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The Hardy–Weinberg equilibrium (HWE) assumption is essential to many population genetics models. Multiple tests were developed to test its applicability in observed genotypes. Current methods are divided into exact tests applicable to small populations and a small number of alleles, and approximate goodness-of-fit tests. Existing tests cannot handle ambiguous typing in multi-allelic loci. We here present a novel exact test Unambiguous Multi Allelic Test (UMAT) not limited to the number of alleles and population size, based on a perturbative approach around the current observations. We show its accuracy in the detection of deviation from HWE. We then propose an additional model to handle ambiguous typing using either sampling into UMAT or a goodness-of-fit test test with a variance estimate taking ambiguity into account, named Asymptotic Statistical Test with Ambiguity (ASTA). We show the accuracy of ASTA and the possibility of detecting the source of deviation from HWE. We apply these tests to the HLA loci to reproduce multiple previously reported deviations from HWE, and a large number of new ones. [ABSTRACT FROM AUTHOR]

Recently, haplo‐identical transplantation with multiple HLA mismatches has become a viable option for stem cell transplants. Haplotype sharing detection requires the imputation of donor and recipient. We show that even in high‐resolution typing when all alleles are known, there is a 15% error rate in haplotype phasing, and even more in low‐resolution typings. Similarly, in related donors, the parents' haplotypes should be imputed to determine what haplotype each child inherited. We propose graph‐based family imputation (GRAMM) to phase alleles in family pedigree HLA typing data, and in mother‐cord blood unit pairs. We show that GRAMM has practically no phasing errors when pedigree data are available. We apply GRAMM to simulations with different typing resolutions as well as paired cord‐mother typings, and show very high phasing accuracy, and improved allele imputation accuracy. We use GRAMM to detect recombination events and show that the rate of falsely detected recombination events (false‐positive rate) in simulations is very low. We then apply recombination detection to typed families to estimate the recombination rate in Israeli and Australian population datasets. The estimated recombination rate has an upper bound of 10%–20% per family (1%–4% per individual). [ABSTRACT FROM AUTHOR]

The outcome of Hematopoietic Stem Cell (HSCT) and organ transplant is strongly affected by the matching of the HLA alleles of the donor and the recipient. However, donors and sometimes recipients are often typed at low resolution, with some alleles either missing or ambiguous. Thus, imputation methods are required to detect the most probably high-resolution HLA haplotypes consistent with a typing. Such imputation algorithms require predefined haplotype frequencies. As such, the phasing of the typing is required for both imputation and frequency generation.We have developed a new approach to HLA haplotype and genotype imputation, where first all candidate phases of a typing are explicated, and then the ambiguity within each phase is solved. This ambiguity is solved through a graph structure of all partial haplotypes and the haplotypes consistent with them.This phasing approach was used to produce an imputation algorithm (GRIMM-Graph Imputation and Matching). GRIMM was then combined with the possibility of combining information from multiple races to produce MR-GRIMM (Multi-Race GRIMM). When family information is available, the phasing of each family member can be restricted by the others. We propose GRAMM (GRaph-bAsed faMily iMputation) to phase alleles in family pedigree HLA typing data and in mother-cord blood unit pairs. Finally, we combined MR-GRIMM with an expectation-maximization (EM) algorithm to estimate haplotype frequencies sharing information between races to produce MR-GRIMME (MR-GRIMM EM).We have shown that these algorithms naturally combine information between races and family members. The accuracy of each of these algorithms is significantly better than its current parallel methods. MR-GRIMM leads to high accuracy in matching predictions. GRAMM better imputes family members than either MR-GRIMM or any existing algorithm and has practically no phasing errors. MR-GRIMME obtains a higher likelihood than existing algorithms.MR-GRIMM, MR-GRIMME, and GRAMM are available as servers or through stand-alone versions in GITHUB and PyPi, as detailed in the appropriate sections., (© 2024. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)