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Sample size estimation: An overview with applications to orthodontic clinical trial designs

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Proper sample size estimation is an important part of clinical trial methodology and closely related to the precision and power of the trial’s results. Trials with sufficient sample sizes are scientifically and ethically justified and more credible compared with trials with insufficient sizes. Planning clinical trials with inadequate sample sizes might be considered as a waste of time and resources, as well as unethical, since patients might be enrolled in a study in which the expected results will not be trusted and are unlikely to have an impact on clinical practice. Because of the low emphasis of sample size calculation in clinical trials in orthodontics, it is the objective of this article to introduce the orthodontic clinician to the importance and the general principles of sample size calculations for randomized controlled trials to serve as guidance for study designs and as a tool for quality assessment when reviewing published clinical trials in our specialty. Examples of calculations are shown for 2-arm parallel trials applicable to orthodontics. The working examples are analyzed, and the implications of design or inherent complexities in each category are discussed.

Section snippets

Key factors in determining sample size

Before we proceed with sample calculations we must define the following13, 14: (1) the research question, (2) the principal outcome measure of the trial (ie, continuous or categorical), (3) the type of analysis and study design that will be used, (4) the expected proportion or mean value of the selected outcome in the comparison or control group, (5) the minimum clinically important difference between treatment arms that we would like to detect, (6) the variance (for continuous outcomes), and

Sample calculations for clinical trials: Parallel arm designs

First we will conduct a sample calculations for a trial with qualitative outcomes, a 1:1 allocation ratio, and a 2-sided test.

We are interested in conducting a trial to compare failures of lingual retainers bonded with chemically cured or a light-cured adhesive, and to determine whether there is a difference at the 0.05 statistical level with 90% power. The procedure for sample calculation for such a study will be as follows.

  • 1.

    We must decide what is an acceptable difference to be observed that is

The Altman nomogram

Altman17 created an easy-to-use nomogram for quick sample calculations for continuous outcomes for equal-size 2-arm trials. In Figure 3, on the left vertical line, is the effect size (standardized difference) for which the sample size is required at the prespecified significance level (shown on the diagonal line in the center) and power level (on the right vertical axis). The effect size in terms of the standardized difference is defined as the ratio of the minimum difference to be detected to

Other trial designs

In certain situations, it is possible to evaluate 2 or more interventions or parameters simultaneously in a single trial. This can be accomplished with a factorial design, which takes the form of 2 × 2 in the simplest form. The advantages of the factorial design are related to the fact that 2 or more parameters can be assessed at the same time, thus creating a more efficient trial in terms of resources, including sample size, compared with separate trials that assess each parameter. However,

Conclusions

  • 1.

    Sample calculations are an important part of solid clinical trial methodology.

  • 2.

    Sample calculations should balance scientific validity with feasibility.

  • 3.

    Important differences between intervention arms might go undetected only because sample size and power are low.

  • 4.

    Sample calculations make certain assumptions, and information from previous studies or pilots are helpful for reliable sample calculations.

  • 5.

    Trial design characteristics such as clustering and pairing should be considered during sample size

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    The authors report no commercial, proprietary, or financial interest in the products or companies described in this article.

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