LIKELIHOOD ESTIMATION OF CONJUGACY RELATIONSHIPS IN LINEAR MODELS WITH APPLICATIONS TO HIGH-THROUGHPUT GENOMICS

In the simultaneous estimation of a large number of related quantities, multilevel models provide a formal mechanism for efficiently making use of the ensemble of information for deriving individual estimates. In this article we investigate the ability of the likelihood to identify the relationship between signal and noise in multilevel linear mixed models. Specifically, we consider the ability of the likelihood to diagnose conjugacy or independence between the signals and noises. Our work was motivated by the analysis of data from high-throughput experiments in genomics. The proposed model leads to a more flexible family. However, we further demonstrate that adequately capitalizing on the benefits of a well fitting fully-specified likelihood in the terms of gene ranking is difficult.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.

COVARIATE-ADJUSTED NONPARAMETRIC ANALYSIS OF MAGNETIC RESONANCE IMAGES USING MARKOV CHAIN MONTE CARLO

Permutation tests are useful for drawing inferences from imaging data because of their flexibility and ability to capture features of the brain that are difficult to capture parametrically. However, most implementations of permutation tests ignore important confounding covariates. To employ covariate control in a nonparametric setting we have developed a Markov chain Monte Carlo (MCMC) algorithm for conditional permutation testing using propensity scores. We present the first use of this methodology for imaging data. Our MCMC algorithm is an extension of algorithms developed to approximate exact conditional probabilities in contingency tables, logit, and log-linear models. An application of our non-parametric method to remove potential bias due to the observed covariates is presented.

On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Determination of histopathological tumor grade in neuroepithelial brain tumors by using spectral pattern analysis of in vivo spectroscopic data

OBJECT: In this study, 1H magnetic resonance (MR) spectroscopy was prospectively tested as a reliable method for presurgical grading of neuroepithelial brain tumors. METHODS: Using a database of tumor spectra obtained in patients with histologically confirmed diagnoses, 94 consecutive untreated patients were studied using single-voxel 1H spectroscopy (point-resolved spectroscopy; TE 135 msec, TE 135 msec, TR 1500 msec). A total of 90 tumor spectra obtained in patients with diagnostic 1H MR spectroscopy examinations were analyzed using commercially available software (MRUI/VARPRO) and classified using linear discriminant analysis as World Health Organization (WHO) Grade I/II, WHO Grade III, or WHO Grade IV lesions. In all cases, the classification results were matched with histopathological diagnoses that were made according to the WHO classification criteria after serial stereotactic biopsy procedures or open surgery. Histopathological studies revealed 30 Grade I/II tumors, 29 Grade III tumors, and 31 Grade IV tumors. The reliability of the histological diagnoses was validated considering a minimum postsurgical follow-up period of 12 months (range 12-37 months). Classifications based on spectroscopic data yielded 31 tumors in Grade I/II, 32 in Grade III, and 27 in Grade IV. Incorrect classifications included two Grade II tumors, one of which was identified as Grade III and one as Grade IV; two Grade III tumors identified as Grade II; two Grade III lesions identified as Grade IV; and six Grade IV tumors identified as Grade III. Furthermore, one glioblastoma (WHO Grade IV) was classified as WHO Grade I/II. This represents an overall success rate of 86%, and a 95% success rate in differentiating low-grade from high-grade tumors. CONCLUSIONS: The authors conclude that in vivo 1H MR spectroscopy is a reliable technique for grading neuroepithelial brain tumors.

Analysis of plasma tocopherols alpha, gamma, and 5-nitro-gamma in rats with inflammation by HPLC coulometric detection

Reactive nitrogen oxide species (RNOS) have been implicated as effector molecules in inflammatory diseases. There is emerging evidence that gamma-tocopherol (gammaT), the major form of vitamin E in the North American diet, may play an important role in these diseases. GammaT scavenges RNOS such as peroxynitrite by forming a stable adduct, 5-nitro-gammaT (NGT). Here we describe a convenient HPLC method for the simultaneous determination of NGT, alphaT, and gammaT in blood plasma and other tissues. Coulometric detection of NGT separated on a deactivated reversed-phase column was linear over a wide range of concentrations and highly sensitive (approximately 10 fmol detection limit). NGT extracted from blood plasma of 15-week-old Fischer 344 rats was in the low nM range, representing approximately 4% of gammaT. Twenty-four h after intraperitoneal injection of zymosan, plasma NGT levels were 2-fold higher compared to fasted control animals when adjusted to gammaT or corrected for total neutral lipids, while alpha- and gammaT levels remained unchanged. These results demonstrate that nitration of gammaT is increased under inflammatory conditions and highlight the importance of RNOS reactions in the lipid phase. The present HPLC method should be helpful in clarifying the precise physiological role of gammaT.

