Data analysis

3.3.7.1 Computations

Total and subscale scores were computed by adding up constituent items, reversed as appropriate. This included the DASS-21 total and subscale score (Henry & Crawford, 2005), total score of the BRS (B. W. Smith et al., 2008), total score of the Brief IPQ (Knowles et al., 2013), and coping styles of the Brief COPE (Carver, 1997).

3.3.7.2 Initial and feasibility analyses

Assumption violations were examined as discussed by Field (2013), Pallant (2005), and Tabachnick and Fidell (2013):

1. Accuracy of input and outliers: Out of range values and the plausibility of means and standard deviations were examined.

Univariate and multivariate outliers were set at α = 0.001 (Field, 2013).

Multivariate outliers were detected via Mahalanobis distance in χ²

distribution (Pallant, 2005). Care was exercised not to exclude possible outliers due to nonnormal distributions so as not to render samples unrepresentative.

2. Normality: Normality was assessed visually via histogram, normality plots, and distributions of residuals (for multivariate analysis of variance, MANOVA), the Kolmogorov-Smirnov test, and skewness and kurtosis significant at α = 0.001 (Field, 2013; Tabachnick & Fidell, 2013). For

MLM, the normality of residuals, intercepts, and slopes was examined via visual inspection of their histograms (Rasbash, Steele, Browne, &

Goldstein, 2015; Twisk, 2006). Transformations were attempted for nonnormal data (Field, 2013) but were not possible due to different distributions across time points.

3. Linearity: Linearity was evaluated via examination of multilevel

bivariate scatter plots of continuous variables whose relationships were examined in main analyses. These included outcome variables (BRS score, DASS-21 total and subscales) plotted against predictors (Brief IPQ total and subscales, Brief COPE styles, days from transplantation, and time points).

4. Homogeneity of variance and homogeneity of covariance

matrices: These assumptions were examined via Levene’s test and Box’s test (α = 0.001; Field, 2013).

5. Multicollinearity and singularity: Two indicators were examined – bivariate correlations with r>0.70 and tolerance approaching zero (in the range of 0.1) or condition index exceeding 30 coupled with variance proportions greater than 0.5 for at least two different variables (Belsey, Kuh, & Welsch, 1980; Tabachnick & Fidell, 2013).

6. Missing data in MLM: Missing data can be tolerated well in MLM particularly when either missing completely at random (MCAR, Little’s test is not significant) or missing at random (MAR; Goldstein, 2003;

Rasbash, Steele, Browne, & Goldstein, 2009; Tabachnick & Fidell, 2013). MAR can be assumed when Little’s test is significant but data are missing in a predictable pattern which is unrelated to the outcome variables (Snijders & Bosker, 2012; Tabachnick & Fidell, 2013).

Missing value analysis (Tabachnick & Fidell, 2013) was conducted for outcomes measured at each time point to determine Little’s test and examine whether missing data were related to demographic and clinical characteristics, baseline measures, or outcomes measured at previous time points.

Descriptive statistics in relation to feasibility variables focused on accrual and uptake to the study and intervention, reasons for declining participation,

attendance, reasons for nonattendance, response rates (attrition), and reasons for attrition.

Group differences between participants randomised to intervention

versus control on demographics, clinical characteristics, and baseline measures were examined in order to assess the success of randomisation (Lewis &

Warlow, 2004). Differences between participants who attended the intervention versus those who did not (overall and from those participants randomised to the intervention only) were also examined to assess sampling bias. Chi-square tests (with continuity correction for 2x2 tables and Fisher’s exact test when expected frequencies did not exceed five; Field, 2013), robust independent t-tests (with Bonferroni corrections, α = 0.01, and bias-corrected bootstrapping with 1000 samples), and robust MANOVA (for theoretically related variables such as distress, coping, and HSCT perceptions subscales) were used. Use of robust statistics and bootstrapping aimed at mitigating the influence of potential outliers and assumption violations (Field, 2013; Wilcox, 2012; Wilcox &

Keselman, 2003).

3.3.7.3 Efficacy and psychological processes

Randomisation (intervention versus control) and its interaction with time were entered as predictors to the baseline model (which contained only time).

Sensitivity analyses also examined the effect of actual group attendance versus nonattendance (instead of randomisation). Sample size estimations for a full trial (power = 0.80) used bootstrapped fixed and random parameter estimates of the overall effects during the acute phase of HSCT (time points 2-4). Sample size estimations took account of the observed nonresponse rates. The

standard sample size calculation was adjusted for the multilevel data structure using the method described in Section 6.1. However, the results of different methods for estimating sample size in MLM can vary considerably depending on the method (Twisk, 2006); therefore, caution is required regarding their interpretation.

In light of limited attendance to the intervention (see Section 7.1.1), multilevel single case analysis (Huber, Klein, Moeller, & Willmes, 2015) was also used to triangulate the results of the main analysis and allow for the

detection of small effects that may not be possible due to lack of power. The intervention aimed to secure lower increases in distress during acute HSCT (time points 2-4) compared to baseline than might be expected otherwise;

therefore, single case analysis examined the change in distress of intervention attendees relative to nonattendees. To conduct the multilevel single case analysis, each case was dummy-coded in the multilevel model. The change of each case compared to nonattendees (β coefficient) was then examined.

The method of using multilevel models for repeated measures has been shown to be mathematically and statistically equivalent to the t-test often used in single-measure methods (Crawford & Garthwaite, 2002; Crawford & Howell, 1998; Huber et al., 2015). A two-tailed test was selected since the study was the first evaluation of the intervention which was, therefore, not assumed to be effective (this is in line with Phase II trial practice; Craig et al., 2008). The within-subjects nature of the comparison was a weak design for establishing causality and control but frequent lower increases in distress in attendees were considered initial evidence of effectiveness prior to further evaluation for the purpose of the present study.

3.3.7.4 MLM configuration

The multilevel data structure was defined with time points as Level 1 (i) units and participants as Level 2 (j) units. With the exception of days from the transplant (zero for transplant day), all continuous Level 1 predictors (those measures at each time point) were centred around the grand mean in order to aid interpretation and improve the stability of the model by mitigating the potential multicollinearity (Twisk, 2006). Predictors were entered first as fixed and then, if the model improved significantly, random at Level 2. Results from random effects models were reported when improvements were significant. The R12 provided an estimation of the variance that was explained by the predictors and random effects added at each stage. The R12 was computed as percentage of 1-((σ22+τ22)/(σ12+τ12)) where σ² and τ² represent Level 1 and Level 2 variance respectively between two successive models (Snijders &

Bosker, 2012). Negative change in variance is generally not interpretable (Snijders & Bosker, 2012). Bootstrap estimation (nonparametric,

bias-corrected, with five sets of 500 iterations) was used to mitigate bias from nonnormal distributions and the small sample size (Rasbash, Steele, et al., 2015)

3.3.7.5 Software

Robust MANOVA was conducted using the mulrank() function (Wilcox, 2012) on R (Version 3.2.2; R Core Team, 2015). An example of the robust MANOVA code testing for differences between the groups as randomised on the distress subscales is provided in Appendix J. MLM was conducted using MLwiN software (Version 2.34; Rasbash, Browne, Healy, Cameron, & Charlton, 2015), power analysis and sample size estimations were conducted using MLPowSim software (Version 1.0; Browne & Golalizadeh, 2009), and SPSS software (Version 22; IBM Corp, 2013) was used in all other analyses. Unless specified otherwise, α was 0.05.