On the application of linear relative risk regression models

Motivations for considering linear relative risk models are described. These include covariate data reduction and the testing of additivity of covariate effects on the relative risk. A simulation study was conducted in order to study properties of asymptotic distributional approximations and iterative convergence properties. Parameter transformations and likelihood ratio approximations are considered for confidence interval calculation.     

Statistical model building and model criticism for human circadian data

Mathematical models have played an important role in the analysis of circadian systems. The models include simulation of differential equation systems to assess the dynamic properties of a circadian system and the use of statistical models, primarily harmonic regression methods, to assess the static properties of the system. The dynamical behaviors characterized by the simulation studies are the response of the circadian pacemaker to light, its rate of decay to its limit cycle, and its response to the rest-activity cycle. The static properties are phase, amplitude, and period of the intrinsic oscillator. Formal statistical methods are not routinely employed in simulation studies, and therefore the uncertainty in inferences based on the differential equation models and their sensitivity to model specification and parameter estimation error cannot be evaluated. The harmonic regression models allow formal statistical analysis of static but not dynamical features of the circadian pacemaker. The authors present a paradigm for analyzing circadian data based on the Box iterative scheme for statistical model building. The paradigm unifies the differential equation-based simulations (direct problem) and the model fitting approach using harmonic regression techniques (inverse problem) under a single schema. The framework is illustrated with the analysis of a core-temperature data series collected under a forced desynchrony protocol. The Box iterative paradigm provides a framework for systematically constructing and analyzing models of circadian data.     

Amplification, mutation and selection of catalytic RNA

RNA, by virtue of its genotypic and phenotypic properties, is a suitable substrate for molecular evolution in the laboratory. We have developed techniques for the rapid amplification, mutation and selection of catalytic RNA. By combining these techniques in an iterative fashion, we are attempting to construct an RNA-based evolving system. Such a system could be used to explore the catalytic potential of RNA.     

Towards Prediction of Metabolic Products of Polyketide Synthases: An In Silico Analysis

Sequence data arising from an increasing number of partial and complete genome projects is revealing the presence of the polyketide synthase (PKS) family of genes not only in microbes and fungi but also in plants and other eukaryotes. PKSs are huge multifunctional megasynthases that use a variety of biosynthetic paradigms to generate enormously diverse arrays of polyketide products that posses several pharmaceutically important properties. The remarkable conservation of these gene clusters across organisms offers abundant scope for obtaining novel insights into PKS biosynthetic code by computational analysis. We have carried out a comprehensive in silico analysis of modular and iterative gene clusters to test whether chemical structures of the secondary metabolites can be predicted from PKS protein sequences. Here, we report the success of our method and demonstrate the feasibility of deciphering the putative metabolic products of uncharacterized PKS clusters found in newly sequenced genomes. Profile Hidden Markov Model analysis has revealed distinct sequence features that can distinguish modular PKS proteins from their iterative counterparts. For iterative PKS proteins, structural models of iterative ketosynthase (KS) domains have revealed novel correlations between the size of the polyketide products and volume of the active site pocket. Furthermore, we have identified key residues in the substrate binding pocket that control the number of chain extensions in iterative PKSs. For modular PKS proteins, we describe for the first time an automated method based on crucial intermolecular contacts that can distinguish the correct biosynthetic order of substrate channeling from a large number of non-cognate combinatorial possibilities. Taken together, our in silico analysis provides valuable clues for formulating rules for predicting polyketide products of iterative as well as modular PKS clusters. These results have promising potential for discovery of novel natural products by genome mining and rational design of novel natural products.     

Bias-reduced estimators of conditional odds ratios in matched case-control studies with unmatched confounding

We study bias-reduced estimators of exponentially transformed parameters in general linear models (GLMs) and show how they can be used to obtain bias-reduced conditional (or unconditional) odds ratios in matched case-control studies. Two options are considered and compared: the explicit approach and the implicit approach. The implicit approach is based on the modified score function where bias-reduced estimates are obtained by using iterative procedures to solve the modified score equations. The explicit approach is shown to be a one-step approximation of this iterative procedure. To apply these approaches for the conditional analysis of matched case-control studies, with potentially unmatched confounding and with several exposures, we utilize the relation between the conditional likelihood and the likelihood of the unconditional logit binomial GLM for matched pairs and Cox partial likelihood for matched sets with appropriately setup data. The properties of the estimators are evaluated by using a large Monte Carlo simulation study and an illustration of a real dataset is shown. Researchers reporting the results on the exponentiated scale should use bias-reduced estimators since otherwise the effects can be under or overestimated, where the magnitude of the bias is especially large in studies with smaller sample sizes.     

Efficient inference for random-coefficient growth curve models with unbalanced data

Growth and dose-response curve studies often result in incomplete or unbalanced data. Random-effects models together with a variety of computer-intensive iterative techniques have been suggested for the analysis of such data. This paper is concerned with a noniterative method for estimating and comparing location parameters in random-coefficient growth curve models. Consistent and asymptotically efficient estimators of the location parameters are obtained using estimated generalized least squares. Two criteria for testing multivariate general linear hypotheses are introduced and their asymptotic properties are investigated. The results are applied to clinical data obtained on the blood ultrafiltration performance of hemodialyzers used in the treatment of patients with end-stage renal disease.     

