Bias Correction in Estimating Proportions by Pooled Testing
- 136 Downloads
In the estimation of proportions by pooled testing, the MLE is biased, and several methods of correcting the bias have been presented in previous studies. We propose a new estimator based on the bias correction method introduced by Firth (Biometrika 80:27–38, 1993), which uses a modification of the score function, and we provide an easily computable, Newton–Raphson iterative formula for its computation. Our proposed estimator is almost unbiased across a range of problems, and superior to existing methods. We show that for equal pool sizes the new estimator is equivalent to the estimator proposed by Burrows (Phytopathology 77:363–365, 1987). The performance of our estimator is examined using pooled testing problems encountered in plant disease assessment and prevalence estimation of mosquito-borne viruses.
Supplementary materials accompanying this paper appear online.
KeywordsBias correction Estimation of proportions Group testing Pooled testing Virus prevalence
- Aranda, C., Sanchez-Seco, M. P., Caceres, F., Escosa, R., Galvez, J. C., Masia, M., Marques, E., Ruz, S., Alba, A., Busquets, N., Vazquez, A., Castella, J., and Tenorio, A. (2009). Detection and monitoring of mosquito flaviviruses in Spain between 2001 and 2005. (2009), Vector-borne and Zoonotic Diseases 9, doi: 10.1089/vbz.2008.0073.
- Brookmeyer, R. (1999). Analysis of multistage pooling studies of biological specimens for estimating disease incidence and prevalence. Biometrics 55, 608–612.Google Scholar
- Ding, J. and Xiong, W. (2016). A new estimator for a population proportion using group testing. Communications in Statistics–Simulation and Computation 45, doi: 10.1080/03610918.2013.854909.
- Durnez, L., Eddyani, M., Mgode, G. F., Katakweba, A., Katholi, C. R., Machang’u, R. R., Kazwala, R. R., and 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
- Freeman, A. J., Spackman, M. E., Aftab, M., McQueen, V., King, S., van Leur, J. A., Loh, M. H., and Rodoni, B. (2013). Comparison of tissue blot immunoassay and reverse transcription polymerase chain reaction assay for virus-testing pulse crops from a South-Eastern Australia survey. Australasian Plant Pathology 42, 675–683.CrossRefGoogle Scholar
- Gart, J. J. (1991). An application of score methodology: Confidence intervals and tests of fit for one-hit curves. In Handbook of Statistics, C. R. Rao, R. Chakraborty (eds), 8, 395–406. Amsterdam: Elsevier.Google Scholar
- 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