Sample calculation for split-mouth designs

Abstract

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.1Lesaffre E. Philstrom B. Needleman I. Worthington H. The design and analysis of split-mouth studies: what statisticians and clinicians should know.Stat Med. 2009; 28: 3470-3482Crossref PubMed Scopus (212) Google Scholar 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)χσ2(μ1−μ2)2 where σ is the standard deviation of the within-person differences (μ1 – μ2), and f(α, β) is a function of power and significance level.3Pocock S.J. Clinical trials: a practical approach. Wiley, Chichester, United Kingdom1983Google Scholar This formula calculates a sample for 2 paired means. It was adapted from Machin and Fayers2Machin D. Fayers D. Randomized clinical trials: design, practice and reporting. Wiley-Blackwell, Chichester, United Kingdom2010Crossref Scopus (28) Google Scholar to correspond with the formula used in the previous article for comparison of 2 means from independent samples. The Table displays the appropriate substitution values.TableValues for various combinations of power and levels of significanceadapted from Pocock3Pocock S.J. Clinical trials: a practical approach. Wiley, Chichester, United Kingdom1983Google Scholarβ0.05 (95% power)0.1 (90% power)0.2 (80% power)0.5 (50% power)α0.0513.010.57.853.840.0117.814.911.76.63 Open table in a new tab In our example, if we assume that space closure in the elastic chain arm will be μ1 = 1 mm per month and that we would like to observe a 0.5-mm difference (μ1 – μ2) from the nickel-titanium arm (SD of the difference σ = 0.7 mm), if such a difference exists, at the 5% significant level with 90% power, the required sample size for this paired design would be:n=10.5∗0.720.52=21 Therefore, 21 extraction sites per space-closure method would be required for a total of 42 sites, or 21 patients with 2 maxillary premolar extractions, since each patient contributes 2 sites. We can see that this split-mouth design is efficient, since it reduces substantially the sample size required compared with the design that randomizes the 2 interventions to different patients. Just as a reminder, the formula for the independent design is the following:n=f(α,β)χ2σ2(μ1−μ2)2 This formula is for the sample calculation of 2 independent means. For the 2 independent means, the standard deviation is multiplied by 2 on the numerator, thus doubling the required number of sites. Split-mouth designs are not appropriate for all interventions, especially when the therapy on 1 quadrant might affect the outcome on the other quadrants, or when it is difficult to find appropriate and similar pairs of quadrants or teeth in the same patients.1Lesaffre E. Philstrom B. Needleman I. Worthington H. The design and analysis of split-mouth studies: what statisticians and clinicians should know.Stat Med. 2009; 28: 3470-3482Crossref PubMed Scopus (212) Google Scholar, 4Hujoel P.P. DeRouen T.A. Validity issues in split-mouth trials.J Clin Periodontol. 1992; 19: 625-627Crossref PubMed Scopus (105) Google Scholar For example, it would be difficult to conduct a split-mouth trial aiming to compare plaque reduction achieved by 2 types of antibacterial mouth rinses because the risk of 1 mouth rinse contaminating the other side is high. •Split-mouth designs are efficient because they require smaller sample sizes.•Split-mouth designs are not appropriate when contamination between sites is suspected and when it is not possible to find matching sites in patients.