Heterosis for biomass-related traits in Arabidopsis investigated by quantitative trait loci analysis of the triple testcross design with recombinant inbred lines

Arabidopsis thaliana has emerged as a leading model species in plant genetics and functional genomics including research on the genetic causes of heterosis. We applied a triple testcross (TTC) design and a novel biometrical approach to identify and characterize quantitative trait loci (QTL) for heterosis of five biomass-related traits by (i) estimating the number, genomic positions, and genetic effects of heterotic QTL, (ii) characterizing their mode of gene action, and (iii) testing for presence of epistatic effects by a genomewide scan and marker x marker interactions. In total, 234 recombinant inbred lines (RILs) of Arabidopsis hybrid C24 x Col-0 were crossed to both parental lines and their F1 and analyzed with 110 single-nucleotide polymorphism (SNP) markers. QTL analyses were conducted using linear transformations Z1, Z2, and Z3 calculated from the adjusted entry means of TTC progenies. With Z1, we detected 12 QTL displaying augmented additive effects. With Z2, we mapped six QTL for augmented dominance effects. A one-dimensional genome scan with Z3 revealed two genomic regions with significantly negative dominance x additive epistatic effects. Two-way analyses of variance between marker pairs revealed nine digenic epistatic interactions: six reflecting dominance x dominance effects with variable sign and three reflecting additive x additive effects with positive sign. We conclude that heterosis for biomass-related traits in Arabidopsis has a polygenic basis with overdominance and/or epistasis being presumably the main types of gene action.

Statistical shape analysis via principal factor analysis

Statistical shape analysis techniques commonly employed in the medical imaging community, such as active shape models or active appearance models, rely on principal component analysis (PCA) to decompose shape variability into a reduced set of interpretable components. In this paper we propose principal factor analysis (PFA) as an alternative and complementary tool to PCA providing a decomposition into modes of variation that can be more easily interpretable, while still being a linear efficient technique that performs dimensionality reduction (as opposed to independent component analysis, ICA). The key difference between PFA and PCA is that PFA models covariance between variables, rather than the total variance in the data. The added value of PFA is illustrated on 2D landmark data of corpora callosa outlines. Then, a study of the 3D shape variability of the human left femur is performed. Finally, we report results on vector-valued 3D deformation fields resulting from non-rigid registration of ventricles in MRI of the brain.

Comparison of magnetic resonance imaging of inhaled SF6 with respiratory gas analysis

Magnetic resonance imaging of inhaled fluorinated inert gases ((19)F-MRI) such as sulfur hexafluoride (SF(6)) allows for analysis of ventilated air spaces. In this study, the possibility of using this technique to image lung function was assessed. For this, (19)F-MRI of inhaled SF(6) was compared with respiratory gas analysis, which is a global but reliable measure of alveolar gas fraction. Five anesthetized pigs underwent multiple-breath wash-in procedures with a gas mixture of 70% SF(6) and 30% oxygen. Two-dimensional (19)F-MRI and end-expiratory gas fraction analysis were performed after 4 to 24 inhaled breaths. Signal intensity of (19)F-MRI and end-expiratory SF(6) fraction were evaluated with respect to linear correlation and reproducibility. Time constants were estimated by both MRI and respiratory gas analysis data and compared for agreement. A good linear correlation between signal intensity and end-expiratory gas fraction was found (correlation coefficient 0.99+/-0.01). The data were reproducible (standard error of signal intensity 8% vs. that of gas fraction 5%) and the comparison of time constants yielded a sufficient agreement. According to the good linear correlation and the acceptable reproducibility, we suggest the (19)F-MRI to be a valuable tool for quantification of intrapulmonary SF(6) and hence lung function.

Fluctuation analysis of lung function as a predictor of long-term response to beta2-agonists

The response to beta(2)-agonists differs between asthmatics and has been linked to subsequent adverse events, even death. Possible determinants include beta(2)-adrenoceptor genotype at position 16, lung function and airway hyperresponsiveness. Fluctuation analysis provides a simple parameter alpha measuring the complex correlation properties of day-to-day peak expiratory flow. The present study investigated whether alpha predicts clinical response to beta(2)-agonist treatment, taking into account other conventional predictors. Analysis was performed on previously published twice-daily peak expiratory flow measurements in 66 asthmatic adults over three 6-month randomised order treatment periods: placebo, salbutamol and salmeterol. Multiple linear regression was used to determine the association between alpha during the placebo period and response to treatment (change in the number of days with symptoms), taking into account other predictors namely beta(2)-adrenoceptor genotype, lung function and its variability, and airway hyperresponsiveness. The current authors found that alpha measured during the placebo period considerably improved the prediction of response to salmeterol treatment, taking into account genotype, lung function or its variability, or airway hyperresponsiveness. The present study provides further evidence that response to beta(2)-agonists is related to the time correlation properties of lung function in asthma. The current authors conclude that fluctuation analysis of lung function offers a novel predictor to identify patients who may respond well or poorly to treatment.

Pulse contour analysis: a valid assessment of central arterial stiffness in children?

