Estimating equations for a latent transition model with multiple discrete indicators

This paper proposes a two-part model for studying transitions between health states over time when multiple, discrete health indicators are available. The includes a measurement model positing underlying latent health states and a transition model between latent health states over time. Full maximum likelihood estimation procedures are computationally complex in this latent variable framework, making only a limited class of models feasible and estimation of standard errors problematic. For this reason, an estimating equations analogue of the pseudo-likelihood method for the parameters of interest, namely the transition model parameters, is considered. The finite sample properties of the proposed procedure are investigated through a simulation study and the importance of choosing strong indicators of the latent variable is demonstrated. The applicability of the methodology is illustrated with health survey data measuring disability in the elderly from the Longitudinal Study of Aging.     

Estimating multiple benefits from vegetation in mediterranean ecosystems

Ecosystems of the Mediterranean region are characterized by a heterogeneous and dynamic landscape mosaic of vegetation formations that provide diverse benefits: agro pastoral products, ecosystem services, and other utilities. Valuation of these benefits in different states of the ecosystem is an important step towards conservation, decision making, and land management. Yet, studies of this kind are scarce, especially cases dealing with more than one benefit. Multiple benefits evaluation is not straightforward; it involves many difficulties and questions which have no agreed solutions, e.g. estimation, common currency, and optimal solution. In this study we present a methodology for the estimation of three benefits in different components of Mediterranean woody vegetation in Israel. Densities of geophyte wildflowers, honey flowers, and fleshy fruits as food for birds were measured within five vegetation components defined by dominant plant functional types, in four sites with different disturbance histories. Each benefit was measured in its own units. The results showed significant differences between vegetation states in values of each benefit. Therefore, it is possible to calculate the contributions of different cover components for these three benefits. Furthermore, this indicates that it is possible to estimate the level of benefits at larger scales as a first approximation, by considering only the composition of the vegetation cover. The values for the three benefits were standardized to illustrate the question of multiple benefits valuation. This method does not lead to an optimization, but can nevertheless provide a useful tool toward conservation and rational management by land managers and policy makers.     

Bayesian robust inference for differential gene expression in microarrays with multiple samples

We consider the problem of identifying differentially expressed genes under different conditions using gene expression microarrays. Because of the many steps involved in the experimental process, from hybridization to image analysis, cDNA microarray data often contain outliers. For example, an outlying data value could occur because of scratches or dust on the surface, imperfections in the glass, or imperfections in the array production. We develop a robust Bayesian hierarchical model for testing for differential expression. Errors are modeled explicitly using a t-distribution, which accounts for outliers. The model includes an exchangeable prior for the variances, which allows different variances for the genes but still shrinks extreme empirical variances. Our model can be used for testing for differentially expressed genes among multiple samples, and it can distinguish between the different possible patterns of differential expression when there are three or more samples. Parameter estimation is carried out using a novel version of Markov chain Monte Carlo that is appropriate when the model puts mass on subspaces of the full parameter space. The method is illustrated using two publicly available gene expression data sets. We compare our method to six other baseline and commonly used techniques, namely the t-test, the Bonferroni-adjusted t-test, significance analysis of microarrays (SAM), Efron's empirical Bayes, and EBarrays in both its lognormal-normal and gamma-gamma forms. In an experiment with HIV data, our method performed better than these alternatives, on the basis of between-replicate agreement and disagreement.     

Purification and differential expression of enolase from maize

Enolase was purified from maze ( Zea mays L. inbred B73)seeds to a 55 and 56 kDa protein doublet based upon sodium dodecyl sulfate – polyacrylamide gel electrophoresis. Purification included ammonium sulfate-precipitation, gel filtration, Mono Q, and Phenyl Superose chromatography. Two-dimensional gels further resolved the 56 kDa protein into three isoselectric forms. Polyclonal antibodies raised against the purified proteins, were found to bind specifically to both the 55 and 56 kDa proteins during purification. Theses antibodies did not recognized a 56 kDa protein when the strain was complemented with maize enolase (pZM245). Maize enolase antibodies recognized a extracts indicated that the 55 kDa form of enolase was more abundant in roots. Enolase protein levels remained unchanged in maize roots after 24 h of anaerobiosis, even though the specific activity of enolase increased to twice its initial levels. A plastid form of enolase in maize could not be found as either enolase activity or protein (with immunoblots).     

