Linear Mixed Effects Models under Inequality Constraints with Applications

Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models.     

Prediction of protein structural class by discriminant analysis

Protein structural class--alpha, beta, mixed (alpha/beta or alpha + beta), irregular--can be predicted from the amino acid sequence by discriminant analysis. Discrimination is based on distributions, in the classes, of vectors of attributes characterizing the sequences. In this paper, two sets of attributes and two methods of estimating their distributions are compared using more than 100 proteins from the Protein Data Bank. The best results were obtained when canonical variates of the frequencies of occurrence of 20 amino acids and non-parametric estimates of their distributions were used. Three variates are sufficient to allocate proteins to one of four classes with 83% reliability (estimated by cross-validation) and four variates allowed allocation to one of five classes with 78% reliability.     

Relating new information to a previous vegetation classification: a case of discriminant coordinates analysis

Discriminant coordinates analysis is an adequate technique for analyzing the linear relationships between a number of new variates (i.e. environmental or functional attributes) and a set of vegetational attributes already summarized in the form of a classification. It displays the principal differences among classes in relation to the new variates considered. The procedure and its rationale are equivalent to a special case of principal components analysis.A case study on radiometer satellite data is presented. Two discriminant coordinates displayed the main differences in the seasonal dynamics of the NDVI (an index of standing green biomass) among broad phytogeo-graphic units in the Patagonia region. The first coordinate can be interpreted as an index of height and convexity of the NDVI seasonal curve. It suggests that the principal difference among regions was the total seasonal growth. The second coordinate represents a contrast that discriminated between two already detected patterns of seasonal NDVI curve.Abbreviations DC Discriminant Coordinate - NDVI Normalized Difference Vegetation Index     

Sparse canonical correlation analysis for identifying, connecting and completing gene-expression networks

Background  

We generalized penalized canonical correlation analysis for analyzing microarray gene-expression measurements for checking completeness of known metabolic pathways and identifying candidate genes for incorporation in the pathway. We used Wold's method for calculation of the canonical variates, and we applied ridge penalization to the regression of pathway genes on canonical variates of the non-pathway genes, and the elastic net to the regression of non-pathway genes on the canonical variates of the pathway genes.     

Evaluating the effects of rater and subject factors on measures of association

Large‐scale agreement studies are becoming increasingly common in medical settings to gain better insight into discrepancies often observed between experts' classifications. Ordered categorical scales are routinely used to classify subjects' disease and health conditions. Summary measures such as Cohen's weighted kappa are popular approaches for reporting levels of association for pairs of raters' ordinal classifications. However, in large‐scale studies with many raters, assessing levels of association can be challenging due to dependencies between many raters each grading the same sample of subjects' results and the ordinal nature of the ratings. Further complexities arise when the focus of a study is to examine the impact of rater and subject characteristics on levels of association. In this paper, we describe a flexible approach based upon the class of generalized linear mixed models to assess the influence of rater and subject factors on association between many raters' ordinal classifications. We propose novel model‐based measures for large‐scale studies to provide simple summaries of association similar to Cohen's weighted kappa while avoiding prevalence and marginal distribution issues that Cohen's weighted kappa is susceptible to. The proposed summary measures can be used to compare association between subgroups of subjects or raters. We demonstrate the use of hypothesis tests to formally determine if rater and subject factors have a significant influence on association, and describe approaches for evaluating the goodness‐of‐fit of the proposed model. The performance of the proposed approach is explored through extensive simulation studies and is applied to a recent large‐scale cancer breast cancer screening study.     

The statistical analysis of fluctuating asymmetry: REML estimation of a mixed regression model

