# A comparative study between a multi-stage adaptive pool testing model without test errors and the non-adaptive model

## DOI:

https://doi.org/10.14419/ijamr.v6i3.7802## Published:

2017-06-26## Keywords:

Pool testing, Adaptive estimator, Test errors, Confidence interval## Abstract

Pool testing for presence or absence of a trait is less expensive, less time consuming and therefore more cost effective. This study presents a multi-stage adaptive pool testing estimator p Ì‚en of prevalence of a trait in the absence of test errors. Pool testing is more efficient, less expensive and less time consuming. An increase in the number of stages improves the efficiency of the estimator, hence construction of a multi-stage model. The study made use of the Maximum Likelihood Estimate (MLE) method and Martingale method to obtain the adaptive estimator and Cramer-Rao lower bound method to determine the variance of the constructed estimator. Matlab and R, statistical softwares were used for Monte-carlo simulation and verification of the model, then analysis and discussion of properties of the constructed estimator in comparison with the non-adaptive estimator in the literature of pool testing done alongside provision of the confidence interval of the estimator. Results have shown that as the number of stages increases, the efficiency of the multi-stage adaptive estimator in the absence of test errors also increases in comparison with the non-adaptive estimator in the absence of test errors. This makes the multi-stage adaptive estimator better than the corresponding non-adaptive estimator in the literature of pool testing.## References

[1] Bhattacharyya, G.K., Karandinos, M.G., and DeFoliart, G. R. (1979). *Point estimates and confidence intervals for infection rates using pooled** **organisms in epidemiologic studies*. American journal of epidemiology 109,124-131.

[2] Brookmeyer, R. (1999). *Analysis of multistage pooling studies of biological specimens for estimating disease incidence and prevalence*. Biometrics 55,608-612.

[3] Chiang, C. L. and Reeves, W. C. (1962). *Statistical estimation of virus infection rates in mosquito vector populations*. American journal on hygiene 75, 377-391

[4] Dorfman R. (1943). *The detection of defective members of large populations*. Annals of mathematical statistics 14, 436-440.

[5] Gastwirth, J.L., and Hammick,P.A. (1989). *Estimation of prevalence of a rare disease, preserving the anonymity of the subjects by group testing: Application to estimate the prevalence of AIDS antibodies in*

*blood donors*. Journal of Statistical Planning and Inference 22, 15-27.

[6] Mood, D. A., Graybill, G. A., Boes, D. C. (1974). Introduction to the theory of statistics. 27, 72.

[7] Nyongesa, L. K. (2011). *Dual estimation of prevalence and disease incidence in pool testing strategy*. Communication in statistics theory and methods, 40, 1-12

[8] Okoth, A. W. (2012). *Two Stage Adaptive Pool Testing for estimating prevalence of a trait in the presence of test errors*. Lambert Academic publishers, 18 and 27

[9] Oliver-Hughes J.M. and Swallow W.H. (1994), *A two-stage adaptive group testing procedure for estimating small proportions*. American statistical association 89, 982-993.

[10] Richards, M. S. (1991). *Interpretation of the results of bacteriological testing of egg laying flocks for salmonella enteritidis*. Proceedings of the 6th international symposium on veterinary epidemiology and

economics, 124-126, Ottawa, Canada.

[11] Sobel M., Ellashoff R.M. (1975).*Group testing with a new goal; estimation*. Biometrika 62, 181-193.

[12] Swallow W.H. (1987).*Relative MSE and cost considerations in choosing group size for group testing to estimate infection rates and probability of disease infection*. Phytopathology 77, 1376-1381.