Systems biotechnology for strain improvement

Various high-throughput experimental techniques are routinely used for generating large amounts of omics data. In parallel, in silico modelling and simulation approaches are being developed for quantitatively analyzing cellular metabolism at the systems level. Thus informative high-throughput analysis and predictive computational modelling or simulation can be combined to generate new knowledge through iterative modification of an in silico model and experimental design. On the basis of such global cellular information we can design cells that have improved metabolic properties for industrial applications. This article highlights the recent developments in these systems approaches, which we call systems biotechnology, and discusses future prospects.     

Mathematical model of the male urinary tract

The paper presents a simplified (but not trivial) mathematical model of the interaction between the urine flow and the male urethra and bladder, respectively. Urine is assumed to be a Newtonian fluid. The flow is considered to be non-stationary, isothermal and turbulent. The urethra and bladder wall, featuring elastic properties, experience large displacements and strains. The dynamic forces are included in the urethra wall motion. When fully extended the urethra attains the shape of an axisymetric tube. An iterative method based on the uncoupled approach is developed.     

Buckley-James-type estimator with right-censored and length-biased data

We present a natural generalization of the Buckley-James-type estimator for traditional survival data to right-censored length-biased data under the accelerated failure time (AFT) model. Length-biased data are often encountered in prevalent cohort studies and cancer screening trials. Informative right censoring induced by length-biased sampling creates additional challenges in modeling the effects of risk factors on the unbiased failure times for the target population. In this article, we evaluate covariate effects on the failure times of the target population under the AFT model given the observed length-biased data. We construct a Buckley-James-type estimating equation, develop an iterative computing algorithm, and establish the asymptotic properties of the estimators. We assess the finite-sample properties of the proposed estimators against the estimators obtained from the existing methods. Data from a prevalent cohort study of patients with dementia are used to illustrate the proposed methodology.     

Computational Algorithm for Least Squares Estimation of Parameters in Compartmental Analysis

This paper presents a new computational algorithm for the estimation of the parameters in multi-compartmental processes. By assuming the initial state of compartmental process known, the Newton-Raphson iterative process is vised to obtain weighted least squares estimates. The estimation procedure considers broad class of structural properties (defined in the sequel) of compartmental models, such as open-closed processes, cyclic pathways, conservative processes, connectivity etc. A computer program, which includes these structural properties is supplied. Two examples of simulated processes illustrate the estimation procedure.     

On the shapes of leaves

The properties of a function G(x, y) of 2-dimensional Cartesian coordinates x, y can be used to obtain complex shapes through a nonlinear iterative procedure. It is conjectured that at least some biological shapes are determined by this procedure, and those of leaves are considered as a test of the hypothesis. It is shown that this procedure will generate the shapes of even very complicated leaves such as those of the holly tree to a considerable degree of accuracy. Certain issues of evolutionary biology appear in our view in a clearer light according to this procedure, and these are discussed towards the end of the paper. © 1994 Wiley-Liss, Inc.     

A new algorithm for voltage clamp by iteration: A learning control of a nonlinear neuronal system

Voltage-clamp of excitable membrane allows the measurement of membrane currents associated with electrical potential changes across the membrane. However, it has been impossible in practice to apply the conventional analog feedback voltageclamp circuits to single electrode voltage clamping in central neurons. The reason for this is that the feedback system becomes unstable because of the positive feedback required for compensation of capacitative loss through the wall of the microelectrode. Park et al. (1981) proposed a new iterative technique to solve this problem. It requires that the potential to be clamped repeats itself with little or no change. The amount of current needed to clamp the membrane potential is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Since the feedback loop is open in real time, the system has great stability, and this advantage can be exploited in single electrode preparations. The computation algorithm which calculates the current waveform based on the voltage deviation during the last trial is the central part of the iterative voltage-clamp system. In this paper, we propose a new algorithm, which has several theoretical and practical advantages over the original one proposed by Park et al. First, two parameters used in the new algorithm are predetermined by a current-clamp experiment. Second, the speed of convergence of the new algorithm is faster than that of the Park's original algorithm. This was shown by computer simulation of iterative voltage clamp of artificial membrane following Hodgkin-Huxley equations for squid axon membrane and Rall's compartment model for a neuron with dendrites. Finally, we offer proof that the new algorithm is certain to converge for the general cases of voltage-clamp experiments with active membrane properties, synaptic membranes, etc. Consequently, the new algorithm for iterative voltage clamp is very suitable for single electrode voltage clamp in the central neurons. The new algorithm has been successfully applied to voltage-clamp experiments on rubrospinal neurons of cats (Tsukahara, Murakami, Kawato, Oda, and Etoh, in preparation).     