The unbiased estimation of fluctuating asymmetry (FA) requires independent repeated measurements on both sides. The statistical analysis of such data is currently performed by a two-way mixed ANOVA analysis. Although this approach produces unbiased estimates of FA, many studies do not utilize this method. This may be attributed in part to the fact that the complete analysis of FA is very cumbersome and cannot be performed automatically with standard statistical software. Therefore, further elaboration of the statistical tools to analyse FA should focus on the usefulness of the method, in order for the correct statistical approaches to be applied more regularly. In this paper we propose a mixed regression model with restricted maximum likelihood (REML) parameter estimation to model FA. This routine yields exactly the same estimates of FA as the two-way mixed ANOVA . Yet the advantages of this approach are that it allows (a) testing the statistical significance of FA, (b) modelling and testing heterogeneity in both FA and measurement error (ME) among samples, (c) testing for nonzero directional asymmetry and (d) obtaining unbiased estimates of individual FA levels. The switch from a mixed two-way ANOVA to a mixed regression model was made to avoid overparametrization. Two simulation studies are presented. The first shows that a previously proposed method to test the significance of FA is incorrect, contrary to our mixed regression approach. In the second simulation study we show that a traditionally applied measure of individual FA [abs(left – right)] is biased by ME. The proposed mixed regression method, however, produces unbiased estimates of individual FA after modelling heterogeneity in ME. The applicability of this method is illustrated with two analyses.     

Canonical correlation analysis of marine macrobenthos survey data

Canonical correlation analysis is applied to measurements of environmental variables and species distributions made during a survey of macrobenthos around a sewage-treatment farm drain. The implications of data reduction, necessary to enable the method to proceed, are discussed. The amount of data was reduced by discarding the rarest species, discarding species occurring at fewest stations, and including only those species and environmental variables which correlated highly with the greatest number of other variables. Only the third data-reduction scheme gave ecologically sensible results. Use of station scores on the first two canonical variates (CV1 and CV2) enabled the sampling grid to be divided into a group of nearshore stations, a group of intermediate depth, and a group of deep offshore stations. Loadings of environmental variables on the canonical variates were found to be unstable but correlations between these variables and canonical variates enabled the variates to be interpreted: CV1 as a gradient of depth and associated changes in sediment characteristics, CV2 with depth- and nutrient-related components, and CV3 as patchiness in sediment characteristics different from that normally expected with depth. Use of correlations between species and canonical variates enables definition of two major species groups, one confined to nearshore environments and a second offshore. These groups (and their sub-groups) related well to groups defined previously by hierarchical classification. It is concluded that, with careful attention to the method of data reduction, canonical correlation analysis can be an effective tool in the analysis of marine benthic survey data.     

典范相关分析技术在植被生态信息中的应用研究

典范相关分析是一种检验两组变量间最大相关的多元统计技术。本文运用此技术结合Pearson's相关系数、PCA分析,对植物群落中植物重要值与土壤组分的相关研究表明:典范相关分析能极好地定量解释生态学中两组变量的相关,并能指示出多个因子的复合作用。同时强调,由于典范相关分析技术对原始数据的线性要求,从而有必要对数据进行标准化和预先的PCA分析。     

Estimation of Box's ε for low‐ and high‐dimensional repeated measures designs with unequal covariance matrices

We present new inference methods for the analysis of low‐ and high‐dimensional repeated measures data from two‐sample designs that may be unbalanced, the number of repeated measures per subject may be larger than the number of subjects, covariance matrices are not assumed to be spherical, and they can differ between the two samples. In comparison, we demonstrate how crucial it is for the popular Huynh‐Feldt (HF) method to make the restrictive and often unrealistic or unjustifiable assumption of equal covariance matrices. The new method is shown to maintain desired α‐levels better than the well‐known HF correction, as demonstrated in several simulation studies. The proposed test gains power when the number of repeated measures is increased in a manner that is consistent with the alternative. Thus, even increasing the number of measurements on the same subject may lead to an increase in power. Application of the new method is illustrated in detail, using two different real data sets. In one of them, the number of repeated measures per subject is smaller than the sample size, while in the other one, it is larger.     

Multivariate slope ratio assay with repeated measurements

A method is given for analyzing a slope ratio assay in which a test drug is compared with a standard drug, two or more response variates being measured on each subject at each of several successively increased drug doses. The method requires all subjects to receive the same number of doses, all subjects on the same drug to receive the same doses, the ratio of corresponding doses of the two drugs to be constant over the successive increases, and response variables to be measured only once on each subject at each dose with no missing data allowed. The technique is also applicable when doses are randomly assigned, provided there is no carry-over effect between doses. For each of the J response variates, the relative potency of the test drug with respect to the standard is defined and estimated in the usual way; a 100(1-alpha)% confidence region is then obtained for the vector of the J relative potencies. A procedure is given for testing the equality of some or all of the J relative potencies; an estimator of a common relative potency is obtained by a standard multivariate least squares method. A common relative potency is of interest because the multiple outcome variables are often different indicators of a general physiologic response. The procedures in the paper are illustrated by a simple example concerning the effects of two anesthetics on children.     

