Adequacy of numerical taxonomic methods: Further experiments using simulated data

The adequacy of various phenetic and phylogenetic estimation methods was evaluated using simulated data sets. Two parsimony programs were used to construct maximum parsimony trees (WAGNER 78 and HENNIG 86). The CAFCA program was used to perform group-compatibility analysis. Four UPGMA clustering strategies were employed. The simulation model GENESIS was used to generate data sets under different evolutionary conditions. The effects of input parameters and tree properties on the accuracy of the estimated trees were evaluated. UPGMA based on product moment correlations of unstandardized characters appeared to perform best, under all evolutionary conditions tested. The effect of input parameters on the accuracy was not very significant. Among the tree statistics the stemminess of the true tree appeared to be the most important estimator of accuracy.     

Weighted analysis of microarray gene expression using maximum-likelihood

MOTIVATION: The numerical values of gene expression measured using microarrays are usually presented to the biological end-user as summary statistics of spot pixel data, such as the spot mean, median and mode. Much of the subsequent data analysis reported in the literature, however, uses only one of these spot statistics. This results in sub-optimal estimates of gene expression levels and a need for improvement in quantitative spot variation surveillance. RESULTS: This paper develops a maximum-likelihood method for estimating gene expression using spot mean, variance and pixel number values available from typical microarray scanners. It employs a hierarchical model of variation between and within microarray spots. The hierarchical maximum-likelihood estimate (MLE) is shown to be a more efficient estimator of the mean than the 'conventional' estimate using solely the spot mean values (i.e. without spot variance data). Furthermore, under the assumptions of our model, the spot mean and spot variance are shown to be sufficient statistics that do not require the use of all pixel data.The hierarchical MLE method is applied to data from both Monte Carlo (MC) simulations and a two-channel dye-swapped spotted microarray experiment. The MC simulations show that the hierarchical MLE method leads to improved detection of differential gene expression particularly when 'outlier' spots are present on the arrays. Compared with the conventional method, the MLE method applied to data from the microarray experiment leads to an increase in the number of differentially expressed genes detected for low cut-off P-values of interest.     

Simulation of the three-dimensional distribution of the red:far-red ratio within crop canopies

It is widely recognized that the red:far-red ratio (zeta) acts as a signal that triggers plant morphogenesis. New insights into photomorphogenesis have been gained through experiments in controlled environments. Extrapolation of such results to field conditions requires characterization of the zeta signal perceived by plant organs within canopies. This paper presents a modeling approach to characterize this signal. A wheat (Triticum aestivum) architectural model was coupled with a three-dimensional light model estimating the irradiances of virtual sensors. Architectural parameters and zeta values were measured on two contrasting spring wheat canopies under outdoor conditions. Light simulations were compared with measurements, and an analysis of sensitivity to measurement conditions was carried out. The model results agreed well with measurements and previously published data. The sensitivity analysis showed that zeta strongly depends on canopy development as well as on sky conditions, sensor orientation, and sensor field of view. This paper shows that modeling enables investigation of zeta distribution in a canopy over space and time. It also shows that the characterization of light quality strongly depends on measurement conditions, and that any discrepancies in results are likely attributable to different experimental set-ups. The usefulness of this modeling approach for crop photomorphogenesis studies is discussed.     

A population‐averaged approach to diagnostic test meta‐analysis

The meta‐analysis of diagnostic accuracy studies is often of interest in screening programs for many diseases. The typical summary statistics for studies chosen for a diagnostic accuracy meta‐analysis are often two dimensional: sensitivities and specificities. The common statistical analysis approach for the meta‐analysis of diagnostic studies is based on the bivariate generalized linear‐mixed model (BGLMM), which has study‐specific interpretations. In this article, we present a population‐averaged (PA) model using generalized estimating equations (GEE) for making inference on mean specificity and sensitivity of a diagnostic test in the population represented by the meta‐analytic studies. We also derive the marginalized counterparts of the regression parameters from the BGLMM. We illustrate the proposed PA approach through two dataset examples and compare performance of estimators of the marginal regression parameters from the PA model with those of the marginalized regression parameters from the BGLMM through Monte Carlo simulation studies. Overall, both marginalized BGLMM and GEE with sandwich standard errors maintained nominal 95% confidence interval coverage levels for mean specificity and mean sensitivity in meta‐analysis of 25 of more studies even under misspecification of the covariance structure of the bivariate positive test counts for diseased and nondiseased subjects.     

Parameter estimation and sensitivity analysis for batch fermentation of recombinant cells

Summary An interactive scheme for estimating parameters in an unstructured model of a recombinant fermentation process is presented. Sensitivity analysis is simultaneously evaluated in this approach so that the instantaneous influence of parameters on state variables can be inspected. The predicted profiles of fermentation by both the model and the sensitivity analysis based on ±50% variations of the initial concentration of glucose fit the experimental observations.     

