial report of this trial [
7] multilevel analyses were conducted to evaluate and compare the effect of the CBT and ACT interventions on symptoms of depression and quality of life at 12-month follow-up. The level-1 model included the time variable, which captures within-person change over time. In the level-2 model, between-person characteristics such as intervention condition were used to predict the slope estimates representing change in the dependent variables. Maximum likelihood estimation was employed providing unbiased estimates in the case of missing data. The assumption that data were missing at random was evaluated by using binary logistic regression to predict measurement drop-outs. Baseline characteristics did not differ significantly between conditions (all
ps > .05). Subject-specific random effects (i.e., random intercept and slope) were retained whenever they significantly contributed to the model. Due to the absence of a significant covariance between the intercept and the slope for all measures, we defined a diagonal covariance structure of random effects at level 2.
We estimated a linear trend indicating the direction and rate of change, a quadratic trend indicating a first reversal in the rate of change, and a cubic trend indicating a second reversal in the rate of change (e.g., relapse of symptoms). Contrast coding was used to evaluate the effect of the categorical variable intervention condition [
36]. The contrast compared the interventions (ACT coded .5 and CBT coded −.5). Any differences in the rate of change of depression and quality of life between the 6-month and 12-month follow-up assessments were represented by a Cubic Time × Intervention Condition interaction.
Within group effect sizes (Cohen’s d) for each outcome measure were calculated by dividing the difference between the pre-treatment and 12-month follow-up means by the standard deviation of each mean. To correct for dependence among these means [
37], we calculated the correlation between the pre-treatment and 12-month follow-up scores. Between-group effect sizes (Cohen’s d) from pre-treatment to 12-month follow-up were calculated by subtracting the means and dividing the result by the pooled standard deviation, adjusting the calculation of the pooled standard deviation with weights for the sample sizes. We used the pooled pre-treatment standard deviation for weighting the differences of the pre-treatment to follow-up means as proposed by Morris [
38]. In both calculations the CBT group was treated as the control group.
Structural equation modelling was conducted in Mplus 6.12 [
39] to evaluate the effects of the potential mediators dysfunctional attitudes, decentering and experiential avoidance on symptom levels of depression. Mediation was assessed in three steps. First, latent growth curve modelling [
40,
41] was conducted to assess change in the mediators during the treatment phase. For each individual mediator, an intercept-only, linear change and quadratic change model was fitted to assess which model best described the shape of change (i.e., no change versus linear change versus curvilinear change) across six time points; pre-treatment, session 1, 6, 11, 16, and post-treatment. Separate models were also fitted for the primary outcome of depressive symptoms (QIDS-SR scores) to obtain estimates of initial levels (i.e., intercept), growth (i.e., slope), and to determine the extent of variation across individuals. The multigroup modeling approach [
42] was applied to test whether change in the mediators and outcome was of different magnitude for ACT and CBT. Bayesian Information Criterion (BIC [
43];) was used to examine the relative strengths of the candidate models, with smaller values indicating a better fit of the model to the observed data. According to Raftery [
44], BIC differences < 2, between 2 and 6, and > 6 indicate respectively, weak, moderate, and strong evidence in favor of the model with the lowest values. The absolute model to data fit for each of the models was evaluated using the Root Mean Square Error of Approximation (RMSEA) and the Comparative Fit Index (CFI).
1 For interpretation of these model fit indices we followed Hu and Bentler [
47]. That is, RMSEA values less than .06 were taken as an indication of a good model fit whereas values between .06 and .10 were taken as an indication of an acceptable model fit. For the CFI, values of .90 or higher were taken as an indication of acceptable model fit, and values of .95 or higher were taken as an indication of good model fit.
In a second step, the best fitting growth curve model for each mediator was combined with the best fitting growth curve model of the outcome in a series of parallel process models. These models allowed us to investigate whether change in each mediator was associated with change in the outcome (i.e., a significant mediator slope to outcome slope regression path) supporting the hypothesis of common developmental trends among mediators and outcome.
As we have discussed in the introduction, mediation requires that change in the mediator occurs before change in the outcome variable [
16]. One criticism of the parallel process model of mediation is that it merely assesses mediation effects for contemporaneous change as opposed to mediation effects for longitudinal change in which prior change in the mediator is related to subsequent levels in the outcome variable [
48]. In a third step, we investigated longitudinal mediation by applying latent difference score models [
49]. In these models, successive latent difference scores for each of the mediators were derived by fixing two paths at 1, the path from the starting point to the end point of an interval (e.g., session 1 to session 6) and the path from the latent difference of that interval to the last time point from which that difference score was derived (e.g., latent difference of session 1 to 6 to the session 6 time point). The residuals of the mediators were set equal to 0. Because of these constraints, latent difference scores for each of the five intervals were obtained that represent dynamic change in terms of the difference between the intervals. The mean of the observed depressive symptom scores was estimated along with the means of the latent difference scores for the mediators. The latent difference scores were used to predict symptom levels of depression at the end of that interval (e.g., latent difference of mediator from session 1 to 6 predicting QIDS-SR scores at session 6) while controlling for earlier depressive symptom levels through the estimation of autoregressive pathways. The multigroup modeling approach was applied to test whether mediation effects were treatment specific as formulated in hypothesis 4 (ACT: decentering and experiential avoidance, CBT: dysfunctional attitudes).
Response rates at the different assessment points varied. All participants filled out the pre-treatment assessment, whereas response rates at the 16th session, at 6-month follow-up and at 12-month follow-up were lowest with 61.0, 70.7, and 63.4% completion, respectively. Response rates at the remaining time points ranged from 80.5 to 98.8%.
For all models the maximum likelihood missing data procedure was used. This maximum likelihood procedure uses all available data from each participant and assumes that data are missing at random. A Little MCAR’s test was performed to determine the pattern of missingness. The results of this test indicated that missing values were completely at random, χ2(41) = 46,58, p = .25.