TY - JOUR

T1 - Relative Efficiency of Unequal Versus Equal Cluster Sizes for the Nonparametric Weighted Sign Test Estimators in Clustered Binary Data

AU - Ahn, Chul

AU - Hu, Fan

AU - Lee, Seung Chun

N1 - Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by National Institutes of Health grants UL1 RR024982, P30CA142543, P50CA70907, and DK081872.

PY - 2012/7

Y1 - 2012/7

N2 - We performed an analysis of clustered binary data from multiple observations for each participant in which any 2 observations from a participant are assumed to have a common correlation coefficient. In the weighted sign test on proportion in clustered binary data, 3 weighting schemes were considered: equal weights to observations, equal weights to clusters, and optimal weights that minimize the variance of the estimator. Because the distribution of cluster sizes may not be exactly specified before the trial starts, the sample size is usually determined using an average cluster size without taking into account any potential imbalance in cluster size, even though cluster size usually varies among clusters. In this article, we investigate the relative efficiency (RE) of unequal versus equal cluster sizes for clustered binary data using the weighted sign test estimators. The REs are computed as a function of correlation among observations for each participant and the various cluster size distributions. The required sample size for unequal cluster sizes will not exceed the sample size for an equal cluster size multiplied by the maximum RE. It is concluded that the maximum RE for various cluster size distributions considered here does not exceed 1.50, 1.61, and 1.12 for equal weights to observations, equal weights to clusters, and optimal weights, respectively. It suggests sampling 50%, 61%, and 12% more clusters, respectively, depending on the weighting schemes than the number of clusters computed using an average cluster size.

AB - We performed an analysis of clustered binary data from multiple observations for each participant in which any 2 observations from a participant are assumed to have a common correlation coefficient. In the weighted sign test on proportion in clustered binary data, 3 weighting schemes were considered: equal weights to observations, equal weights to clusters, and optimal weights that minimize the variance of the estimator. Because the distribution of cluster sizes may not be exactly specified before the trial starts, the sample size is usually determined using an average cluster size without taking into account any potential imbalance in cluster size, even though cluster size usually varies among clusters. In this article, we investigate the relative efficiency (RE) of unequal versus equal cluster sizes for clustered binary data using the weighted sign test estimators. The REs are computed as a function of correlation among observations for each participant and the various cluster size distributions. The required sample size for unequal cluster sizes will not exceed the sample size for an equal cluster size multiplied by the maximum RE. It is concluded that the maximum RE for various cluster size distributions considered here does not exceed 1.50, 1.61, and 1.12 for equal weights to observations, equal weights to clusters, and optimal weights, respectively. It suggests sampling 50%, 61%, and 12% more clusters, respectively, depending on the weighting schemes than the number of clusters computed using an average cluster size.

KW - intraclass correlation coefficient

KW - sample size

KW - variable cluster sizes

UR - http://www.scopus.com/inward/record.url?scp=84873829978&partnerID=8YFLogxK

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U2 - 10.1177/0092861512449818

DO - 10.1177/0092861512449818

M3 - Article

C2 - 23486929

AN - SCOPUS:84873829978

VL - 46

SP - 428

EP - 433

JO - Therapeutic Innovation and Regulatory Science

JF - Therapeutic Innovation and Regulatory Science

SN - 2168-4790

IS - 4

ER -