A new u-statistic with superior design sensitivity in matched observational studies

Summary In an observational or nonrandomized study of treatment effects, a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naïve analysis that presumes adjustments for observed covariates suffice to remove all bias. The power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude; in particular, if this specified magnitude is “no departure” then this is the same as the power of a randomization test in a randomized experiment. A new family of u‐statistics is proposed that includes Wilcoxon's signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study. Wilcoxon's statistic has high power to detect small effects in large randomized experiments—that is, it often has good Pitman efficiency—but small effects are invariably sensitive to small unobserved biases. Members of this family of u‐statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis. For example, in one situation with 250 pair differences that are Normal with expectation 1/2 and variance 1, the power of a sensitivity analysis that uses Wilcoxon's statistic is 0.08 while the power of another member of the family of u‐statistics is 0.66. The topic is examined by performing a sensitivity analysis in three observational studies, using an asymptotic measure called the design sensitivity, and by simulating power in finite samples. The three examples are drawn from epidemiology, clinical medicine, and genetic toxicology.     

Robust genomic control for association studies

Population-based case-control studies are a useful method to test for a genetic association between a trait and a marker. However, the analysis of the resulting data can be affected by population stratification or cryptic relatedness, which may inflate the variance of the usual statistics, resulting in a higher-than-nominal rate of false-positive results. One approach to preserving the nominal type I error is to apply genomic control, which adjusts the variance of the Cochran-Armitage trend test by calculating the statistic on data from null loci. This enables one to estimate any additional variance in the null distribution of statistics. When the underlying genetic model (e.g., recessive, additive, or dominant) is known, genomic control can be applied to the corresponding optimal trend tests. In practice, however, the mode of inheritance is unknown. The genotype-based chi (2) test for a general association between the trait and the marker does not depend on the underlying genetic model. Since this general association test has 2 degrees of freedom (df), the existing formulas for estimating the variance factor by use of genomic control are not directly applicable. By expressing the general association test in terms of two Cochran-Armitage trend tests, one can apply genomic control to each of the two trend tests separately, thereby adjusting the chi (2) statistic. The properties of this robust genomic control test with 2 df are examined by simulation. This genomic control-adjusted 2-df test has control of type I error and achieves reasonable power, relative to the optimal tests for each model.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

New inferences from tree shape: numbers of missing taxa and population growth rates

The relative positions of branching events in a phylogeny contain information about evolutionary and population dynamic processes. We provide new summary statistics of branching event times and describe how these statistics can be used to infer rates of species diversification from interspecies trees or rates of population growth from intraspecies trees. We also introduce a phylogenetic method for estimating the level of taxon sampling in a clade. Different evolutionary models and different sampling regimes can produce similar patterns of branching events, so it is important to consider explicitly the model assumptions involved when making evolutionary inferences. Results of an analysis of the phylogeny of the mosquito-borne flaviviruses suggest that there could be several thousand currently unidentified viruses in this clade.     

On the stability of the high-latitude climate-vegetation system in a coupled atmosphere-biosphere model

In order to investigate the hypothesis that the Earth's climate and vegetation patterns may have more than one basic state, we use the fully coupled GENESIS-IBIS model. GENESIS is an atmospheric general circulation model. IBIS is a dynamic global vegetation model that integrates biophysical, physiological, and ecological processes. GENESIS and IBIS are coupled by way of a common land surface interface to allow for the full and transient interaction between changes in the vegetation structure and changes in the general circulation of the atmosphere. We examine two modern climate simulations of the coupled model initialized with two different initial conditions. In one case, we initialize the model vegetation cover with the modern observed distribution of vegetation. In the other case, we initialize the vegetation cover with evergreen boreal forests extending to the Arctic coast, replacing high-latitude tundra. We interpret the coupled model's behaviour using a conceptual model for multistability and demonstrate that in both simulations the climate-vegetation system converges to the same equilibrium state. In the present climate, feedbacks between land, ocean, sea ice, and the atmosphere do not result in the warming required to support an expanded boreal forest.     

MCMC estimation of Markov models for ion channels

Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data. In this article, different approaches for the MCMC sampling of Markov models are combined. This method, new to our knowledge, detects overparameterizations and gives more accurate results than existing MCMC methods. It shows similar performance as QuB-MIL, which indicates that it also compares well with maximum likelihood estimators. Data collected from an inositol trisphosphate receptor is used to demonstrate how the best model for a given data set can be found in practice.     

Role of CAMKII in reinforcement learning: a computational model of glutamate and dopamine signaling pathways

Timely release of dopamine (DA) at the striatum seems to be important for reinforcement learning (RL) mediated by the basal ganglia. Houk et al. (in: Houk et al (eds) Models of information processing in the basal ganglia, (1995) proposed a cellular signaling pathway model to characterize the interaction between DA and glutamate pathways that have a role in RL. The model simulation results, using GENESIS KINETIKIT simulator, point out that there is not only prolongation of duration as proposed by Houk et al. (1995), but also an enhancement in the amplitude of autophosphorylation of CaMKII. Further, the autophosphorylated form of CaMKII may form a basis for the “eligibility trace” condition required in RL. This simulation study is the first of its kind to support the comprehensive theoretical proposal of Houk et al. (1995).     

