Bias Correction in Estimating Proportions by Imperfect Pooled Testing

Graham Hepworth () and Brad J. Biggerstaff
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Graham Hepworth: The University of Melbourne
Brad J. Biggerstaff: Centers for Disease Control and Prevention

Journal of Agricultural, Biological and Environmental Statistics, 2021, vol. 26, issue 1, No 5, 90-104

Abstract: Abstract In the estimation of proportions by pooled testing, the MLE is biased. Hepworth and Biggerstaff (JABES, 22:602–614, 2017) proposed an estimator based on the bias correction method of Firth (Biometrika 80:27–38, 1993) and showed that it is almost unbiased across a range of pooled testing problems involving no misclassification. We now extend their work to allow for imperfect testing. We derive the estimator, provide a Newton–Raphson iterative formula for its computation and test it in situations involving equal or unequal pool sizes, drawing on problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses. Our estimator is highly effective at reducing the bias for prevalences consistent with the pooled testing procedure employed.

Keywords: Diagnostic testing; Firth’s correction; Group testing; Sensitivity; Specificity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13253-020-00411-5

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