Generalization of the Mantel-Haenszel estimating function for sparse clustered binary data

We extend the Mantel-Haenszel estimating function to estimate both the intra-cluster pairwise correlation and the main effects for sparse clustered binary data. We propose both a composite likelihood approach and an estimating function approach for the analysis of such data. The proposed estimators are consistent and asymptotically normally distributed. Simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency; however, the estimating equation approach is computationally simpler. Analysis of the Georgia High Blood Pressure survey is used for illustration.     

Quadratic variance models for adaptively preprocessing SELDI-TOF mass spectrometry data

Background  

Surface enhanced laser desorption/ionization time-of-flight mass spectrometry (SELDI) is a proteomics tool for biomarker discovery and other high throughput applications. Previous studies have identified various areas for improvement in preprocessing algorithms used for protein peak detection. Bottom-up approaches to preprocessing that emphasize modeling SELDI data acquisition are promising avenues of research to find the needed improvements in reproducibility.     

Use and abuse of variance models in regression

In (nonlinear) regression with heteroscedastic errors, introduction of a variance model can be useful to obtain good estimators of the regression parameter. For example, the variance model can be used to obtain the optimal weights in weighted least squares. Methodology of this kind is often used in the analysis of assay data in clinical chemistry, pharmacokinetics, and toxicology. In a series of papers in the pharmacological literature, Sheiner and Beal and others advocate the extended least squares (ELS) methodology that combines regression and variance model into a single objective function based on normal-theory maximum likelihood. The inadequacy of this method is folklore in the (mathematical) statistical literature. In this article it is pointed out that this methodology may lead to inconsistent estimators in practically relevant situations. A review is given of other methods that may be preferable to ELS.     

Estimating overdispersion in sparse multinomial data

Multinomial data arise in many areas of the life sciences, such as mark-recapture studies and phylogenetics, and will often by overdispersed, with the variance being higher than predicted by a multinomial model. The quasi-likelihood approach to modeling this overdispersion involves the assumption that the variance is proportional to that specified by the multinomial model. As this approach does not require specification of the full distribution of the response variable, it can be more robust than fitting a Dirichlet-multinomial model or adding a random effect to the linear predictor. Estimation of the amount of overdispersion is often based on Pearson's statistic X² or the deviance D. For many types of study, such as mark-recapture, the data will be sparse. The estimator based on X² can then be highly variable, and that based on D can have a large negative bias. We derive a new estimator, which has a smaller asymptotic variance than that based on X², the difference being most marked for sparse data. We illustrate the numerical difference between the three estimators using a mark-recapture study of swifts and compare their performance via a simulation study. The new estimator has the lowest root mean squared error across a range of scenarios, especially when the data are very sparse.     

Assessing the adequacy of variance function in heteroscedastic regression models

Heteroscedastic data arise in many applications. In heteroscedastic regression analysis, the variance is often modeled as a parametric function of the covariates or the regression mean. We propose a kernel-smoothing type nonparametric test for checking the adequacy of a given parametric variance structure. The test does not need to specify a parametric distribution for the random errors. It is shown that the test statistic has an asymptotical normal distribution under the null hypothesis and is powerful against a large class of alternatives. We suggest a simple bootstrap algorithm to approximate the distribution of the test statistic in finite sample size. Numerical simulations demonstrate the satisfactory performance of the proposed test. We also illustrate the application by the analysis of a radioimmunoassay data set.     

Nonconjugate Bayesian analysis of variance component models

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.     

Analysis of variance components in gene expression data

MOTIVATION: A microarray experiment is a multi-step process, and each step is a potential source of variation. There are two major sources of variation: biological variation and technical variation. This study presents a variance-components approach to investigating animal-to-animal, between-array, within-array and day-to-day variations for two data sets. The first data set involved estimation of technical variances for pooled control and pooled treated RNA samples. The variance components included between-array, and two nested within-array variances: between-section (the upper- and lower-sections of the array are replicates) and within-section (two adjacent spots of the same gene are printed within each section). The second experiment was conducted on four different weeks. Each week there were reference and test samples with a dye-flip replicate in two hybridization days. The variance components included week-to-week, animal-to-animal and between-array and within-array variances. RESULTS: We applied the linear mixed-effects model to quantify different sources of variation. In the first data set, we found that the between-array variance is greater than the between-section variance, which, in turn, is greater than the within-section variance. In the second data set, for the reference samples, the week-to-week variance is larger than the between-array variance, which, in turn, is slightly larger than the within-array variance. For the test samples, the week-to-week variance has the largest variation. The animal-to-animal variance is slightly larger than the between-array and within-array variances. However, in a gene-by-gene analysis, the animal-to-animal variance is smaller than the between-array variance in four out of five housekeeping genes. In summary, the largest variation observed is the week-to-week effect. Another important source of variability is the animal-to-animal variation. Finally, we describe the use of variance-component estimates to determine optimal numbers of animals, arrays per animal and sections per array in planning microarray experiments.     

