A statistical method for the analysis of nonlinear temperature time series from compost

Temperature is widely accepted as a critical indicator of aerobic microbial activity during composting but, to date, little effort has been made to devise an appropriate statistical approach for the analysis of temperature time series. Nonlinear, time-correlated effects have not previously been considered in the statistical analysis of temperature data from composting, despite their importance and the ubiquity of such features. A novel mathematical model is proposed here, based on a modified Gompertz function, which includes nonlinear, time-correlated effects. Methods are shown to estimate initial values for the model parameter. Algorithms in SAS are used to fit the model to different sets of temperature data from passively aerated compost. Methods are then shown for testing the goodness-of-fit of the model to data. Next, a method is described to determine, in a statistically rigorous manner, the significance of differences among the time-correlated characteristics of the datasets as described using the proposed model. An extra-sum-of-squares method was selected for this purpose. Finally, the model and methods are used to analyze a sample dataset and are shown to be useful tools for the statistical comparison of temperature data in composting.     

Statistical methods for estimating doubling time in in vitro cell growth

Summary Doubling time has been widely used to represent the growth pattern of cells. A traditional method for finding the doubling time is to apply gray-scaled cells, where the logarithmic transformed scale is used. As an alternative statistical method, the log-linear model was recently proposed, for which actual cell numbers are used instead of the transformed gray-scaled cells. In this paper, I extend the log-linear model and propose the extended log-linear model. This model is designed for extra-Poisson variation, where the log-linear model produces the less appropriate estimate of the doubling time. Moreover, I compare statistical properties of the gray-scaled method, the log-linear model, and the extended log-linear model. For this purpose, I perform a Monte Carlo simulation study with three data-generating models: the additive error model, the multiplicative error model, and the overdispersed Poisson model. From the simulation study, I found that the gray-scaled method highly depends on the normality assumption of the gray-scaled cells; hence, this method is appropriate when the error model is multiplicative with the log-normally distributed errors. However, it is less efficient for other types of error distributions, especially when the error model is additive or the errors follow the Poisson distribution. The estimated standard error for the doubling time is not accurate in this case. The log-linear model was found to be efficient when the errors follow the Poisson distribution or nearly Poisson distribution. The efficiency of the log-linear model was decreased accordingly as the overdispersion increased, compared to the extended log-linear model. When the error model is additive or multiplicative with Gamma-distributed errors, the log-linear model is more efficient than the gray-scaled method. The extended log-linear model performs well overall for all three data-generating models. The loss of efficiency of the extended log-linear model is observed only when the error model is multiplicative with log-normally distributed errors, where the gray-scaled method is appropriate. However, the extended log-linear model is more efficient than the log-linear model in this case.     

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.     

Comparative analyses for adaptive radiations

Biologists generally agree that most morphological variation between closely related species is adaptive. The most common method of comparative analysis to test for co-evolved character variation is based on a Brownian-motion model of character evolution. If we are to test for the evolution of character-covariation, and we believe that characters have evolved adaptively to fill niches during an adaptive radiation, then it is appropriate to employ appropriate models for character evolution. We show here that under several models of adaptive character evolution and coevolution during an adaptive radiation, which result in closely related species being more similar to each other than to more distantly related species, cross-species analyses are statistically more appropriate than contrast analyses. If the evolution of some traits fits the Brownian-motion model, while others evolve to fill niches during an adaptive radiation, it might be necessary to identify the number of relevant niche dimensions and the modes of character evolution before deciding on appropriate statistical procedures. Alternatively, maximum-likelihood procedures might be used to determine appropriate transformations of phylogenetic branch lengths that accord with particular models of character evolution.     

A Bayesian approach for subgroup analysis

Several penalization approaches have been developed to identify homogeneous subgroups based on a regression model with subject-specific intercepts in subgroup analysis. These methods often apply concave penalty functions to pairwise comparisons of the intercepts, such that the subjects with similar intercept values are assigned to the same group, which is very similar to the procedure of the penalization approaches for variable selection. Since the Bayesian methods are commonly used in variable selection, it is worth considering the corresponding approaches to subgroup analysis in the Bayesian framework. In this paper, a Bayesian hierarchical model with appropriate prior structures is developed for the pairwise differences of intercepts based on a regression model with subject-specific intercepts, which can automatically detect and identify homogeneous subgroups. A Gibbs sampling algorithm is also provided to select the hyperparameter and estimate the intercepts and coefficients of the covariates simultaneously, which is computationally efficient for pairwise comparisons compared to the time-consuming procedures for parameter estimation of the penalization methods (e.g., alternating direction method of multiplier) in the case of large sample sizes. The effectiveness and usefulness of the proposed Bayesian method are evaluated through simulation studies and analysis of a Cleveland Heart Disease Dataset.     

