One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Stabilization of zeylenone in rat plasma by the presence of esterase inhibitors and its LC‐MS/MS assay for pharmacokinetic study

Six esterase inhibitors, namely EDTA·2Na⁺, NaF, phenylmethanesulfonyl fluoride, dichlorvos, bis‐nitrophenyl phosphate (BNPP) and thenoyltrifluoroacetone, and the mixture of NaF and BNPP, were evaluated for the stabilization of labile benzoate containing zeylenone in rat plasma. The mixture appeared to exhibit the most effectively stabilizing effect with the degraded content of zeylenone decreasing from >60% (in the absence of inhibitors) to <6%. Following the stabilization by the addition of NaF (5 mm ) and BNPP (5 mm ), the analytes in rat plasma were acidified by formic acid and extracted into ethyl acetate at 0°C. After chromatographic separation, the detection of zeylenone was performed on a 3200 Q‐Trap with positive ion electrospray mode, monitoring the ion transition m/z 383.2 → 105.0. The method was validated over the range from 2.68 to 1340 ng/mL with inter‐ and intra‐run precision for the quality control samples being less than 6.8%. The assay accuracy was within 100 ± 7.0%. The validated method was successfully applied to a pharmacokinetic study in rats after the intratracheal administration of zeylenone in free drug or polymeric micellar solutions. The results showed that the pulmonary absorption of zeylenone loaded in micelles was significantly retarded compared with that of free drug solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

Structure‐guided RP‐HPLC chromatography of diastereomeric α‐helical peptide analogs substituted with single amino acid stereoisomers

An α‐helical model peptide (Ac‐EAEKAAKE‐X‐EKAAKEAEK‐amide) was used as a template to examine the efficacy of conventional reversed‐phase high‐performance liquid chromatography (RP‐HPLC) in separating peptide analogs with single substitutions (at position X) of diasteromeric amino acids Ile, allo‐Ile, d ‐Ile and d ‐allo‐Ile. We compared differences in peptide retention behavior on a C₈ column and a C₁₈ column at different temperatures. We demonstrated how subtle differences in peptide secondary structure affected by the different substitutions of amino acids with identical overall hydrophobicity enabled effective resolution of these peptide analogs. We also demonstrated the ability of RP‐HPLC to separate Ile‐ and allo‐Ile‐substituted analogs of a 26‐residue α‐helical antimicrobial peptide (AMP), with the substitution site towards the C‐terminus of the α‐helix. These peptides show different values of antibacterial activity and hemolytic activity, and different selectivity against bacteria and human cells. Our results underline the ability of RP‐HPLC to resolve even difficult diasteromeric peptide mixtures as well as its value in monitoring very subtle hydrophobicity changes in de novo‐designed AMP. Copyright © 2013 John Wiley & Sons, Ltd.     

Four forbidden subgraph pairs for hamiltonicity of 3-connected graphs

Acta Mathematicae Applicatae Sinica, English Series - For non-negative integers i, j and k, we denote the generalized net as N i,j,k , which is a triangle with disjoint paths of length i, j and k,...