An approximate likelihood estimator for the prevalence of infections in vectors using pools of varying sizes

Efficient methods for the estimation of the multinomial parameter for the two-trait group testing model

Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of situations routinely encountered in applications. More recently, there has been growing interest in using group testing to simultaneously estimate the joint probabilities of two correlated traits using a multinomial model. Unfortunately, basic estimation results, such as the maximum likelihood estimator (MLE), have not been adequately addressed in the literature for such cases. In this paper, we show that finding the MLE for this problem is equivalent to maximizing a multinomial likelihood with a restricted parameter space. A solution using the EM algorithm is presented which is guaranteed to converge to the global maximizer, even on the boundary of the parameter space. Two additional closed form estimators are presented with the goal of minimizing the bias and/or mean square error. The methods are illustrated by considering an application to the joint estimation of transmission prevalence for two strains of the Potato virus Y by the aphid Myzus persicae.

Random walk designs for selecting pool sizes in group testing estimation with small samples

Group testing estimation, which utilizes pooled rather than individual units for testing, has been an ongoing area of research for over six decades. While it is often argued that such methods can yield large savings in terms of resources and/or time, these benefits depend very much on the initial choice of pool sizes. In fact, when poor group sizes are used, the results can be much worse than those obtained using standard techniques. Tools for addressing this problem in the literature have been based on either large sample results or prior knowledge of the parameter being estimated, with little guidance when these assumptions are not met. In this paper, we introduce and study random walk designs for choosing pool sizes when only a small number of tests can be run and prior knowledge is vague. To illustrate these methods, application is made to the estimation of prevalence for two diseases among Australian chrysanthemum crops.