On the analysis of very small samples of Gaussian repeated measurements: an alternative approach

The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference.