Next generation high-throughput sequencing devices have brought the promise of personalized genotyping to the field of human genomics. Advances in personalized genotyping depend on developments of procedures for cost-efficient large-scale association studies. Such large-scale experiments and studies face a number of obstacles related to constraints imposed by bioengineering systems and test subjects, including a) the restriction that tests have to be performed with small samples of individuals' genetic material; b) the constraint that subjects have to be multiplexed, so that genetic sequences have to be barcoded; c) the fact that the outcomes of the tests are semi-quantitative; d) the reality that many tests have to be performed within groups of related individuals, thereby significantly increasing the cost of screening whole families; e) the fact that tests have to deal with the challenge of variant discovery and individuals that may exhibit different gene copy numbers. A natural way to overcome these and many other obstacles is to perform genotyping via group testing. The goals of this project include developing of a comprehensive, yet analytically or computationally tractable general theory of group testing for genotyping. The proposed theory will answer the unique challenges arising in genotyping by sequencing, although parts of the theory may find independent applications in areas as diverse as constrained multiple access channel analysis, fingerprinting and identification coding, and error-control coding. In particular, the investigators introduce several new models into the field of group testing, including subjects with different types and strengths, semi-quantitative testing, two-dimensional pooling, and Poisson probabilistic testing.
