Sample size estimation for heterogeneous growth curve models with attrition

In this study, two approaches were employed to calculate how large the sample size needs to be in order to achieve a desired statistical power to detect a significant group-by-time interaction in longitudinal intervention studies—a power analysis method, based on derived formulas using ordinary least squares estimates, and an empirical method, based on restricted maximum likelihood estimates. The performance of both procedures was examined under four different scenarios: (a) complete data with homogeneous variances, (b) incomplete data with homogeneous variances, (c) complete data with heterogeneous variances, and (d) incomplete data with heterogeneous variances. Several interesting findings emerged from this research. First, in the presence of heterogeneity, larger sample sizes are required in order to attain a desired nominal power. The second interesting finding is that, when there is attrition, the sample size requirements can be quite large. However, when attrition is anticipated, derived formulas enable the power to be calculated on the basis of the final number of subjects that are expected to complete the study. The third major finding is that the direct mathematical formulas allow the user to rigorously determine the sample size required to achieve a specified power level. Therefore, when data can be assumed to be missing at random, the solution presented can be adopted, given that Monte Carlo studies have indicated that it is very satisfactory. We illustrate the proposed method using real data from two previously published datasets.