Identifying differential expression in multiple SAGE libraries: an overdispersed log-linear model approach

Background  

In testing for differential gene expression involving multiple serial analysis of gene expression (SAGE) libraries, it is critical to account for both between and within library variation. Several methods have been proposed, including the t test, t _w test, and an overdispersed logistic regression approach. The merits of these tests, however, have not been fully evaluated. Questions still remain on whether further improvements can be made.     

The expression of multiple forms of troponin T in chicken-fast-skeletal muscle may result from differential splicing of a single gene

Troponin T isolated from chicken fast skeletal muscle has been shown to be present in three different molecular forms, one in breast and two in leg muscle. The three forms differ in both size and charge. Troponin T from breast muscle has a molecular mass of 33.5 kDa and a pI of about 7. Of the two leg muscle forms the larger has a molecular mass of 30.5 kDa and a pI of about 8.5 and the smaller a molecular mass of 29.8 kDa and a pI of about 10. Considerably more heterogeneity has been found in the leg than in the breast muscle proteins although this is not reflected in their N-terminal sequences. The reason for this is not clear. Troponin T from breast or leg muscle can be phosphorylated with troponin T kinase at the single serine residue at the N-terminus. No difference in the rate or extent of phosphorylation could be found between proteins from breast or leg muscle. The three proteins have been shown to differ only in the amino acid sequence of their N-terminal tryptic peptides. These peptides are of different length, that from breast troponin T being 58 residues and those from leg troponin T being 36 and 42 residues, these differences account for the difference in molecular mass of the parent proteins. Despite this difference the sequence of the first 12 and last 14 residues is identical in all three N-terminal peptides. The remainder of the sequence of the smallest peptide is also repeated in the other two but they each contain an extra piece of unique sequence. On the basis of these sequences it is proposed that chicken troponin T is coded for by a single gene containing, at the 5' end, a number of small exons and that three different mRNA molecules may be produced by alternative pathways of RNA splicing. The possible significance of these N-terminal sequence variations is discussed.     

The heterogeneity and differential expression of multiple species of the protein kinase C family

Although once considered as a single entity, enzymological and molecular cloning analysis has revealed that protein kinase C exists as a family of multiple subspecies with subtle individual characteristics. The members of this family have closely related structures, but their mode of activation, and kinetic and catalytic properties appear to differ slightly from one another. Biochemical and immunocytochemical studies indicate their differential regional expression and distinct cellular localization. It is attractive to surmise that each member of this family has a defined function in processing and modulating the physiological and pathological response of different cell types to a variety of external stimuli.     

Estimating gene regulatory networks and protein-protein interactions of Saccharomyces cerevisiae from multiple genome-wide data

MOTIVATION: Biological processes in cells are properly performed by gene regulations, signal transductions and interactions between proteins. To understand such molecular networks, we propose a statistical method to estimate gene regulatory networks and protein-protein interaction networks simultaneously from DNA microarray data, protein-protein interaction data and other genome-wide data. RESULTS: We unify Bayesian networks and Markov networks for estimating gene regulatory networks and protein-protein interaction networks according to the reliability of each biological information source. Through the simultaneous construction of gene regulatory networks and protein-protein interaction networks of Saccharomyces cerevisiae cell cycle, we predict the role of several genes whose functions are currently unknown. By using our probabilistic model, we can detect false positives of high-throughput data, such as yeast two-hybrid data. In a genome-wide experiment, we find possible gene regulatory relationships and protein-protein interactions between large protein complexes that underlie complex regulatory mechanisms of biological processes.     

Stress-related differential expression of multiple beta-carotene ketolase genes in the unicellular green alga Haematococcus pluvialis

The unicellular green alga Haematococcus pluvialis is used as a biological production system for astaxanthin. It accumulates large amounts of this commercially interesting ketocarotenoid under a variety of environmental stresses. Here we report the identification and expression of three different beta-carotene ketolase genes (bkt) that are involved in the biosynthesis of astaxanthin in a single strain of the alga. Bkt1 and bkt2 proved to be the crtO and bkt previously isolated from two different strains of H. pluvialis. Bkt3 is a novel third gene, which shared 95% identical nucleotide sequence with bkt2. Nitrogen deficiency alone could not induce the alga cells to produce astaxanthin in 3 days even though it enhances the expression of the bkt genes to three times of that in normal growing cells within 16 h. High light irradiation (125 micromol m(-2)s(-1)) or 45 mM sodium acetate greatly increased the expression of bkt genes to 18 or 52 times of that in normal growing cells, resulting in an accumulation of substantial astaxanthin (about 6 mg g(-1) dry biomass) in 3 days. It is suggested that the existence of the multiple bkt genes and their strong up-regulation by different stress conditions is one of the reasons that H. pluvialis accumulates large amounts of astaxanthin in an instant response to stress environments.     

