Pooling Design and Bias Correction in DNA Library Screening

We study the group test for DNA library screening based on probabilistic approach. Group test is a method of detecting a few positive items from among a large number of items, and has wide range of applications. In DNA library screening, positive item corresponds to the clone having a specified DNA segment, and it is necessary to identify and isolate the positive clones for compiling the libraries. In the group test, a group of items, called pool, is assayed in a lump in order to save the cost of testing, and positive items are detected based on the observation from each pool. It is known that the design of grouping, that is, pooling design is important to achieve accurate detection. In the probabilistic approach, positive clones are picked up based on the posterior probability. Naive methods of computing the posterior, however, involves exponentially many sums, and thus we need a device. Loopy belief propagation (loopy BP) algorithm is one of popular methods to obtain approximate posterior probability efficiently. There are some works investigating the relation between the accuracy of the loopy BP and the pooling design. Based on these works, we develop pooling design with small estimation bias of posterior probability, and we show that the balanced incomplete block design (BIBD) has nice property for our purpose. Some numerical experiments show that the bias correction under the BIBD is useful to improve the estimation accuracy.