Piecewise Whittle estimator for trabecular bone radiograph characterization

Osteoporosis is a disease in which low bone mass and microarchitectural deterioration of bone tissue lead to increased bone fragility and a consequent increase in fracture risk. The objective of this paper is to develop and validate a new method to assess bone microarchitecture on radiographs. Taking into account the piecewise fractal nature of bone radiograph images, an appropriate fractal model (piecewise fractional Brownian motion) is used to characterize the trabecular bone network. Based on the Whittle estimator, a new method for calculating the Hurst exponent H is developed to better consider the piecewise fractal nature of the data. Different estimators are used and compared to the proposed method to discriminate two populations composed of healthy controls and osteoporotic patients. Our findings demonstrate that the new estimator proposed here provides effective results in terms of discrimination of the subjects and is better adapted to bone radiograph image analysis.     

Knowledge based modelling of homologous proteins, Part I: Three-dimensional frameworks derived from the simultaneous superposition of multiple structures

An approach is described for modelling the three-dimensional structure of a protein from the tertiary structures of several homologous proteins that have been determined by X-ray analysis. A method is developed for the simultaneous superposition of several protein molecules and for the calculation of an 'average structure' or 'framework'. Investigation of the convergence properties of this method, in the case of both weighted and unweighted least squares, demonstrates that both give a unique answer and the latter is robust for an homologous family of proteins. Multi-dimensional scaling is used to subgroup of the proteins with respect to structural homology. The framework calculated on the basis of the family of homologous proteins, or of an appropriate subgroup, is used to align fragments of the known protein structures of high sequence homology with the unknown. This alignment provides a basis for model building the tertiary structure. Different techniques for using the framework to model the mainchain of various globins and an immunoglobulin domain in the structurally conserved regions are investigated.     

Reconstruction of adaptive radiation in insular habitats using integrated biogeographic information

Aim To develop an analytical method for accurately reconstructing the biogeographic events associated with adaptive radiation in a system of insular habitats. Location An idealized, two-dimensional model system of insular habitats is based on the altitudinally stratified vegetation zones on the island-like mountains of eastern Africa. Methods The model system is treated as a two-dimensional array of insular habitats, and adaptive radiation is treated as a ‘space-filling’ process according to six premises based on uniformitarian principles. Previous approaches to this class of problems have used (1) Hennig's progression rule, (2) optimization of biogeographic character states, and (3) reasoned argumentation with an intuitive synthesis of information. The strengths and limitations of these previous approaches are evaluated. Results A closed analytical method is presented that accurately reconstructs biogeographic events. This methodological approach integrates atomized information back up to the appropriate level of biological organization and has general applicability to phylogenetic analysis. Main conclusions In a truly evolutionary approach to phylogenetic systematics and biogeography, the initial analysis of the pattern of descent should be complemented with a subsequent analysis of the pattern of modification. The method presented here offers one approach to analysing the pattern of modification, which in this case constitutes biogeographic movement.     

Telomere length measurement-caveats and a critical assessment of the available technologies and tools

Studies of telomeres and telomere biology often critically rely on the detection of telomeric DNA and measurements of the length of telomere repeats in either single cells or populations of cells. Several methods are available that provide this type of information and it is often not clear what method is most appropriate to address a specific research question. The major variables that need to be considered are the material that is or can be made available and the accuracy of measurements that is required. The goal of this review is to provide a comprehensive summary of the most commonly used methods and discuss the advantages and disadvantages of each. Methods that start with genomic DNA include telomere restriction fragment (TRF) length analysis, PCR amplification of telomere repeats relative to a single copy gene by Q-PCR or MMQPCR and single telomere length analysis (STELA), a PCR-based approach that accurately measures the full spectrum of telomere lengths from individual chromosomes. A different set of methods relies on fluorescent in situ hybridization (FISH) to detect telomere repeats in individual cells or chromosomes. By including essential calibration steps and appropriate controls these methods can be used to measure telomere repeat length or content in chromosomes and cells. Such methods include quantitative FISH (Q-FISH) and flow FISH which are based on digital microscopy and flow cytometry, respectively. Here the basic principles of various telomere length measurement methods are described and their strengths and weaknesses are highlighted. Some recent developments in telomere length analysis are also discussed. The information in this review should facilitate the selection of the most suitable method to address specific research question about telomeres in either model organisms or human subjects.     

Automated method for modeling seven-helix transmembrane receptors from experimental data.

A rule-based automated method is presented for modeling the structures of the seven transmembrane helices of G-protein-coupled receptors. The structures are generated by using a simulated annealing Monte Carlo procedure that positions and orients rigid helices to satisfy structural restraints. The restraints are derived from analysis of experimental information from biophysical studies on native and mutant proteins, from analysis of the sequences of related proteins, and from theoretical considerations of protein structure. Calculations are presented for two systems. The method was validated through calculations using appropriate experimental information for bacteriorhodopsin, which produced a model structure with a root mean square (rms) deviation of 1.87 A from the structure determined by electron microscopy. Calculations are also presented using experimental and theoretical information available for bovine rhodopsin to assign the helices to a projection density map and to produce a model of bovine rhodopsin that can be used as a template for modeling other G-protein-coupled receptors.     

The role of the Womersley number in pulsatile blood flow a theoretical study of the Casson model.

The purpose of this Note is to clarify the meaning of the Womersley number alpha in pulsatile blood flow in small vessels. In particular. we explain why the use of alpha as aperturbation parameter to obtain approximate solutions of the Casson model (frequently used in the literature) is not appropriate. Using the techniques of dimensional analysis and scaling, we show that alpha is the product of the Reynolds and Strouhal numbers. Since the latter is very small for physiological flows, the result is that alpha < 1 even at relatively high values of the Reynolds number (i.e., for non-negligible inertia) and we validate our perturbation theory results by comparison with a numerical integration of the full model. Although this analysis is based on the Casson model, our method has general validity and may be applied to other models which describe more accurately the rheological properties of blood.     

Statistical analysis of antigen receptor spectratype data

MOTIVATION: The effectiveness of vertebrate adaptive immunity depends crucially on the establishment and maintenance of extreme diversity in the antigen receptor repertoire. Spectratype analysis is a method used in clinical and basic immunological settings in which antigen receptor length diversity is assessed as a surrogate for functional diversity. The purpose of this paper is to describe the systematic derivation and application of statistical methods for the analysis of spectratype data. RESULTS: The basic probability model used for spectratype analysis is the multinomial model with n, the total number of counts, indeterminate. We derive the appropriate statistics and statistical procedures for testing hypotheses regarding differences in antigen receptor distributions and variable repertoire diversity in different treatment groups.We then apply these methods to spectratype data obtained from several healthy donors to examine the differences between normal CD4+ and CD8+ T cell repertoires, and to data from a thymus transplant patient to examine the development of repertoire diversity following the transplant.     

一类求解约束非线性规划问题的神经网络模型

提出一类求解闭凸集上非线性规划问题的神经网络模型。理论分析和计算机模拟表明在适当的假设下所提出的神经网络模型大范围指数级收敛于非线性规划问题的解集。本文神经网络所采用的方法属于广义的最速下降法,甚至当规划问题地正定二次时,本文的模型也比已有的神经网络模型简单。     

Analysis of longitudinal multinomial outcome data

Analysis of categorical outcomes in a longitudinal study has been an important statistical issue. Continuous outcome in a similar study design is commonly handled by the mixed effects model. The longitudinal binary or Poisson-like outcome analysis is often handled by the generalized estimation equation (GEE) method. Neither method is appropriate for analyzing a multinomial outcome in a longitudinal study, although the cross-sectional multinomial outcome is often analyzed by generalized linear models. One reason that these methods are not used is that the correlation structure of two multinomial variables can not be easily specified. In addition, methods that rely upon GEE or mixed effects models are unsuitable in instances when the focus of a longitudinal study is on the rate of moving from one category to another. In this research, a longitudinal model that has three categories in the outcome variable will be examined. A continuous-time Markov chain model will be used to examine the transition from one category to another. This model permits an unbalanced number of measurements collected on individuals and an uneven duration between pairs of consecutive measurements. In this study, the explicit expression for the transition probability is derived that provides an algebraic form of the likelihood function and hence allows the implementation of the maximum likelihood method. Using this approach, the instantaneous transition rate that is assumed to be a function of the linear combination of independent variables can be estimated. For a comparison between two groups, the odds ratios of occurrence at a particular category and their confidence intervals can be calculated. Empirical studies will be performed to compare the goodness of fit of the proposed method with other available methods. An example will also be used to demonstrate the application of this method.     

Saccharomyces cerevisiae as a model organism: a comparative study

Background

Model organisms are used for research because they provide a framework on which to develop and optimize methods that facilitate and standardize analysis. Such organisms should be representative of the living beings for which they are to serve as proxy. However, in practice, a model organism is often selected ad hoc, and without considering its representativeness, because a systematic and rational method to include this consideration in the selection process is still lacking.

Methodology/Principal Findings

In this work we propose such a method and apply it in a pilot study of strengths and limitations of Saccharomyces cerevisiae as a model organism. The method relies on the functional classification of proteins into different biological pathways and processes and on full proteome comparisons between the putative model organism and other organisms for which we would like to extrapolate results. Here we compare S. cerevisiae to 704 other organisms from various phyla. For each organism, our results identify the pathways and processes for which S. cerevisiae is predicted to be a good model to extrapolate from. We find that animals in general and Homo sapiens in particular are some of the non-fungal organisms for which S. cerevisiae is likely to be a good model in which to study a significant fraction of common biological processes. We validate our approach by correctly predicting which organisms are phenotypically more distant from S. cerevisiae with respect to several different biological processes.

Conclusions/Significance

The method we propose could be used to choose appropriate substitute model organisms for the study of biological processes in other species that are harder to study. For example, one could identify appropriate models to study either pathologies in humans or specific biological processes in species with a long development time, such as plants.     

What research with stored samples teaches us about research with human subjects

There is widespread discussion concerning the safeguards appropriate for human research subjects. Less discussed is the fact that the safeguards one deems appropriate depend, in large part, on the model of research participation that one assumes. Therefore, to determine what safeguards are appropriate, it is necessary first to clarify the competing models of research participation. The ostensibly obscure debate over informed consent for research on stored biological samples is of particular interest in this regard because such research can involve varying subsets of the three central elements of research involvement. As a result, analysis of this debate provides an opportunity to identify the competing models of research participation. Based on this analysis, this paper describes a new model of research participation that is emerging, and considers its implications for clinical research.     

Confidence Intervals for Relative Risks in Disease Mapping

Several analysis of the geographic variation of mortality rates in space have been proposed in the literature. Poisson models allowing the incorporation of random effects to model extra‐variability are widely used. The typical modelling approach uses normal random effects to accommodate local spatial autocorrelation. When spatial autocorrelation is absent but overdispersion persists, a discrete mixture model is an alternative approach. However, a technique for identifying regions which have significant high or low risk in any given area has not been developed yet when using the discrete mixture model. Taking into account the importance that this information provides to the epidemiologists to formulate hypothesis related to the potential risk factors affecting the population, different procedures for obtaining confidence intervals for relative risks are derived in this paper. These methods are the standard information‐based method and other four, all based on bootstrap techniques, namely the asymptotic‐bootstrap, the percentile‐bootstrap, the BC‐bootstrap and the modified information‐based method. All of them are compared empirically by their application to mortality data due to cardiovascular diseases in women from Navarra, Spain, during the period 1988–1994. In the small area example considered here, we find that the information‐based method is sensible at estimating standard errors of the component means in the discrete mixture model but it is not appropriate for providing standard errors of the estimated relative risks and hence, for constructing confidence intervals for the relative risk associated to each region. Therefore, the bootstrap‐based methods are recommended for this matter. More specifically, the BC method seems to provide better coverage probabilities in the case studied, according to a small scale simulation study that has been carried out using a scenario as encountered in the analysis of the real data.     

Efficacy or convenience? Model‐based approaches to phylogeny estimation using morphological data

Model‐based approaches (e.g. maximum likelihood, Bayesian inference) are widely used with molecular data, where they might be more appropriate than maximum parsimony for estimating phylogenies under various models of molecular evolution. Recently, there has been an increase in the application of model‐based approaches with morphological (mainly fossil) data; however, there is some doubt as to the effectiveness of the model of morphological evolution. The input parameters (prior probabilities) for the model are unclear, particularly when concerned with unobserved character states. Despite this, some systematists are suggesting superiority of these model‐based methods over maximum parsimony based on, for example, increased resolution or, in the current study, the preferred phylogenetic placement of an iconic taxon. Here, we revisit a recently published analysis implying such superiority and document the discrepancies between parsimony‐based and model‐based approaches to phylogeny estimation. We find that although some taxa are shifted back to their “traditional” phylogenetic placement, other clades are disturbed. The model‐based phylogenies are better resolved; however, due to the lack of an appropriate model of morphological evolution, the increase in resolving power is probably not meaningful. Similarly, some of the preferred phylogenetic positions of taxa, particularly of labile taxa such as Archaeopteryx, are based solely on analyses employing maximum parsimony as the optimality criterion. Poor resolution and labile taxa indicate a need for further examination of the morphology and not a change in method.