Statistical Analysis. The investigator will use the biopsychomarkers identified as the highest prediction value to determine the relative accuracy to predict response to the Mindful Intervention (i.e., disease outcome). For response to the mindful intervention, the investigator will use the use the combination of markers to study whether they correctly predict the response to the intervention. The investigator will study the accuracy of the markers using area under the curve (AUC) summary index for ROC curves.181 If the classification accuracy of the markers is high then the area under the curve will be close to 1. If the predictive accuracy of the combined set of markers were poor then the (AUC) will be close to 0.5.
Power Estimates UC disease flare-up was quite common in this sample, occurring in well over half of subjects in the samples collected in the discovery phase. The power analyses, assuming α = 0.05 for all tests indicated that for models involving analyses of correlational data, there will be sufficient power at even small effect sizes for the smallest possible sample with full data across all data points and virtually all variables. For the most conservative estimate, the investigator base their calculations on having 50 participants with data with full integrity. With an effect size of r = 0.15 and n = 50, power is 80 or greater to detect effect sizes of r = 0.20. Effect sizes below this threshold would likely not be clinically significant or substantively interpretable, as they would explain less than 2% in the variance of the dependent variable. Thus, most effect sizes that would be reasonably and substantially interpretable will have good power. Each factor that is suspected of varying between groups can be examined with the chi-square test based on 1 degrees of freedom, by setting it invariant in one model and then allowing it to be freely estimated in the other. Such a chi-square test provides a power of 0.80 with effect size difference of 0.15.
For binary categorical measures, such as responsiveness to MSRB, the investigator conducted separate power analyses.
The power for adjusted analyses of primary predictors of interest will be evaluated as a function of the risk of outcome when all ancillary variables are set to their mean value, the predictor is set to the mean value, and proportion of variance in predictor explained by the ancillary variables, and the odds ratio of outcome variable from increasing the predictor by an amount equal to one of its standard deviation. The range in probabilities of outcome variables can be anywhere from 20% for less likely events and 50% for more likely events, the investigator will provide power calculations over a wide range of probabilities. The investigator believe that the amount of variation of our typical model ranges from about 20% to 50%. The table (below) represents the minimum odds ratio than can be detected with 80% power, which indicate good power for expected outcome.
Proportions R2 =.20 R2=.50 0.10 1.64 1.87 0.20 1.46 1.63 0.30 1.39 1.53 0.40 1.35 1.48 0.50 1.32 1.43
