How many measurements for time-averaged differences in repeated measurement studies?

In many studies, investigators have perceived the number of repeated measurements as a fixed design characteristic. However, the number of repeated measurements is a design choice that can be informed by statistical considerations. In this paper, we investigate how the number of repeated measurements affects the required sample size in longitudinal studies with scheduled assessment times and a fixed total duration. It is shown that the required sample size always decreases as the number of measurements per subject increases under the compound symmetry (CS) correlation. The magnitude of sample size reduction, however, quickly shrinks to less than 5% when the number of measurements per subject increases beyond 4. We then reveal a counterintuitive property of the AR(1) correlation structure, under which making additional measurements from each subject might increase the sample size requirement. This observation suggests that practitioners should be cautious about assuming the AR(1) model in repeated measurements studies, whether in experimental design or in data analysis. Finally, we show that by introducing measurement error into the AR(1) model, the counterintuitive behavior disappears. That is, additional measurements per subject result in reduced sample sizes.