Bias Reduction and a Solution for Separation of Logistic Regression with Missing Covariates

Summary Logistic regression is an important statistical procedure used in many disciplines. The standard software packages for data analysis are generally equipped with this procedure where the maximum likelihood estimates of the regression coefficients are obtained iteratively. It is well known that the estimates from the analyses of small‐ or medium‐sized samples are biased. Also, in finding such estimates, often a separation is encountered in which the likelihood converges but at least one of the parameter estimates diverges to infinity. Standard approaches of finding such estimates do not take care of these problems. Moreover, the missingness in the covariates adds an extra layer of complexity to the whole process. In this article, we address these three practical issues—bias, separation, and missing covariates by means of simple adjustments. We have applied the proposed technique using real and simulated data. The proposed method always finds a solution and the estimates are less biased. A SAS macro that implements the proposed method can be obtained from the authors.     

岷江柏四个地理种群分布格局比较研究

岷江柏是我国特有珍稀树种,其种群分布格局一直缺乏必要的研究。采用Greig-Smith的相邻格子样方调查法,调查了四川西部四个岷江柏地理种群,用方差/均值比率法和聚集度指标法分析了种群空间并进行了比较。结果表明,岷江柏种群分布格局与取样尺度有关。在2m×2m、4m×4m、6m×6m、8m×8m四个取样尺度下,小金种群均表现为集群分布,马尔康种群均表现为随机分布,金川种群和理县种群却随着取样尺度的增大,表现出聚集分布→均匀分布→随机分布的变化趋势。四个取样尺度中以2m×2m取样尺度来分析岷江柏种群空间分布格局时效果最好。方差/均值比率法运用统计方法确定T值的显著性,数学推导严密,运算简单,在分布格局分析中是一种较可靠的方法。     

Optimised separation procedures for the simultaneous assay of three plant hormones in liquid biofertilisers

Introduction – The overuse of petrochemical‐based synthetic fertilisers has caused detrimental effects to soil, water supplies, foods and animal health. This, in addition to increased awareness of organic farming, has generated considerable interest in the evaluation of renewable biofertilisers. Objective – The three objectives of the current research were: (1) to evaluate and optimise a solid phase extraction procedure for extraction of three plant hormones, IAA, GA₃ and ABA from two model biofertilisers produced from coconut shells and pineapple peels; (2) to develop an HPLC analysis procedure for the simultaneous separation and quantification of three plant hormones (IAA, GA₃ and ABA); and (3) to evaluate the changes in three plant hormones levels at four different fermentation time periods and varying number of general bacteria, lactic acid bacteria and yeast. Result – An optimised procedure for sample preparation, separation and simultaneous analysis of three plant hormones [indole‐3‐acetic acid (IAA), gibberellic acid (GA₃) and abscisic acid (ABA)] produced in liquid biofertilisers was developed. This method involves sample cleanup using a Sep‐pack Oasis^®MAX cartridge containing mixed‐mode anion‐exchange and reverse‐phase sorbents that provided optimum recovery of 85.6, 91.9 and 94.3%, respectively, for the three hormones, IAA, GA₃, and ABA. Baseline separation of three hormones was achieved using mobile phase consisting of 1% acetic acid and acetonitrile (75:25, v/v) at pH 4.0. The amounts of hormones produced in liquid biofertilisers were influenced by fruit types, fermentation time and total number of general bacteria, lactic acid bacteria and yeasts. The quantities of three plant hormones produced during fermentation correlated well with the total number of microorganisms present in the liquid biofertilisers. Conclusion – A simple and rapid sample preparation procedure followed by RP‐HPLC with UV detection was optimised and developed for simultaneous quantification and identification of three plant hormones namely, IAA, GA₃ and ABA in the liquid biofertilisers. This procedure allows quantification of the three plant hormones in their natural states without any prior derivatisation step. The results presented illustrate that the contents of the three plant hormones depended on the type of fruit wastes, fermentation time and the number of microorganisms found in liquid biofertilisers. This method can be extended to determine the quantity of three hormones in other matrices. This assay procedure will aid in the development of liquid biofertilisers, a valuable alternative fertilisers to promote plant growth. This process will help farmers to reduce production cost and pollution problems. Copyright © 2009 John Wiley & Sons, Ltd.     

Sample Size Considerations for GEE Analyses of Three‐Level Cluster Randomized Trials

Summary Cluster randomized trials in health care may involve three instead of two levels, for instance, in trials where different interventions to improve quality of care are compared. In such trials, the intervention is implemented in health care units (“clusters”) and aims at changing the behavior of health care professionals working in this unit (“subjects”), while the effects are measured at the patient level (“evaluations”). Within the generalized estimating equations approach, we derive a sample size formula that accounts for two levels of clustering: that of subjects within clusters and that of evaluations within subjects. The formula reveals that sample size is inflated, relative to a design with completely independent evaluations, by a multiplicative term that can be expressed as a product of two variance inflation factors, one that quantifies the impact of within‐subject correlation of evaluations on the variance of subject‐level means and the other that quantifies the impact of the correlation between subject‐level means on the variance of the cluster means. Power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total, when data were analyzed using bias‐corrected estimating equations for the correlation parameters in combination with the model‐based covariance estimator or the sandwich estimator with a finite sample correction.     

