Power and sample size for random coefficient regression models in randomized experiments with monotone missing data

Random coefficient regression (also known as random effects, mixed effects, growth curve, variance component, multilevel, or hierarchical linear modeling) can be a natural and useful approach for characterizing and testing hypotheses in data that are correlated within experimental units. Existing power and sample size software for such data are based on two variance component models or those using a two-stage formulation. These approaches may be markedly inaccurate in settings where more variance components (i.e., intercept, rate of change, and residual error) are warranted. We present variance, power, sample size formulae, and software (R Shiny app) for use with random coefficient regression models with possible missing data and variable follow-up. We illustrate sample size and study design planning using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We additionally examine the drivers of variability to better inform study design.