Sample calculation for split-mouth designs

In the 2 previous articles, we discussed sample calculations for proportions and means from independent observations. In orthodontics, a common scenario is when 2 interventions are applied in the same patient in a split-mouth approach. In this case, we have paired observations, and the required sample size is smaller because of the reduced variability. The split-mouth design resembles the crossover design, more often encountered in trials in medicine, without the period effects.

In this article, we will perform a sample calculation for 2 paired means with a 1:1 allocation ratio, assuming normality, for a 2-sided test with a split-mouth design.

In our working example, we are interested in evaluating space-closure differences in Class II Division 1 maxillary premolar extraction patients by using an elastic chain on 1 side and a nickel-titanium coil on the contralateral side. This is a paired observation case, with the participant serving as the control, since both intervention and comparison treatments are applied in each patient. This design is more efficient because the sites that receive the interventions are similar, thus reducing variance and sample-size requirements. This formula would apply.

n = f ( α , β ) χ σ 2 ( μ 1 − μ 2 ) 2