Analysis of serial measurements in medical research.

In medical research data are often collected serially on subjects. The statistical analysis of such data is often inadequate in two ways: it may fail to settle clinically relevant questions and it may be statistically invalid. A commonly used method which compares groups at a series of time points, possibly with t tests, is flawed on both counts. There may, however, be a remedy, which takes the form of a two stage method that uses summary measures. In the first stage a suitable summary of the response in an individual, such as a rate of change or an area under a curve, is identified and calculated for each subject. In the second stage these summary measures are analysed by simple statistical techniques as though they were raw data. The method is statistically valid and likely to be more relevant to the study questions. If this method is borne in mind when the experiment is being planned it should promote studies with enough subjects and sufficient observations at critical times to enable useful conclusions to be drawn. Use of summary measures to analyse serial measurements, though not new, is potentially a useful and simple tool in medical research.     

Exact inference for matched case-control studies

In an epidemiological study with a small sample size or a sparse data structure, the use of an asymptotic method of analysis may not be appropriate. In this paper we present an alternative method of analyzing data for case-control studies with a matched design that does not rely on large-sample assumptions. A recursive algorithm to compute the exact distribution of the conditional sufficient statistics of the parameters of the logistic model for such a design is given. This distribution can be used to perform exact inference on model parameters, the methodology of which is outlined. To illustrate the exact method, and compare it with the conventional asymptotic method, analyses of data from two case-control studies are also presented.     

Craniometric Variation In The Northern And Central Plains

Abstract

Cranial measurements of 13 male and 12 female samples from the Central and Northern Plains region were subjected to canonical analysis. The samples include historic or protohistoric crania that can be ascribed to the Arikara, Mandan, Pawnee, Ponca and Omaha tribes. In addition, two samples belong to the archaeologically defined St. Helena Focus. Both sexes yielded five significant canonical variates, although only four were readily interpretable. The first canonical variate is clearly a Siouan-Caddoan discriminator and reflects variation in cranial vault height. St. Helena sites associate with the Arikara on this axis, supporting previous craniometric analyses which suggest a relationship between these two groups. Subsequent canonical variates deal with more particular aspects of craniometric variation among groups, but are still interpretable in historic or evolutionary terms. The classificatory analysis shows that the Arikara sites are closely related. A major exception to this is the Sully site, which frequently misclassifies with non-Arikara groups. This suggests that the Sully crania have little collective reality; and that there may be non-Arikara components represented at the Sully Site.     

Determination of glucose metabolites in stored erythrocytes and in erythrocytes from patients with thalassemia by analytical isotachophoresis

Glycolysis is for some cells, such as erythrocytes, neutrophil granulocytes and many cancer cells, the only or most important source of energy (ATP) production. Based on previous studies we developed an isotachophoretic (ITP) method which allows, in principle, the simultaneous determination of all metabolites of glycolysis. Since glucose metabolites are small anions, mobility of some of them may overlap in isotachophoresis and, therefore, partial mixed zones are generated. By variation of the leading/terminating system, however, it is possible to separate the compounds of interest. In this communication, we describe a method for analysis of glucose metabolites in erythrocytes from healthy donors during storage in blood bags, and from patients with thalassemia, with special respect to intracellular 2,3 bisphosphoglycerate, lactate and ATP/ADP. The well known characteristic changes of glycolysis in erythrocytes during blood storage and in erythrocytes from thalassemia patients, which are often analysed by separate enzymatic assays, could be confirmed with this isotachophoretic procedure. The method is currently adapted for analysis of glycolysis in neutrophil granulocytes and cancer cells which requires some modifications of sample preparation and performance of the isotachophoretic analysis.     

Edge vulnerability in neural and metabolic networks

Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific aspects of robustness, such as molecular mechanisms of repair, this article focuses more generally on how local structural features in networks may give rise to their global stability. In many networks the failure of single connections may be more likely than the extinction of entire nodes, yet no analysis of edge importance (edge vulnerability) has been provided so far for biological networks. We tested several measures for identifying vulnerable edges and compared their prediction performance in biological and artificial networks. Among the tested measures, edge frequency in all shortest paths of a network yielded a particularly high correlation with vulnerability and identified intercluster connections in biological but not in random and scale-free benchmark networks. We discuss different local and global network patterns and the edge vulnerability resulting from them.     

