Construction of Bootstrap Confidence Intervals for Proportions Using Group Testing with Groups of Unequal Size

Abstract

Group testing is a method of pooling a number of units together and performing a single test on the resulting group. It is an appealing option when few individual units are thought to be infected and when the cost of group testing is minimal as compared to individual testing. Studies have shown that the problem of estimation of prevalence rate p of a disease is much

more important than that of identification of infected units. Recent results on point and confidence interval estimates of the binomial proportion are based on a single overdispersed data set and hence are not accurate. Bootstrapping resampling applied on an observed data set produces confidence intervals with high coverage probabilities. Bootstrapping has not been applied on group testing. In this study the focus was on the application of Bootstrapping to group testing to obtain highly accurate confidence intervals for the proportion of defective or positive units. Data was simulated from the binomial distribution; this data was assumed to be overdispersed and independent between groups but correlated within these groups. The quasi-likelihood technique corrected for overdispersion, and consequently CIs of the proportion were constructed using interval estimation methods based on the Wald interval, and on intervals based on the Logit and Complementary log–log functions. The widths and coverage probabilities from the three methods of estimation were compared with and without bootstrapping technique. The study showed that bootstrapping technique generated confidence intervals with high coverage probabilities for each of the three interval methods as compared to those based on a single sample of data. Interval widths of the each of the three methods were shorter after the bootstrapping technique was applied.