2.7. Statistical Analysis
fullness, hunger and desire
INTERACTION
The sample size estimation was calculated with an alpha of 0.05 and power of 0.80 to detect 10% within-group differences in appetite ratings in different settings. The number of participants needed to detect relevant differences between the two study settings has been estimated based on previous interventions studies with similar populations and designs. A total of >16 participants were needed to complete interventions in both settings: free-living and clinic, to detect a contrast with the anticipated variation observed in similar studies before [Data were analyzed according to modified intention to treat (mITT), defined as dropouts occurring after randomization but before the intervention start or after the first out of five intervention days were not included in the final analysis. Analyses of appetite in free-living vs. clinic and for rye vs. wheat for the response variables fullness, hunger and desire to eat were performed with linear mixed effects models for repeated measures, using R (version 4.1.2 and the packages lme4, dplyr, tidyverse, emmeans, ggeffects, lmetest). In model A, we evaluated the effect of location and diet for whole-day responses (0–780 min) with time, occasion, blood sampling and baseline values as covariates. Subject was included as a random effects variable and the interaction terms diet x occasion; diet x time were evaluated in separate models entitled model A.1 and A.2, respectively. Interaction terms that were not statistically significant were removed in the final model A.3: fullness~diet + location + occasion + time + blood sampling + fullness baseline + (1|subject). The final model was modified to evaluate each of the response variables (fullness, hunger and desire to eat) for both dietary comparison and by location, separately. Model B was built to evaluate the effect of location and diet for postprandial periods following breakfast, lunch, snack and dinner and included all above-mentioned covariates, except for the baseline value. Interaction effects were tested and excluded from the final model if not significant. In a third model we evaluated the effect of location and diet measured as tAUC. Total area under the curve (tAUC) for appetite responses was calculated using approximating integrals according to the trapezoidal rule [The third model, model C, included the covariates occasion, blood sampling and subject as random effects variables in the analysis of whole-day response as well as postprandial periods of breakfast–dinner. Physical activity, measured as total step count in the free-living setting and on clinic-based intervention days, was evaluated with subjects modeled as a random variable and occasion as a covariate. Data presented are model-adjusted least-square means with standard error of the mean and considered statistically significant at 