In adults the contour analysis of peripheral pressure waves in the upper limb reflects central aortic stiffness. Here, we wanted to demonstrate the appropriateness of pulse contour analysis to assess large artery stiffness in children. Digital volume pulse analysis, with the computation of the stiffness index and pulse wave velocity between carotid and femoral artery, were simultaneously determined in 79 healthy children between 8 years and 15 years (mean age 11.4 years, 32 girls). The stiffness index of 42 healthy adults (mean age 45.6 years, 26 women) served as control. Pulse wave velocity between carotid and femoral artery was directly correlated with systolic pressure and mean blood pressure, as well as with pulse pressure. The results from the stiffness index of children revealed the expected values extrapolated from the linear regression of adulthood stiffness index vs. age. Childhood stiffness index positively correlated with pulse wave velocity (r(2) = 0.07, P = 0.02) but not with blood pressure parameters. The exclusion of individuals with an increased vascular tone, as indicated by a reflexion index > 90%, improved the correlation between stiffness index and pulse wave velocity (r(2) = 0.13, P = 0.001). Our data indicate that digital volume pulse-based analysis has limitations if compared with pulse wave velocity to measure arterial stiffness, mostly in patients with a high vascular tone.

Analysis of spring break-up and its effects on a biomass feedstock supply chain in northern Michigan

Demand for bio-fuels is expected to increase, due to rising prices of fossil fuels and concerns over greenhouse gas emissions and energy security. The overall cost of biomass energy generation is primarily related to biomass harvesting activity, transportation, and storage. With a commercial-scale cellulosic ethanol processing facility in Kinross Township of Chippewa County, Michigan about to be built, models including a simulation model and an optimization model have been developed to provide decision support for the facility. Both models track cost, emissions and energy consumption. While the optimization model provides guidance for a long-term strategic plan, the simulation model aims to present detailed output for specified operational scenarios over an annual period. Most importantly, the simulation model considers the uncertainty of spring break-up timing, i.e., seasonal road restrictions. Spring break-up timing is important because it will impact the feasibility of harvesting activity and the time duration of transportation restrictions, which significantly changes the availability of feedstock for the processing facility. This thesis focuses on the statistical model of spring break-up used in the simulation model. Spring break-up timing depends on various factors, including temperature, road conditions and soil type, as well as individual decision making processes at the county level. The spring break-up model, based on the historical spring break-up data from 27 counties over the period of 2002-2010, starts by specifying the probability distribution of a particular county’s spring break-up start day and end day, and then relates the spring break-up timing of the other counties in the harvesting zone to the first county. In order to estimate the dependence relationship between counties, regression analyses, including standard linear regression and reduced major axis regression, are conducted. Using realizations (scenarios) of spring break-up generated by the statistical spring breakup model, the simulation model is able to probabilistically evaluate different harvesting and transportation plans to help the bio-fuel facility select the most effective strategy. For early spring break-up, which usually indicates a longer than average break-up period, more log storage is required, total cost increases, and the probability of plant closure increases. The risk of plant closure may be partially offset through increased use of rail transportation, which is not subject to spring break-up restrictions. However, rail availability and rail yard storage may then become limiting factors in the supply chain. Rail use will impact total cost, energy consumption, system-wide CO2 emissions, and the reliability of providing feedstock to the bio-fuel processing facility.

Long-term immunologic response to antiretroviral therapy in low-income countries: a collaborative analysis of prospective studies

BACKGROUND: Few data are available on the long-term immunologic response to antiretroviral therapy (ART) in resource-limited settings, where ART is being rapidly scaled up using a public health approach, with a limited repertoire of drugs. OBJECTIVES: To describe immunologic response to ART among ART patients in a network of cohorts from sub-Saharan Africa, Latin America, and Asia. STUDY POPULATION/METHODS: Treatment-naive patients aged 15 and older from 27 treatment programs were eligible. Multilevel, linear mixed models were used to assess associations between predictor variables and CD4 cell count trajectories following ART initiation. RESULTS: Of 29 175 patients initiating ART, 8933 (31%) were excluded due to insufficient follow-up time and early lost to follow-up or death. The remaining 19 967 patients contributed 39 200 person-years on ART and 71 067 CD4 cell count measurements. The median baseline CD4 cell count was 114 cells/microl, with 35% having less than 100 cells/microl. Substantial intersite variation in baseline CD4 cell count was observed (range 61-181 cells/microl). Women had higher median baseline CD4 cell counts than men (121 vs. 104 cells/microl). The median CD4 cell count increased from 114 cells/microl at ART initiation to 230 [interquartile range (IQR) 144-338] at 6 months, 263 (IQR 175-376) at 1 year, 336 (IQR 224-472) at 2 years, 372 (IQR 242-537) at 3 years, 377 (IQR 221-561) at 4 years, and 395 (IQR 240-592) at 5 years. In multivariable models, baseline CD4 cell count was the most important determinant of subsequent CD4 cell count trajectories. CONCLUSION: These data demonstrate robust and sustained CD4 response to ART among patients remaining on therapy. Public health and programmatic interventions leading to earlier HIV diagnosis and initiation of ART could substantially improve patient outcomes in resource-limited settings.