On-line monitoring of lipid storage in yeasts using impedance spectroscopy

Bioremediation technologies and many environmentally sound biosyntheses rely on the catalytic potential of whole cells. For analyzing and controlling such processes robust real-time indicators for the concentration of intact cells such as impedance are required. The conventional method measures the capacitances of cell suspensions at one or two frequencies and correlates them with biomass concentrations. However, cell inclusions such as lipid droplets or overproduced enzymes may block intracellular ion paths, thereby possibly modifying the dielectric properties of the cells. To test the hypothesis that the total impedance spectrum into the analysis may provide useful information about cell inclusions, the impedance spectrum of a technical culture of the oleaginous yeast Arxula adeninivorans was measured and evaluated every 15 s. This yeast is a good test object since it stores the excess of assimilated carbon in experimentally controllable lipid droplets. Upon correction for possible impedance signal interferences, we derived different empirical methods suitable to indicate incipient lipid formation. The methods were designed to act on-line and are thus principally suited for real-time monitoring of cell inclusions. In search for optimised bioprocess monitoring we tested a heuristic spectrum analysis using integrative statistics (RDA). With this approach we were able to accurately detect the formation of cell inclusions, which is potentially valuable for future bioprocess control strategies.     

A systematic statistical linear modeling approach to oligonucleotide array experiments

We outline and describe steps for a statistically rigorous approach to analyzing probe-level Affymetrix GeneChip data. The approach employs classical linear mixed models and operates on a gene-by-gene basis. Forgoing any attempts at gene presence or absence calls, the method simultaneously considers the data across all chips in an experiment. Primary output includes precise estimates of fold change (some as low as 1.1), their statistical significance, and measures of array and probe variability. The method can accommodate complex experiments involving many kinds of treatments and can test for their effects at the probe level. Furthermore, mismatch probe data can be incorporated in different ways or ignored altogether. Data from an ionizing radiation experiment on human cell lines illustrate the key concepts.     

Socioeconomic status as a risk factor for HIV infection in women in East, Central and Southern Africa: a systematic review

This is a critical, systematic review of the relationship between socioeconomic status (SES) and HIV infection in women in Southern, Central and Eastern Africa. In light of the interest in micro-credit programmes and other HIV prevention interventions structured to empower women through increasing women's access to funds and education, this review examines the epidemiological and public health literature, which ascertains the association between low SES using different measurements of SES and risk of HIV infection in women. Also, given the focus on structural violence and poverty as factors driving the HIV epidemic at a structural/ecological level, as advocated by Paul Farmer and others, this study examines the extent to which differences in SES between individuals in areas with generalized poverty affect risk for SES. Out of 71 studies retrieved, 36 studies met the inclusion criteria including 30 cross-sectional, one case-control and five prospective cohort or nested case-control studies. Thirty-five studies used at least one measurement of female's SES and fourteen also included a measurement of partner's SES. Studies used variables measuring educational level, household income and occupation or employment status at the individual and neighbourhood level to ascertain SES. Of the 36 studies, fifteen found no association between SES and HIV infection, twelve found an association between high SES and HIV infection, eight found an association between low SES and HIV infection and one was mixed. In interpreting these results, this review examines the role of potential confounders and effect modifiers such as history of STDs, number of partners, living in urban or rural areas and time and location of study in sub-Saharan Africa. It is argued that STDs and number of partners are on the causal pathway under investigation between HIV and SES and should not be adjusted as confounders in any analysis. In conclusion, it is argued that in low-income sub-Saharan Africans countries, where poverty is widespread, increasing access to resources for women may initially increase risk of HIV or have no effect on risk-taking behaviours. In some parts of Southern Africa where per capita income is higher and within-country inequalities in wealth are greater, studies suggest that increasing SES may decrease risk. This review concludes that increased SES may have differential effects on married and unmarried women and further studies should use multiple measures of SES. Lastly, it is suggested that the partner's SES (measured by education or income/employment) may be a stronger predictor of female HIV serostatus than measures of female SES.