Advertisement

Improved Estimation of Proportions Using Inverse Binomial Group Testing

  • Graham HepworthEmail author
Article

Abstract

Inverse sampling for proportions is useful when there is a need to estimate the prevalence of a disease without delay. This can be combined with group (pooled) testing, in which individuals are pooled together and tested as a group for the disease. Pritchard and Tebbs (in Journal of Agricultural, Biological, and Environmental Statistics 16, 70–87, 2011a) introduced this combination to the statistical literature, and we have addressed some of the key problems raised, for groups of equal size. Most point estimators of the proportion are biased, especially the MLE, but by applying a suitable correction we have developed an estimator which is almost unbiased in the region of interest. We propose two interval estimators which improve on existing methods and have excellent coverage properties. Our recommendation is a score-based method with a correction for skewness, but a good alternative is an exact method with a mid-P correction.

Key Words

Bias correction Coverage Estimation of proportions Group testing Inverse sampling Mid-P Negative binomial distribution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Biggerstaff, B. J. (2006), “Pooled Infection Rate: An Excel Add-In to Compute Point and Interval Estimates of Infection Rates and Their Difference Using Pooled Samples”. CDC, Fort Collins, CO, USA. Google Scholar
  2. — (2008), “Confidence Intervals for the Difference of Two Proportions Estimated From Pooled Samples,” Journal of Agricultural, Biological, and Environmental Statistics, 13, 478–497. MathSciNetCrossRefGoogle Scholar
  3. Burrows, P. M. (1987), “Improved Estimation of Pathogen Transmission by Group Testing,” Phytopathology, 77, 363–365. CrossRefGoogle Scholar
  4. Chen, P., Tebbs, J. M., and Bilder, C. R. (2009), “Global Goodness of Fit Tests for Group Testing Regression Models,” Statistics in Medicine, 28, 2912–2928. MathSciNetCrossRefGoogle Scholar
  5. Dorfman, R. (1943), “The Detection of Defective Members of Large Populations,” The Annals of Mathematical Statistics, 14, 436–440. CrossRefGoogle Scholar
  6. Durnez, L., Eddyani, M., Mgode, G. F., Katakweba, A., Katholi, C. R., Machang’u, R. R., Kazwala, R. R., Portaeis, F., and Leirs, H. (2008), “First Detection of Mycobacteria in African Rodents and Insectivores, Using Stratified Pool Screening,” Applied and Environmental Microbiology, 74, 768–773. CrossRefGoogle Scholar
  7. Gart, J. J. (1991), “An Application of Score Methodology: Confidence Intervals and Tests of Fit for One-Hit Curves,” in Handbook of Statistics, Vol. 8, eds. C. R. Rao and R. Chakraborty. Amsterdam: Elsevier, pp. 395–406. Google Scholar
  8. George, V. T., and Elston, R. C. (1993), “Confidence Limits Based on the First Occurrence of an Event,” Statistics in Medicine, 12, 685–690. CrossRefGoogle Scholar
  9. Haldane, J. (1945), “On a Method of Estimating Frequencies,” Biometrika, 33, 222–225. MathSciNetzbMATHCrossRefGoogle Scholar
  10. Hanson, T. E., Johnson, W. O., and Gastwirth, J. L. (2006), “Bayesian Inference for Prevalence and Diagnostic Test Accuracy Based on Dual-Pooled Screening,” Biostatistics, 7, 41–57. zbMATHCrossRefGoogle Scholar
  11. Hepworth, G. (1996), “Exact Confidence Intervals for Proportions Estimated by Group Testing,” Biometrics, 52, 1134–1146. MathSciNetzbMATHCrossRefGoogle Scholar
  12. — (2004), “Mid-P Confidence Intervals Based on the Likelihood Ratio for Proportions Estimated by Group Testing,” Australian & New Zealand Journal of Statistics, 46, 391–405. MathSciNetzbMATHCrossRefGoogle Scholar
