Hypothesis testing based on pool screening with unequal pool sizes

Pool screening is a widely applied technique to estimate the prevalence of a rare event. This focus of this research is on developing statistical test of hypothesis procedures under the assumption that pool sizes are unequal but known. One of the proposed test procedures is, an exact test based on the number of positive pools (denoted by T). Another set of proposed test procedures is a modification of the likelihood ratio, Wald's and Score tests which are commonly-used likelihood-based tests.;In paper 1, we derive the distribution of T which will be the basis of the exact test. Other distributional properties of T are obtained using generating functions. Due to the complexity of the form of the distribution, we propose several methods of computing probabilities using the distribution of T. It was found that in the setting being considered, the double recursion method based on the recursion relationship introduced by Marcus and Lopes is the recommended computational method.;In paper 2, we proposed an exact two-sided hypothesis test procedure based on the statistic T. We also propose modified versions of the likelihood-ratio, Wald's and Score tests where simulated quantiles are used instead of the quantiles based on the standard asymptotic distribution to obtain the rejection region for each test. Monte Carlo simulations show that the modified test procedures perform better in terms of statistical power than their original counterpart. However, the exact test based on number of positive pools outperforms the other test when the number of pools screened is small and/or the prevalence close to zero.;The last paper focuses on the one-sided hypothesis test and the likelihood ratio (LR) test procedure. We first investigate the distributional properties and behavior of the likelihood ratio test statistic both in the finite and large sample cases. It will be shown that the distribution of one-sided LR test statistic is a mixture of distributions. We propose ways to compute the weights of the finite mixture distribution and use these weights to modify the LR test. We also propose the use of simulated quantiles for one-sided LR test to define the rejection region. Our results show that: (1) LR test with modified weight and conventional LR test have power functions that are very similar; (2) Quantile based LR test improves the LR test but require moderate or large number of pools to be screened; and (3) When number of pools is small, exact test based on number of positive pools performs the best.;Keywords: Pool Screening, Hypothesis Testing, Number of Positive Pools, One-sided Likelihood Ratio Test, Statistical Power, Mixture Chi-square Distribution...