Design Based on Intra-Class Correlation Coefficients

Abstract

Problem statement: Reliability studies are concerned with the study o f consistency or repeatability of measurements. Often times (but n ot always) the reliability coefficients are Intra-c lass Correlation Coefficients (ICC). Depending on the de sign or the conceptual intent of the study there ar e three types of intra-class correlation coefficients , termed intra-class correlation coefficients Case 1, 2 and 3, for measuring the reliability of a single in terval measure. While methods for sample size calculations for intra-class correlation coefficien ts 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 availa ble. Objective: Develop a method for calculating the size of a reliability study based on intra-class co rrelation coefficients Case 1 and 2. Approach: A practical method for computing sample size using si mulations was proposed. We proposed to compute sample size based on the expected width of the conf idence interval. For a given target value of the intra-class correlation coefficient, the proposed m ethod chooses the design assures a 95% confidence interval with average length shorter than a pre-spe cified value. The applicability of the proposed method in practice for intra-class coefficients Cas e 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 t he calculations was developed in R. The method was used to size a trial aimed to study the reliabi lity of a scale that measures the cleanness of the colon at the time of colonoscopy. Conclusion: A simple method for sample size calculation for int ra-class correlation coefficient Case 1 and 2 based on the a verage 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 intr a-class correlation coefficients Case 2 were studie d by simulations. These properties are an important tool when considering the design of this type of studie s.