State of the art and challenges of time-of-flight PET

After a brief review of the history of time-of-flight (TOF) positron emission tomography (PET) instrumentation from the 1980s to present, the principles of TOF PET are introduced, the concept of time resolution and its effect on TOF gain in signal-to-noise ratio (SNR) are discussed. The factors influencing the time resolution of a TOF PET scanner are presented, with focus on the intrinsic properties of scintillators of particular interest for TOF PET. Finally, some open issues, challenges and achievements of today's TOF PET reconstruction are reviewed: the structure of the data organization, the choice of analytical or iterative method, the recent experimental assessment of TOF image quality, and the most promising applications of TOF PET.     

Probing the SELEX process with next-generation sequencing

Background

SELEX is an iterative process in which highly diverse synthetic nucleic acid libraries are selected over many rounds to finally identify aptamers with desired properties. However, little is understood as how binders are enriched during the selection course. Next-generation sequencing offers the opportunity to open the black box and observe a large part of the population dynamics during the selection process.

Methodology

We have performed a semi-automated SELEX procedure on the model target streptavidin starting with a synthetic DNA oligonucleotide library and compared results obtained by the conventional analysis via cloning and Sanger sequencing with next-generation sequencing. In order to follow the population dynamics during the selection, pools from all selection rounds were barcoded and sequenced in parallel.

Conclusions

High affinity aptamers can be readily identified simply by copy number enrichment in the first selection rounds. Based on our results, we suggest a new selection scheme that avoids a high number of iterative selection rounds while reducing time, PCR bias, and artifacts.     

Statistical Analysis of Nonrectangular Family Data

MINQUE (Minimum Norm Quadratic Unbiased Estimators) theory is applied to the problem of estimation of variance components in family data (siblings) with variable family size. Using this approach, the traditional iterative maximum likelihood estimators are shown to be asymptotically normal, even though the data come from non-identical parent distributions. Asymptotic expressions are also obtained for the variance of the MINQUE estimators which hold even if the data are decidedly non-normal (e.g. a mixture of normals). In the case of normal data, exact small-sample variance estimates are derived. Simulations demonstrate the fast rate of convergence to asymptotic properties as the number of families increases. These desirable qualities suggest that the easy to compute MINQUE class of estimators may provide a useful alternative method for modelling familial aggregation.     

A negative binomial model for sampling mosquitoes in a malaria survey

Sampling models are investigated for counts of mosquitoes from a malaria field survey conducted by the World Health Organization in Nigeria. The data can be described by a negative binomial model for two-way classified counted data, where the cell means are constrained to satisfy row-by-column independence and the parameter k is constant across rows. An algorithm, based on iterative proportional fitting, is devised for finding maximum likelihood estimates. Sampling properties of the estimates and likelihood-ratio statistics for the small sample sizes of the data are investigated by Monte Carlo experiments. The WHO reported an observation that the relative efficiencies of four trapping methods vary over time. Out of eight villages in the survey area, this observation is found to be true in only the one village that is near a swamp.     

Monotonicity and performance evaluation: applications to high speed and mobile networks

We illustrate through examples how monotonicity may help for performance evaluation of networks. We consider two different applications of stochastic monotonicity in performance evaluation. In the first one, we assume that a Markov chain of the model depends on a parameter that can be estimated only up to a certain level and we have only an interval that contains the exact value of the parameter. Instead of taking an approximated value for the unknown parameter, we show how we can use the monotonicity properties of the Markov chain to take into account the error bound from the measurements. In the second application, we consider a well known approximation method: the decomposition into Markovian submodels. In such an approach, models of complex networks or other systems are decomposed into Markovian submodels whose results are then used as parameters for the next submodel in an iterative computation. One obtains a fixed point system which is solved numerically. In general, we have neither an existence proof of the solution of the fixed point system nor a convergence proof of the iterative algorithm. Here we show how stochastic monotonicity can be used to answer these questions and provide, to some extent, the theoretical foundations for this approach. Furthermore, monotonicity properties can also help to derive more efficient algorithms to solve fixed point systems.     

An Approximate EM Algorithm for Nonlinear Mixed Effects Models

In this article, we construct an approximate EM algorithm to estimate the parameters of a nonlinear mixed effects model. The iterative procedure can be viewed as an iterative method of moments procedure for estimating the variance components and an iterative reweighted least squares estimates for estimating the fixed effects. Therefore, it is valid without the normality assumptions on the random components. A computationally simple method of moments estimates of the model parameters are used as the starting values for our iterative procedure. A simulation study was conducted to compare the performances of the proposed procedure with the procedure proposed by Lindstrom and Bates (1990) for some normal models and nonnormal models.     

New insights into the formation of fungal aromatic polyketides

Fungal aromatic polyketides constitute a large family of bioactive natural products and are synthesized by the non-reducing group of iterative polyketide synthases (PKSs). Their diverse structures arise from selective enzymatic modifications of reactive, enzyme-bound poly-β-keto intermediates. How iterative PKSs control starter unit selection, polyketide chain initiation and elongation, intermediate folding and cyclization, selective redox or modification reactions during assembly, and product release are central mechanistic questions underlying iterative catalysis. This Review highlights recent insights into these questions, with a particular focus on the biosynthetic programming of fungal aromatic polyketides, and draws comparisons with the allied biosynthetic processes in bacteria.