Power for <Emphasis Type="Italic">T</Emphasis>-test comparisons of unbalanced cluster exposure studies |
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Authors: | Donald R Hoover |
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Institution: | (1) Department of Statistics, Rutgers University, 473 Hill Center, 110 Frelinghuysen Road, 08854-8019 Piscataway, NJ |
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Abstract: | Studies of individuals sampled in unbalanced clusters have become common in health services and epidemiological research,
but available tools for power/sample size estimation and optimal design are currently limited. This paper presents and illustrates
power estimation formulas for t-test comparisons of effect of an exposure at the cluster level on continuous outcomes in unbalanced studies with unequal
numbers of clusters and/or unequal numbers of subjects per cluster in each exposure arm. Iterative application of these power
formulas obtains minimal sample size needed and/or minimal detectable difference. SAS subroutines to implement these algorithms
are given in the Appendices. When feasible, power is optimized by having the same number of clusters in each arm k
A
=k
B
and (irrespective of numbers of clusters in each arm) the same total number of subjects in each arm n
A
k
A
=n
B
k
B
. Cost beneficial upper limits for numbers of subjects per cluster may be approximately (5/ρ) −5 or less where ρ is the intraclass
correlation. The methods presented here for simple cluster designs may be extended to some settings involving complex hierarchical
weighted cluster samples. |
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Keywords: | Cluster Sampling Power Sample Size T Tests Unbalanced Designs |
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