The rank product method with two samples

Breitling et al. (2004) [1] introduced a statistical technique, the rank product method, for detecting differentially regulated genes in replicated microarray experiments. The technique has achieved widespread acceptance and is now used more broadly, in such diverse fields as RNAi analysis, proteomics, and machine learning. In this note, we extend the rank product method to the two sample setting, provide distribution theory attending the rank product method in this setting, and give numerical details for implementing the method.     

DNA extraction from bovine faeces: current status and future trends

There is an increasing interest in the detection and enumeration of micro‐organisms pathogenic for human and present in bovine faeces. This interest is because pollution of the environment by animal faeces may affect the safety of food and of drinking or recreational water. Detection and quantification of microbial pathogens carried out using DNA extracted from the faecal matrix are affected by the quality and the quantity of the DNA extracts, which are critical factors that limit the accuracy and sensitivity of molecular studies. This review compares published methods on DNA extraction from bovine faeces, focusing on the extent to which the success of DNA amplification is affected by issues related to the faeces. Following a general discussion on the DNA extraction methods used for faeces, we focus particularly on issues related to the faecal environment itself. The objective is to identify information that can be used to improve the sensitivity of those PCR methods used after direct DNA extraction.     

Advances in determination of vitamin D related compounds in biological samples using liquid chromatography–mass spectrometry: A review

The measurements of the serum/plasma concentrations of vitamin D metabolites are widely used for the diagnostic assessment and follow-up of several diseases, such as chronic renal failure and osteoporosis. These metabolites have usually been measured by protein binding assays, such as radioimmunoassay and radioreceptor assay. Although these techniques will doubtless continue to be the methods of choice for routine use in the clinical field, their specificity and accuracy are sometimes poor due to interference from other metabolites and lipids. Among the alternative methods, liquid chromatography (LC) coupled with mass spectrometry (MS) has been used for the analysis of these metabolites and even synthetic vitamin D analogues (therapeutic agents) due to its sensitivity and selectivity. This article reviews recent advances in the determination of vitamin D metabolites and related compounds in biological samples using LC–MS.     

Determination of ticagrelor and two metabolites in plasma samples by liquid chromatography and mass spectrometry

Rapid and sensitive analytical methods using liquid chromatography with tandem mass spectrometry (LC/MS/MS) were developed for the determination of ticagrelor, the first reversible oral platelet P2Y₁₂ receptor inhibitor, and its metabolites AR-C124910XX and AR-C133913XX in human plasma. Ticagrelor and its metabolites were extracted using protein precipitation with acetonitrile. Chromatographic separations were performed on reversed phase columns and detection using atmospheric pressure chemical ionization (APCI). Ticagrelor and AR-C124910XX were analyzed in the same assay, with the internal standard, d7-ZD6140, on a C18 column using negative ionization; AR-C133913XX analyzed separately on a phenyl column using positive ionization. Full validation of the methods was performed including selectivity, lower limit of quantification, accuracy, precision stability and incurred sample reproducibility and incurred sample stability. Total analytical run time was short (2 min). Calibration curves were established in the range 5–5000 ng/mL for ticagrelor, 2.5–2500 ng/mL for AR-C124910XX and 2–1000 ng/mL for AR-C133913XX. Lower limits of quantification for ticagrelor, AR-C124910XX and AR-C133913XX were determined to be 5, 2.5 and 2.0 ng/mL, respectively from 100 μL of human plasma. For ticagrelor, AR-C124910XX and AR-C133913XX, mean intra-batch accuracy was 91.9–109.0%, 86.8–109.2% and 100.5–112.0%, respectively; intra-batch precision was 4.0–8.4%, 5.2–16.9% and 3.9–12.3%, respectively. The methods were also applied to quantification of ticagrelor, AR-C124910XX and AR-C133913XX in rabbit, rat, mouse and marmoset, using 25 μL of animal plasma. A modified methodology was developed to quantify ticagrelor and AR-C124910XX in plasma from dog and cynomolgus monkey. Human incurred samples were found to generate consistent reproducibility and stability results. This method was successfully applied to determine plasma concentrations following administration of ticagrelor in human volunteers and patients, and animal safety evaluation studies. This validated methods has the advantages of being straightforward, robust and allows a fast throughput of samples.     

Pooled samples bias fungal community descriptions

We tested the accuracy of molecular analyses for recovering the species richness and structure of pooled fungal communities of known composition. We constructed replicate pools of 2-20 species and analysed these pools by two separate pooling-DNA extraction procedures and three different molecular analyses (Automated Ribosomal Intergenic Spacer Analysis (ARISA), terminal restriction fragment length polymorphism (T-RFLP) and clone library-sequencing). None of the methods correctly described the known communities. Only clone library-sequencing with high sequencing per pool (～100 clones) recovered reasonable estimates of richness. Frequency data were skewed with all procedures and analyses. These results indicate that the error introduced by pooling samples is significant and problematic for ecological studies of fungal communities.     

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.