Technical Report 2022-005

Consistency Study of a Reconstructed Genotype Probability Distribution via Clustered Bootstrapping in NORB Pooling Blocks

Camille Clouard and Carl Nettelblad

June 2022

For applications with biallelic genetic markers, group testing techniques, synonymous to pooling techniques, are usually applied for decreasing the cost of large-scale testing as e.g. when detecting carriers of rare genetic variants. In some configurations, the results of the grouped tests cannot be decoded and the pooled items are missing. Inference of these missing items can be performed with specific statistical methods that are for example related to the Expectation-Maximization algorithm. Pooling has also been applied for determining the genotype of markers in large populations. The particularity of full genotype data for diploid organisms in the context of group testing are the ternary outcomes (two homozygous genotypes and one heterozygous), as well as the distribution of these three outcomes in a population, which is often ruled by the Hardy-Weinberg Equilibrium and depends on the allele frequency in such situation. When using a nonoverlapping repeated block pooling design, the missing items are only observed in particular arrangements. Overall, a data set of pooled genotypes can be described as an inference problem in Missing Not At Random data with nonmonotone missingness patterns. This study presents a preliminary investigation of the consistency of various iterative methods estimating the most likely genotype probabilities of the missing items in pooled data. We use the Kullback-Leibler divergence and the L2 distance between the genotype distribution computed from our estimates and a simulated empirical distribution as a measure of the distributional consistency.

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