Riparian plant species differ in sensitivity to both the mean and variance in groundwater stores

确定气候的长期缓慢变化与放大的气候变异性之间相互作用的生态后果是植物生态学的一个重要前沿研究。我们将最近的气候敏感性函数方法与修订的水文“水桶模型”相结合,以改进对植物物种如何响应地下水资源平均值和方差变化的预测。利用河岸植被覆盖和地下水位长期数据集的时空变化,构建了旱地河岸廊道常见植物种类的首个地下水敏感性函数。我们的研究结果展示了这种方法的重要性,它可以识别在日益变化的气候层,随着地下水储量的下降,哪些植物物种能够繁茂的生长(或衰落)。研究结果表明,河岸带植物物种对地下水位平均值和方差的敏感性各不相同。杨树(Populus deltoides ssp. wislizenii)随着地下水年际方差的增大,植被覆盖度预计将下降,而狼柳树 (Salix exigua)和其他原生湿地物种预计将受益于更大的年际方差。非本地物种对地下水变化不敏感,但俄罗斯橄榄(Elaeagnus angustifolia)在更深的平均地下水位条件下敏感性将降低。暖空气温度调节了杨树对地下水的敏感性,在最高温度更高的年份/地点,杨树对地下水的变化比在低温地点/时期更敏感。地下水年内变异系数越大,杨树覆盖度下降幅度越大,但与年际变异系数相关性不显著,这可能因为相对于杨树的寿命,这个时间(16 a)太短。与此相反,非本地柳树(Tamarix chinensis)覆盖度随地下水年内和年际变异系数的增加而增加。总之,我们的研究结果预测,地下水变异性和平均值的变化将通过单个植物物种对地下水储量中的平均值和方差的不同敏感性影响河岸带植物群落。     

Deciphering phenotypic variance in different models of DNA-PKcs deficiency

DNA-PKcs deficiency has been studied in numerous animal models and cell culture systems. In previous studies of kinase inactivating mutations in cell culture systems, ablation of DNA-PK's catalytic activity results in a cell phenotype that is virtually indistinguishable from that ascribed to complete loss of the enzyme. However, a recent compelling study demonstrates a remarkably more severe phenotype in mice harboring a targeted disruption of DNA-PK's ATP binding site as compared to DNA-PKcs deficient mice. Here we investigate the mechanism for these divergent results. We find that kinase inactivating DNA-PKcs mutants markedly radiosensitize immortalized DNA-PKcs deficient cells, but have no substantial effects on transformed DNA-PKcs deficient cells. Since the non-homologous end joining mechanism likely functions similarly in all of these cell strains, it seems unlikely that kinase inactive DNA-PK could impair the end joining mechanism in some cell types, but not in others. In fact, we observed no significant differences in either episomal or chromosomal end joining assays in cells expressing kinase inactivated DNA-PKcs versus no DNA-PKcs. Several potential explanations could explain these data including a non-catalytic role for DNA-PKcs in promoting cell death, or alteration of gene expression by loss of DNA-PKcs as opposed to inhibition of its catalytic activity.Finally, controversy exists as to whether DNA-PKcs autophosphorylates or is the target of other PIKKs; we present data demonstrating that DNA-PK primarily autophosphorylates.     

Models for the continuous culture of microorganisms under both oxygen and carbon limiting conditions

Two models for predicting the behavior of cultures of microorganisms under both oxygen and carbon limiting conditions have been evlauated on a chemostat growing Candida utilis on a glycolysis suppressing glycerol medium. The work indicated that parameter values obtained under wholly oxygen limiting or wholly carbon limiting conditions successfully predict the behavior of the chemostat under the wide range of flow and substrate concentration conditions tested. Both models are satisfactory and hence it is deduced that the simpler one may be used with confidence. It was found that Monod kinetics were applicable to the growth rate dependence on oxygen concentration but that Contois kinetics were superior for the corresponding dependence on carbon substrate concentration.