Design Based on Intra-Class Correlation Coefficients
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Copyright: © 2021 Gheorghe Doros and Robert Lew. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Problem statement: Reliability studies are concerned with the study of "consistency" or "repeatability" of measurements. Often times (but not always) the reliability coefficients are Intra-class Correlation Coefficients (ICC). Depending on the design or the conceptual intent of the study there are three types of intra-class correlation coefficients, termed intra-class correlation coefficients Case 1, 2 and 3, for measuring the reliability of a single interval measure. While methods for sample size calculations for intra-class correlation coefficients in Case 1 are available and implemented in Power Analysis and Sample Size System (PASS); to our knowledge, no methods based on intra-class correlation coefficients in Case 2 and 3 are available. Objective: Develop a method for calculating the size of a reliability study based on intra-class correlation coefficients Case 1 and 2. Approach: A practical method for computing sample size using simulations was proposed. We proposed to compute sample size based on the expected width of the confidence interval. For a given target value of the intra-class correlation coefficient, the proposed method chooses the design assures a 95% confidence interval with average length shorter than a pre-specified value. The applicability of the proposed method in practice for intra-class coefficients Case 2 was supported by demonstrating three invariance properties of the proposed confidence intervals. Results: Tables with sample size requirements were derived and displayed. A program for carrying out the calculations was developed in R. The method was used to size a trial aimed to study the reliability of a scale that measures the cleanness of the colon at the time of colonoscopy. Conclusion: A simple method for sample size calculation for intra-class correlation coefficient Case 1 and 2 based on the average length of confidence intervals was proposed. The proposed was implemented by the authors in R (freely available software). Three invariance properties of the confidence intervals for the intra-class correlation coefficients Case 2 were studied by simulations. These properties are an important tool when considering the design of this type of studies.
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- Intra-class correlation coefficients
- sample size based on confidence interval
- reliability studies