While statistical software such as nQuery Advisor and SAS can handle power and sample size calculations for detecting interaction effects, a modest body of literature exists describing the effect of the magnitude of the interaction effect and distribution of the prognostic factor have on power and sample size.
For positive misspecifications of the distribution of the prognostic factor, the modified quota sampling procedure attained 80% for all combinations of the magnitude of the interaction effect and planned distribution of the prognostic factor (Table 3).
We varied the magnitude of the interaction effect, the distribution of the prognostic factor, and the magnitude of the misspecification.
The likelihood of switching to quota sampling was related to the magnitude of the interaction effect, the planned distribution of the prognostic factor, and the magnitude of the negative misspecification.
When measurement of the environmental exposure has substantial error, genotyping errors of the order of 3% can lead to substantial under-estimation of the magnitude of an interaction effect [ 67].
We varied the magnitude of the interaction effect, the distribution of the prognostic factor, and the magnitude and direction of the misspecification of the distribution of the prognostic factor.
Since there were 10 different combinations of prevalence of the prognostic factor and magnitude of the interaction effect and 10 trials for each combination, the plot generated 100 points.
When the magnitude of the interaction effect was five and the misspecification of the distribution of the prognostic factor was −15%, greater than 99.8% of the trials switched to the quota sampling method and the procedure attained 80% power.
However, when the magnitude of the interaction effect was 15, and the misspecification of the distribution of the prognostic factor was −5%, the modified quota sampling approach only attained 80% power when the planned distribution of the prognostic factor was 40% or 50% (Table 3).
Given the modest magnitude of the interaction effect and the lack of significant differences between groups at any time point, it is also possible that neither of the intervention arms had any true impact on adherence and the observed fluctuation is merely a function of being part of a study (i.e., Hawthorne Effect) followed by regression to the mean over time.
Although independence of treatment effects is assumed, the magnitude of any interaction effect will be examined (but is not intended for the main analyses).
