Accurate estimation of disease prevalence is crucial for effective public health intervention and resource allocation. Generating data by individual testing methods is often impractical and expensive for large populations, particularly when disease prevalence is low. Pool testing involves combining samples from multiple individuals into a pool and performing a single test, and offers a cost-effective and efficient alternative. In pool testing strategy with retesting, if a pool tests negative, it is classified as non-defective, whereas if it is positive, then a retest is needed. The retesting strategy mitigates the effects of initial test errors, thereby enhancing the accuracy of the estimation of the prevalence rate. Evidence in the literature indicates that the traditional Wald method has been used to construct approximate confidence intervals for the prevalence rate. However, this interval estimation method is based on the normality approximation and hence may not be accurate when the true prevalence rate is close to zero. In this paper, we propose a Bayesian interval estimation approach which is not affected by extreme values of the prevalence rate and allows for incorporating prior information about the prevalence rate. We assumed that the prior distribution for the unknown prevalence rate
is a Beta distribution with parameters
and
and based on pool testing outcomes for the
pools each of size
,
credible intervals were constructed from the resulting posterior distribution. Simulation studies were carried out to compare the efficiencies of the Bayesian and Wald interval estimation methods for various values of
.
References
[1]
Dorfman, R. (1943) The Detection of Defective Members of Large Populations. The Annals of Mathematical Statistics, 14, 436-440. https://doi.org/10.1214/aoms/1177731363
[2]
Spiegelhalter, D.J. and Best, N.G. (2003) Bayesian Approaches to Multiple Sources of Evidence and Uncertainty in Complex Cost‐Effectiveness Modelling. Statistics in Medicine, 22, 3687-3709. https://doi.org/10.1002/sim.1586
[3]
Tamba, C.L., and Nandelenga, M.W. (2014) Computation of Moments in Group Testing with Retesting and with Errors in Inspection. International Journal of Contemporary Advanced Mathematics (IJCM), 3, 1-15.
[4]
Nyongesa, L.K. (2017) Pool Testing Algorithm for Estimating Prevalence with Im-Perfect Test. International Journal of Statistics and Systems, 12, 823-830.
[5]
Liu, A. and Liu, C. (2012) Bayesian Group Testing for the Estimation of the Prevalence Rate. Journal of Statistical Planning and Inference, 142, 750-763.
[6]
Hepworth, G. (2005) Confidence Intervals for Proportions Estimated by Group Testing with Groups of Unequal Size. Journal of Agricultural, Biological, and Environmental Statistics, 10, 478-497. https://doi.org/10.1198/108571105x81698
[7]
Orawo, L.A. (2021) Confidence Intervals for the Binomial Proportion: A Comparison of Four Methods. Open Journal of Statistics, 11, 806-816. https://doi.org/10.4236/ojs.2021.115047
[8]
Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. and Rubin, D.B. (2013) Bayesian Data Analysis. 3rd Edition, CRC Press.
[9]
Brett, T.S., Rohani, P., and Drake, J.M. (2018) Anticipating Epidemic Transitions with Imperfect Data. PLOS Computational Biology, 14, e1006204.
[10]
McDonald, J.L. and Hodgson, D.J. (2018) Prior Precision, Prior Accuracy, and the Estimation of Disease Prevalence Using Imperfect Diagnostic Tests. Frontiers in Veterinary Science, 5, Article 83. https://doi.org/10.3389/fvets.2018.00083
[11]
Helman, S.K., Thompson, R.A. and Fox, S.E. (2020) Bayesian Latent Class Analysis to Estimate Disease Prevalence and Diagnostic Test Accuracy in Wildlife Populations. Preventive Veterinary Medicine, 180, Article 105030.
[12]
Biggerstaff, B.J. (2008) Confidence Intervals for the Difference of Two Proportions Estimated from Pooled Samples. Journal of Agricultural, Biological, and Environmental Statistics, 13, 478-496. https://doi.org/10.1198/108571108x379055