Optimal sample sizes for group testing in two-stage sampling

Osval Antonio Montesinos-López,Abelardo Montesinos-López,Kent Eskridge,José Crossa

doi:10.1017/s096025851400035x

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.

Highlights

Group testing is becoming increasingly popular because it can substantially reduce the number of required diagnostic tests compared to individual testing
Dorfman (1943) proposed the original group testing method in which g pools of size s are randomly formed from a sample of n individuals selected from the population using simple random sampling (SRS)
One approach used to compensate for this loss of efficiency is to develop correction factors to convert the variance of equal cluster size into the variance of the unequal cluster size (Moerbeek et al, 2001a; Van Breukelen et al, 2007, 2008; Candel and Van Breukelen 2010). This correction factor is normally constructed as the inverse of the relative efficiency (RE), which is calculated as the ratio of the variances of the parameter of interest of equal versus unequal cluster sizes

Summary

Introduction

Group testing is becoming increasingly popular because it can substantially reduce the number of required diagnostic tests compared to individual testing. Dorfman (1943) proposed the original group testing method in which g pools of size s are randomly formed from a sample of n individuals selected from the population using simple random sampling (SRS). This correction factor is normally constructed as the inverse of the relative efficiency (RE), which is calculated as the ratio of the variances of the parameter of interest of equal versus unequal cluster sizes This RE concept has been used in mixed-effects models for continuous and binary data to study loss of efficiency due to varying cluster sizes in a nongroup testing context for the estimation of fixed parameters and for variance components (Van Breukelen et al, 2007, 2008; Candel et al, 2008). Equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible For this reason, we derived an approximate formula for the relative efficiency of unequal versus equal cluster sizes for adjusting the required sample sizes for estimating the proportion in a group testing context. The proposed expressions are useful for estimating the budget required to achieve a certain power or precision when the goal is to achieve a confidence interval of a certain width or to obtain a pre-specified power for a given hypothesis

Materials and methods

Ed ðpiÞ

Tables for determining sample size

Findings

Conclusions