  13. — (2005), “Confidence Intervals for Proportions Estimated by Group Testing With Groups of Unequal Size,” Journal of Agricultural, Biological, and Environmental Statistics, 10, 478–497. CrossRefGoogle Scholar
  14. Hepworth, G., and Watson, R. K. (2009), “Debiased Estimation of Proportions in Group Testing,” Journal of the Royal Statistical Society. Series C. Applied Statistics, 58, 105–121. MathSciNetCrossRefGoogle Scholar
  15. Hughes, G., Gottwald, T. R., and Levy, L. (2002), “The Use of Hierarchical Sampling in the Surveillance Program for Plum Pox Virus Incidence in the United States,” Plant Disease, 86, 259–263. CrossRefGoogle Scholar
  16. Katholi, C. R., and Unnasch, T. R. (2006), “Important Experimental Parameters for Determining Infection Rates in Arthropod Vectors Using Pool Screening Approaches,” American Journal of Tropical Medicine and Hygiene, 74, 779–785. Google Scholar
  17. Lancaster, H. O. (1961), “Significance Tests in Discrete Distributions,” Journal of the American Statistical Association, 56, 223–234. MathSciNetzbMATHCrossRefGoogle Scholar
  18. Lui, K. (1995), “Confidence Limits for the Population Prevalence Rate Based on the Negative Binomial Distribution,” Statistics in Medicine, 14, 1278–1290. Google Scholar
  19. Montesinos-Lopez, O. A., Montesinos-Lopez, A., Crossa, J., Eskridge, K., and Hernandez-Suarez, C. M. (2010), “Sample Size for Detecting and Estimating the Proportion of Transgenic Plants With Narrow Confidence Intervals,” Seed Science Research, 20, 123–136. CrossRefGoogle Scholar
  20. Newcombe, R. G. (1998), “Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods,” Statistics in Medicine, 17, 857–872. CrossRefGoogle Scholar
  21. Pritchard, N. A., and Tebbs, J. M. (2011a), “Estimating Disease Prevalence Using Inverse Binomial Pooled Testing,” Journal of Agricultural, Biological, and Environmental Statistics, 16, 70–87. MathSciNetCrossRefGoogle Scholar
  22. — (2011b), “Bayesian Inference for Disease Prevalence Using Negative Binomial Group Testing,” Biometrical Journal, 53, 40–56. MathSciNetzbMATHCrossRefGoogle Scholar
  23. Rodriguez-Perez, M. A., Katholi, C. R., Hassan, H. K., and Unnasch, T. R. (2006), “Large-Scale Entomologic Assessment of Onchocerca volvulus Transmission by Poolscreen PCR in Mexico,” American Journal of Tropical Medicine and Hygiene, 74, 1026–1033. Google Scholar
  24. Schaarschmidt, F. (2007), “Experimental Design for One-Sided Confidence Intervals or Hypothesis Tests in Binomial Group Testing,” Communications in Biometry and Crop Science, 2, 32–40. Google Scholar
  25. Tebbs, J. M., and Bilder, C. R. (2004), “Confidence Interval Procedures for the Probability of Disease Transmission in Multiple-Vector-Transfer Designs,” Journal of Agricultural, Biological, and Environmental Statistics, 9, 75–90. CrossRefGoogle Scholar
  26. Thompson, K. (1962), “Estimation of the Proportion of Vectors in a Natural Population of Insects,” Biometrics, 18, 568–578. CrossRefGoogle Scholar
  27. Tu, X. M., Litvak, E., and Pagano, M. (1995), “On the Informativeness and Accuracy of Pooled Testing in Estimating Prevalence of a Rare Disease: Application to HIV Screening,” Biometrika, 82, 287–297. MathSciNetzbMATHCrossRefGoogle Scholar
  28. Verstraeten, T., Farah, B., Duchateau, L., and Matu, R. (1998), “Pooling Sera to Reduce the Cost of HIV Surveillance: A Feasibility Study in a Rural Kenyan District,” Tropical Medicine and International Health, 3, 747–750. CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2013

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

Personalised recommendations