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Extensive multiallelic analysis of the relationship between HLA-DRB1 and rheumatoid arthritis using a Bayesian partition model

Abstract

To analyse the association between individual HLA-DRB1 locus genotypes and rheumatoid arthritis (RA) susceptibility, taking in account the multiallelic nature of the shared epitope (SE). In total, 538 patients and 536 controls were genotyped for 12 alleles of the HLA-DRB1 locus. A Bayesian partition model and multivariate logistic models were used to assess the role of the SE and of its individual components. The SE was associated with RA susceptibility (odds ratio (OR) 2 versus 0 SE copy=9.99 (95 CI 4.69–15.30) and OR 1 versus 0 SE copy=3.16 (95% CI 2.42–4.12)). The Bayesian partition model supplied a permutation of the HLA-DRBA locus alleles ordered by increasing disease risk. Alleles associated with highest risks are those that code for the SE. The individual OR estimations for the HLA-DRB1 locus genotypes went from OR=1.00 (95% CI 1.00–1.25) for the less associated genotype to OR=21.40 (95% CI 8.02–65.79) for the most associated one. In conclusion, the allele order risk and the OR estimations for individual genotypes of the HLA-DRB1 locus were consistent with the SE theory. Using an exploratory statistical method without a priori hypothesis, our study allowed a detailed analysis of the multiallelic nature of the SE.

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Acknowledgements

We thank Shaun Seaman who kindly gave us the source code (C language) of the Bayesian partition model.

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Correspondence to P Miossec.

Appendix A

Appendix A

Details on Seaman's Bayesian partition model

The basic assumptions of the partition model are that all possible genotypes of the HLA-DRB1 locus belong to a number of groups, that all genotypes in the same group convey the same risk of disease for the positive individuals and that genotypes in different groups convey different risks. A genotype partition is built from an allele order risk that corresponds to a classification of the alleles by increasing disease risk. Each genotype partition satisfies a particular assumption: if two genotypes share one allele but differ for the other, then the risk conveyed by a genotype with a higher allele in the order risk cannot be less than the risk conveyed by a genotype with a lower allele in that order risk. Accordingly, if an allele Aj is higher than the allele Ai in the allele order risk, whatever the allele Ak, the risk associated with the Aj/Ak genotype is greater than the risk associated with Ai/Ak. Although the Bayesian partition model clusters the genotypes, it supplies one disease risk estimation per genotype. Indeed, at each iteration of the fitting algorithm, an allele order risk, a partition model and group disease risks are sampled from their posterior distribution. The posterior distribution of each genotype risk is then recovered from the group disease risk the genotype belonged to at each iteration.

Uniform priors were placed on the allele order risk and the partition model. The prior distribution of the log (disease risk) of each group was the normal distribution N(0, σ2), σ2=2.34. This value of σ2 implied the assumption that 95% of groups of genotypes had disease risk in the range (0.05–20).

Results were based on 100 000 iterations. OR estimation and 95% credibility intervals were supplied for each genotype. 95% credibility intervals were constructed from the posterior distributions and could be interpreted as the classical 95% confidence intervals. The posterior probabilities of each allele to be at each rank as well as the mean rank of each allele were also computed. The mean rank of each allele provided the retained allele order risk. Results are presented in Table 5.

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Marotte, H., Tournoud, M., Cazalis, MA. et al. Extensive multiallelic analysis of the relationship between HLA-DRB1 and rheumatoid arthritis using a Bayesian partition model. Genes Immun 7, 487–493 (2006). https://doi.org/10.1038/sj.gene.6364319

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