We describe an algorithm for computing, for all primes $p \leq X$, the mod-$p$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive in time quasilinear in $X$. This combines the Beukers--Cohen--Mellit trace formula with average polynomial time techniques of Harvey et al.

The immune responses of natural killer cells are regulated, in part, by killer cell immunoglobulin-like receptors (KIR). The 16 closely-related genes in the KIR gene system have been diversified by gene duplication and unequal crossing over, thereby generating haplotypes with variation in gene copy number. Allelic variation also contributes to diversity within the complex. In this study, we estimated allele-level haplotype frequencies and pairwise linkage disequilibrium statistics for 14 KIR loci. The typing utilized multiple methodologies by four laboratories to provide at least 2x coverage for each allele. The computational methods generated maximum-likelihood estimates of allele-level haplotypes. Our results indicate the most extensive allele diversity was observed for the KIR framework genes and for the genes localized to the telomeric region of the KIR A haplotype. Particular alleles of the stimulatory loci appear to be nearly fixed on specific, common haplotypes while many of the less frequent alleles of the inhibitory loci appeared on multiple haplotypes, some with common haplotype structures. Haplotype structures cA01 and/or tA01 predominate in this cohort, as has been observed in most populations worldwide. Linkage disequilibrium is high within the centromeric and telomeric haplotype regions but not between them and is particularly strong between centromeric gene pairs KIR2DL5∼KIR2DS3S5 and KIR2DS3S5∼KIR2DL1, and telomeric KIR3DL1∼KIR2DS4. Although 93% of the individuals have unique pairs of full-length allelic haplotypes, large genomic blocks sharing specific sets of alleles are seen in the most frequent haplotypes. These high-resolution, high-quality haplotypes extend our basic knowledge of the KIR gene system and may be used to support clinical studies beyond single gene analysis.

Rationale

Primary graft dysfunction (PGD) is a form of acute lung injury that occurs after lung transplantation. The definition of PGD was standardized in 2005. Since that time, clinical practice has evolved, and this definition is increasingly used as a primary endpoint for clinical trials; therefore, validation is warranted.

Objectives

We sought to determine whether refinements to the 2005 consensus definition could further improve construct validity.

Methods

Data from the Lung Transplant Outcomes Group multicenter cohort were used to compare variations on the PGD definition, including alternate oxygenation thresholds, inclusion of additional severity groups, and effects of procedure type and mechanical ventilation. Convergent and divergent validity were compared for mortality prediction and concurrent lung injury biomarker discrimination.

Measurements and main results

A total of 1,179 subjects from 10 centers were enrolled from 2007 to 2012. Median length of follow-up was 4 years (interquartile range = 2.4-5.9). No mortality differences were noted between no PGD (grade 0) and mild PGD (grade 1). Significantly better mortality discrimination was evident for all definitions using later time points (48, 72, or 48-72 hours; P < 0.001). Biomarker divergent discrimination was superior when collapsing grades 0 and 1. Additional severity grades, use of mechanical ventilation, and transplant procedure type had minimal or no effect on mortality or biomarker discrimination.

Conclusions

The PGD consensus definition can be simplified by combining lower PGD grades. Construct validity of grading was present regardless of transplant procedure type or use of mechanical ventilation. Additional severity categories had minimal impact on mortality or biomarker discrimination.

Bronchoalveolar lavage (BAL) is a key clinical and research tool in lung transplantation (LTx). However, BAL collection and processing are not standardized across LTx centers. This International Society for Heart and Lung Transplantation-supported consensus document on BAL standardization aims to clarify definitions and propose common approaches to improve clinical and research practice standards. The following 9 areas are covered: (1) bronchoscopy procedure and BAL collection, (2) sample handling, (3) sample processing for microbiology, (4) cytology, (5) research, (6) microbiome, (7) sample inventory/tracking, (8) donor bronchoscopy, and (9) pediatric considerations. This consensus document aims to harmonize clinical and research practices for BAL collection and processing in LTx. The overarching goal is to enhance standardization and multicenter collaboration within the international LTx community and enable improvement and development of new BAL-based diagnostics.