Optimal sample sizes for group testing in two-stage sampling
TLDR
In this article, the optimal allocations of clusters and individuals are obtained under the assumption of equal cluster sizes, and the relative efficiency of unequal versus equal clusters sizes when estimating the average population proportion is obtained.Abstract:
Optimal sample sizes under a budget constraint for estimating a proportion in a two-stage sampling process have been derived using individual testing. However, when group testing is used, these optimal sample sizes are not appropriate. In this study, optimal sample sizes at the cluster and individual levels are derived for group testing. First, optimal allocations of clusters and individuals are obtained under the assumption of equal cluster sizes. Second, we obtain the relative efficiency (RE) of unequal versus equal cluster sizes when estimating the average population proportion, . By multiplying the sample of clusters obtained assuming equal cluster size by the inverse of the RE, we adjust the sample size required in the context of unequal cluster sizes. We also show the adjustments that need to be made to allocate clusters and individuals correctly in order to estimate the required budget and achieve a certain power or precision.read more
Citations
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References
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TL;DR: In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.
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Approximate is Better than “Exact” for Interval Estimation of Binomial Proportions
Alan Agresti,Brent A. Coull +1 more
TL;DR: For example, this paper showed that using the adjusted Wald test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes, and that the 95% score interval has similar behavior as the adjusted-Wald interval obtained after adding two "successes" and two "failures" to the sample.
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Interval Estimation for a Binomial Proportion
TL;DR: In this paper, the problem of interval estimation of a binomial proportion is revisited, and a number of natural alternatives are presented, each with its motivation and con- text, each interval is examined for its coverage probability and its length.