Matrix-Tilted Archimedean Copulas

The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this copula construction are discussed and a further extension outlined.

On the Role of F8 Sequence Mismatch and Class-II Human Leukocyte Antigen Binding in the Development of Neutralizing Antibodies ("Inhibitors") Directed Against Therapeutic Factor VIII Proteins (tFVIIIs): Evidence from the PATH Study

The development of inhibitors against tFVIIIs represents a serious impediment to efficacious management of bleeding episodes in patients with hemophilia A (HA). It is therefore critical to understand the etiology of inhibitors to improve HA outcomes. Our group has recently presented evidence (Diego et al. Res Pract Thromb Haemost. 2019;3(Suppl. 1):50-51) on the validity of the Sequence Mismatch hypothesis, which posits that a sequence mismatch between the patient's endogenous FVIII sequence (i.e., due to the presence of a non-HA-causing non-synonymous single-nucleotide variation) and that underlying their tFVIII increases the risk that inhibitors will be induced during FVIII replacement therapy. For our study, 442 North American HA patients (237 Whites & 205 Blacks; 88% severely affected) were: 1) Immuno-Chip genotyped at ~167,000 SNPs in genes implicated in autoimmune disease risk; 2) Evaluated by Sanger DNA sequencing and assays for the recurrent intron (I)1- and I22-inversions to identify their F8-causal-mutations; and 3) Tested with the Nijmegen-modified Bethesda assay to determine their inhibitor status. The Immuno-Chip genotypes were used to construct a genetic-relationship matrix (GRM), and the F8 sequence data along with results from the I1- and I22-inversion (I22I) assays were used to construct a shared F8-mutation matrix (FMM). These matrices were used to estimate the heritable genetic and shared F8-mutation effects. Importantly, modeling a F8-mutation effect has the added advantage of accounting for the mutational heterogeneity in F8-mutations. We found that heritability and F8-mutation effects respectively accounted for 50% and 23% of the phenotypic variance in inhibitor (both p < 0.0001). Under the Sequence Mismatch hypothesis, it is assumed that tFVIII-derived peptides spanning the sequence mismatch must first be bound and presented on HLAcII molecules. In Diego et al. (2019), we reported a significant sequence mismatch effect but did not account for the effect of HLAcII binding. In a previous study of PATH data, it was shown using an area under the curve (AUC) estimate from receiver operator characteristic (ROC) curve analysis that HLAcII binding affinities estimated from the then-current version of NetMHCIIpan algorithm with respect to 15-mer peptides spanning sequence mismatches significantly predicted inhibitor status in a sample of 25 patients with the I22I mutation (Pandey et al. Nat Med. 2013;19(10): 1318-24). Here we adopt two strategies to extend this latter analysis to account for genetic relatedness and mutational heterogeneity. In the first strategy, we initially performed a Cholesky decomposition of the phenotypic covariance matrix expressed as a function of the GRM and FMM and their associated heritability and F8-mutation effect estimates, respectively. Following this, the derived Cholesky factor was used to decorrelate the HLAcII binding data, and then a bootstrap with replacement followed by ROC curve analysis each time (for 1,000 resampling's of the data) was used to generate an empirical distribution of the estimated AUC estimates. In the second strategy, we stratified the sample into the subset with the I22I mutation. We next performed a Cholesky decomposition of the GRM multiplied by the heritability and then used the resulting Cholesky factor to decorrelate the data for this subset. Finally, bootstrap with replacement followed by ROC curve analysis each time was used to generate an empirical distribution of the estimated AUC estimates. The p-values for both strategies are determined as the number of AUC estimates greater than that for the original transformed sample plus 1 divided by the total number of bootstraps plus 1. For the first time, we report results on the validity of the sequence mismatch hypothesis while modeling the effects of genetic relatedness, mutational heterogeneity, and HLAcII binding affinity. Disclosures Luu: Haplogenics Corporation: Employment. Chitlur:CSL-Behring: Consultancy, Membership on an entity's Board of Directors or advisory committees; Takeda/Shire: Consultancy, Membership on an entity's Board of Directors or advisory committees; Agios: Research Funding; Bayer: Consultancy, Membership on an entity's Board of Directors or advisory committees; Bioveritiv/Sanofi: Consultancy, Membership on an entity's Board of Directors or advisory committees; Novo Nordisk Inc.: Consultancy, Membership on an entity's Board of Directors or advisory committees; Octapharma: Consultancy, Membership on an entity's Board of Directors or advisory committees. Dinh:Haplogenics Corporation: Employment. Mead:CSL Behring: Employment. Powell:Haplogenics: Membership on an entity's Board of Directors or advisory committees. Escobar:Novo Nordisk: Consultancy, Membership on an entity's Board of Directors or advisory committees; Genentech: Consultancy, Membership on an entity's Board of Directors or advisory committees; Sanofi: Consultancy, Membership on an entity's Board of Directors or advisory committees; Takeda: Consultancy, Membership on an entity's Board of Directors or advisory committees; National Hemophilia Foundation: Consultancy, Membership on an entity's Board of Directors or advisory committees; Pfizer: Consultancy, Membership on an entity's Board of Directors or advisory committees. Howard:Haplogenics Corporation: Equity Ownership, Membership on an entity's Board of Directors or advisory committees.