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Stat Med. 2010 Jan 30;29(2):229-35. doi: 10.1002/sim.3766.

Optimal two-stage reliability studies.

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Business and Industrial Statistics Research Group (BISRG), Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo, Canada N2L 3G1.


The intraclass correlation is often used to assess the reliability of a measurement system. There is a considerable literature devoted to optimizing the standard assessment plan in which a number of subjects are measured repeatedly. We propose a two-stage investigation, here called a leveraged plan (LP), where in Stage I, we measure a number of subjects once. Then in Stage II, we select a subset of subjects with extreme initial measurements for repeated measurement. For a fixed total number of measurements, we show that the optimal LP provides a more precise estimate of the intraclass correlation coefficient than does the optimal standard plan (SP). We provide a table for finding the optimal LP given the true intraclass correlation and a specified precision for the estimate. For a fixed total number of measurements N, a nearly optimal LP makes roughly N/2 measurements in Stage I and then selects roughly N/6 extreme subjects to re-measure thrice each in Stage II. We also compare optimal leveraged with optimal SPs when there is a limit on the number of times each subject can be re-measured.

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