Sequential expression and differential function of multiple adhesion molecules during the formation of cerebellar cortical layers

We have correlated the times of appearance of the neural cell adhesion molecule (N-CAM), the neuron-glia cell adhesion molecule (Ng-CAM), and the extracellular matrix protein, cytotactin, during the development of the chicken cerebellar cortex, and have shown that these molecules make different functional contributions to granule cell migration. Immunofluorescent staining showed distinct spatiotemporal expression sequences for each adhesion molecule. N-CAM was present at all times in all layers. However, the large cytoplasmic domain polypeptide of N-CAM was always absent from the external granular layer and was enriched in the molecular layer as development proceeded. Ng-CAM began to be expressed in the premigratory granule cells just before migration and later disappeared from cell bodies but remained on parallel fibers. Cytotactin, which is synthesized by glia and not by neurons, appeared first in a speckled pattern within the external granular layer and later appeared in a continuous pattern along the Bergmann glia; it was also enriched in the molecular layer. After we established their order of appearance, we tested the separate functions of these adhesion molecules in granule cell migration by adding specific antibodies against each molecule to cerebellar explant cultures that had been labeled with tritiated thymidine and then measuring the differential distribution of labeled cells in the forming layers. Anti-N-CAM showed marginal effects. In contrast, anti-Ng-CAM arrested most cells in the external granular layer, while anti-cytotactin arrested most cells in the molecular layer. Time course analyses combined with sequential addition of different antibodies in different orders showed that anti-Ng-CAM had a major effect in the early period (first 36 h in culture) and a lesser effect in the second part of the culture period, while anti-cytotactin had essentially no effect at the earlier time but had major effects at a later period (18-72 h in culture). The two major stages of cerebellar granule cell migration thus appear to be differentially affected by distinct adhesion molecules of different cellular origins, binding mechanisms, and overall distributions. The results indicated that local cell surface modulation of adhesion molecules of different specificities at defined stages and sites is essential to the formation of cerebellar cortical layers.     

Estimating treatment effects with partially observed covariates using outcome regression with missing indicators

Missing data is a common issue in research using observational studies to investigate the effect of treatments on health outcomes. When missingness occurs only in the covariates, a simple approach is to use missing indicators to handle the partially observed covariates. The missing indicator approach has been criticized for giving biased results in outcome regression. However, recent papers have suggested that the missing indicator approach can provide unbiased results in propensity score analysis under certain assumptions. We consider assumptions under which the missing indicator approach can provide valid inferences, namely, (1) no unmeasured confounding within missingness patterns; either (2a) covariate values of patients with missing data were conditionally independent of treatment or (2b) these values were conditionally independent of outcome; and (3) the outcome model is correctly specified: specifically, the true outcome model does not include interactions between missing indicators and fully observed covariates. We prove that, under the assumptions above, the missing indicator approach with outcome regression can provide unbiased estimates of the average treatment effect. We use a simulation study to investigate the extent of bias in estimates of the treatment effect when the assumptions are violated and we illustrate our findings using data from electronic health records. In conclusion, the missing indicator approach can provide valid inferences for outcome regression, but the plausibility of its assumptions must first be considered carefully.     

Unifying gene expression measures from multiple platforms using factor analysis

In the Cancer Genome Atlas (TCGA) project, gene expression of the same set of samples is measured multiple times on different microarray platforms. There are two main advantages to combining these measurements. First, we have the opportunity to obtain a more precise and accurate estimate of expression levels than using the individual platforms alone. Second, the combined measure simplifies downstream analysis by eliminating the need to work with three sets of expression measures and to consolidate results from the three platforms.We propose to use factor analysis (FA) to obtain a unified gene expression measure (UE) from multiple platforms. The UE is a weighted average of the three platforms, and is shown to perform well in terms of accuracy and precision. In addition, the FA model produces parameter estimates that allow the assessment of the model fit.The R code is provided in File S2. Gene-level FA measurements for the TCGA data sets are available from http://tcga-data.nci.nih.gov/docs/publications/unified_expression/.