Using group testing to estimate a proportion, and to test the binomial model.

Group testing has been extensively studied as an efficient way to classify units as defective or satisfactory when the proportion (p) of defectives is small. It can also be used to estimate p, often substantially reducing the mean squared error (MSE) of p and cost per unit information. Group testing is useful for larger p in the estimation problem than in the classification problem, but for larger p more care must be taken in choosing the group size (k); k being too large not only increases MSE (p), but adversely affects the robustness of p to both errors in testing (misclassification) and errors in the assumed binomial model. Procedures that retest units from defective groups, if even feasible, are shown to reduce cost per unit information very little in the estimation problem, but can provide useful information for testing the model. Methods are given for using data from tests of unequal-sized groups to estimate p and for testing the validity of the binomial model.

[1]  P. Ungar.  The cutoff point for group testing , 1960 .

[2]  William H. Swallow,et al.  Group testing for estimating infection rates and probabilities of disease transmission , 1985 .

[3]  M. Sobel,et al.  Group testing to eliminate efficiently all defectives in a binomial sample , 1959 .

[4]  F. K. Hwang,et al.  Robust Group Testing , 1984 .

[5]  J. Moyer,et al.  Alteration of Efficiencies of Acquisition and Inoculation of Watermelon Mosaic Virus 2 by Plant Resistance to the Virus and to an Aphid Vector , 1986 .

[6]  W. Reeves,et al.  Statistical estimation of virus infection rates in mosquito vector populations. , 1962, American journal of hygiene.

[7]  Keith H. Thompson,et al.  Estimation of the Proportion of Vectors in a Natural Population of Insects , 1962 .

[8]  Milton Sobel,et al.  Group testing with a new goal, estimation , 1975 .

[9]  M. Watson.  Factors Affecting the Amount of Infection Obtained by Aphis Transmission of the Virus Hy. III , 1936 .

[10]  R. Dorfman.  The Detection of Defective Members of Large Populations , 1943 .

[11]  W. Swallow.  Relative Mean Squared Error and Cost Considerations in Choosing Group Size for Group Testing to Estimate Infection Rates and Probabilities of Disease Transmission , 1987 .

[12]  C. Le.  A new estimator for infection rates using pools of variable size. , 1981, American journal of epidemiology.

[13]  S D Walter,et al.  Estimation of infection rates in population of organisms using pools of variable size. , 1980, American journal of epidemiology.

[14]  J. Gower,et al.  The use of a multiple-transfer method in plant virus transmission studies- some statistical points arising in the analysis of results , 1960 .

[15]  F. K. Hwang,et al.  Group testing with a dilution effect , 1976 .

[16]  J. Kalbfleisch.  Statistical Inference Under Order Restrictions , 1975 .

[17]  G. Bhattacharyya,et al.  Point estimates and confidence intervals for infection rates using pooled organisms in epidemiologic studies. , 1979, American journal of epidemiology.