A Guide to Choosing the Effect Size for Sample Size Calculation

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Choosing the Effect Size for Sample Size Calculations

Selecting an appropriate effect size is crucial in sample size determination. Choosing an effect size that is too small can lead to overestimating the necessary sample size.

Conversely, choosing an effect size that is too large can result in an underpowered trial due to an underestimated sample size. Additionally, the uncertainty associated with effect size estimation adds complexity, emphasizing the need for careful consideration and accurate estimation.

Learning objectives of this webinar:

In this tutorial, Calvin O'Brien, research statistician at nQuery, takes you through the challenges you might face when selecting an appropriate effect size. We have examined basing estimates on the minimum clinically important difference (MCID), versus the conventional method, along with techniques for addressing uncertainty in effect size estimation.

1. Understand Effect Size in Sample Size Determination

• Comprehend the role of effect size in calculating the necessary sample size for studies.

• Recognize how effect size influences the power and validity of statistical conclusions.

2. Explore Methods for Choosing Effect Size

• Learn about the Minimum Clinically Important Difference (MCID) and its application in determining effect size.

• Examine conventional approaches to effect size selection based on existing evidence and realistic differences.

3. Address Uncertainty in Effect Size Estimation

• Understand the importance of sensitivity analysis in assessing how variations in effect size impact study outcomes.

• Explore the concept of assurance (Bayesian power) as a method to account for uncertainty in effect size and enhance study design robustness.

Choosing the Effect Size for Sample Size Calculations: A Quick Guide for Biostatisticians 

Understanding MCID, Sensitivity Analysis and Assurance

Choosing an appropriate effect size is one of the five essential steps in sample size determination, requiring careful consideration.

In the past, effect size was typically chosen in line with the conventional method for sample size determination, where a realistic difference is determined from existing evidence and a sample size is determined from this estimate. 

Recently, there has been a notable shift towards alternative methods for estimating effect size. The minimum clinically important difference has become a popular alternative to the conventional method. There are criticisms of this shift, questioning how important the MCID is in sample size determination.

Another step in the 5 essential steps in sample size determination, is, exploring uncertainty. Given that effect size may only be an estimate, it is important to consider the uncertainty surrounding it.

Sensitivity analysis is employed to explore various scenarios, while assurance involves characterizing our uncertainty in the effect size, using a statistical prior rather than a set of distinct values.

Understanding Effect Size in Sample Size Calculations

Effect size quantifies the magnitude of the difference or relationship being studied. In hypothesis testing, it determines the minimum detectable difference that a study is powered to identify. The selection of an effect size impacts statistical power—small effect sizes require larger sample sizes to achieve adequate power, whereas larger effect sizes reduce the sample size requirement. Biostatisticians must balance practical feasibility with scientific rigor when determining an appropriate effect size.

Methods for Selecting an Appropriate Effect Size

Several approaches can guide effect size selection. The Minimum Clinically Important Difference (MCID) is a widely used method that defines the smallest difference that is meaningful from a clinical or practical perspective. Alternatively, effect sizes may be determined from previous research, meta-analyses, or pilot studies to ensure consistency with existing literature. In some cases, standardized measures, such as Cohen’s d for mean differences or odds ratios for binary outcomes, can provide reference points for effect size estimation.

Addressing Uncertainty in Effect Size Estimation

Effect size is rarely known with certainty, and incorrect assumptions can lead to underpowered or overpowered studies. Sensitivity analyses allow researchers to evaluate how variations in effect size impact sample size and statistical power, providing a range of possible outcomes. Additionally, assurance (Bayesian power analysis) can be used to incorporate prior knowledge and account for uncertainty in effect size estimates, leading to more robust study designs.

Best Practices for Biostatisticians

To ensure accurate and defensible effect size selection, biostatisticians should:

• Review relevant literature to identify realistic effect size estimates.
• Consider clinical and practical significance rather than just statistical significance.
• Use sensitivity analyses to assess the impact of effect size variation.
• Apply Bayesian methods or prior knowledge where appropriate to refine estimates.

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