A NARX modeling-based approach for evaluation of insulin sensitivity

Evaluation of insulin sensitivity is of prime importance in the clinical investigation of glucose related diseases. This paper deals with a novel model-based technique for the evaluation of an index for insulin sensitivity. A set of nonlinear autoregressive models are identified from the clinical test data of normal subjects. The two-stage identification procedure involves proper structure selection for approximating the input–output data followed by estimating the parameters of the polynomial model. The models obtained are analyzed to derive an index for insulin sensitivity by determining the effect of insulin on glucose utilization. A median bootstraped correlation (sampling with replacement) of 0.97 with 90% confidence interval of [0.92 0.98], is obtained between the indexes of the proposed model and the widely used minimal model. The proposed model is able to achieve a good fitting performance on the validation dataset. The results also suggest that for representing the dynamics of insulin action on glucose disposal, the proposed model overcomes some of the well known limitations of the minimal model, and thus gives a better representation of insulin sensitivity.     

Estimating Diagnostic Accuracy of Raters Without a Gold Standard by Exploiting a Group of Experts

Summary In diagnostic medicine, estimating the diagnostic accuracy of a group of raters or medical tests relative to the gold standard is often the primary goal. When a gold standard is absent, latent class models where the unknown gold standard test is treated as a latent variable are often used. However, these models have been criticized in the literature from both a conceptual and a robustness perspective. As an alternative, we propose an approach where we exploit an imperfect reference standard with unknown diagnostic accuracy and conduct sensitivity analysis by varying this accuracy over scientifically reasonable ranges. In this article, a latent class model with crossed random effects is proposed for estimating the diagnostic accuracy of regional obstetrics and gynaecological (OB/GYN) physicians in diagnosing endometriosis. To avoid the pitfalls of models without a gold standard, we exploit the diagnostic results of a group of OB/GYN physicians with an international reputation for the diagnosis of endometriosis. We construct an ordinal reference standard based on the discordance among these international experts and propose a mechanism for conducting sensitivity analysis relative to the unknown diagnostic accuracy among them. A Monte Carlo EM algorithm is proposed for parameter estimation and a BIC‐type model selection procedure is presented. Through simulations and data analysis we show that this new approach provides a useful alternative to traditional latent class modeling approaches used in this setting.     

A Riemannian manifold analysis of endothelial cell monolayer impedance parameter precision

Endothelial cell adhesion and barrier function play a critical role in many biological and pathophysiological processes. The decomposition of endothelial cell adhesion and barrier function into cell–cell and cell–matrix components using frequency dependent cellular micro-impedance measurements has, therefore, received widespread application. Few if any studies, however, have examined the precision of these model parameters. This study presents a parameter sensitivity analysis of a representative cellular barrier function model using a concise geometric formulation that includes instrumental data acquisition settings. Both model state dependence and instrumental noise distributions are accounted for within the framework of Riemannian manifold theory. Experimentally acquired microimpedance measurements of attached endothelial cells define the model state domain, while experimentally measured noise statistics define the data space Riemannian metric based on the Fisher information matrix. The results of this analysis show that the sensitivity of cell–cell and cell–matrix impedance components are highly model state dependent and several well defined regions of low precision exist. The results of this study further indicate that membrane resistive components can significantly reduce the precision of the remaining parameters in these models. This work was supported by a National Science Foundation CAREER Award (AE), BES-0238905, and in part by the American Heart Association under Grant 0265029B (AE).     

A Method for Estimating the Predictive Power in a Model of a Biological System with Low Sensitivity to Parameters

The ambiguity of parameter estimates for the model of a biological system may be due to low sensitivity of the model to perturbations of input data (parameters), which mathematically reflects biological mechanisms of robustness. We developed a novel method for estimating the predictive power of a model with the ambiguity of parameter estimates. The predictions are understood as a correct reproduction of the system behavior by the model when changing input data and parameters. The method is based on the relative sensitivity analysis of the fitted model to stiff parameters of the predicted model. The application principles of our approach are demonstrated using a model for the formation of the mRNA expression pattern of the hb gene in the Drosophila embryo and its ability to predict the hb pattern in the Kr null mutant. The nonlinear nature of the system is simulated by a saturating sigmoid function, which is the cause of low sensitivity. Our method allows us to estimate the predictive power of the model and uncover the causes of poor predictions, as well as choose the relevant level of the model detail in terms of predictions.     

Drugs, sex and HIV: a mathematical model for New York City.

A data-based mathematical model was formulated to assess the epidemiological consequences of heterosexual, intravenous drug use (IVDU) and perinatal transmission in New York City (NYC). The model was analysed to clarify the relationship between heterosexual and IVDU transmission and to provide qualitative and quantitative insights into the HIV epidemic in NYC. The results demonstrated the significance of the dynamic interaction of heterosexual and IVDU transmission. Scenario analysis of the model was used to suggest a new explanation for the stabilization of the seroprevalence level that has been observed in the NYC IVDU community; the proposed explanation does not rely upon any IVDU or sexual behavioural changes. Gender-specific risks of heterosexual transmission in IVDUs were also explored by scenario analysis. The results showed that the effect of the heterosexual transmission risk factor on increasing the risk of HIV infection depends upon the level of IVDU. The model was used to predict future numbers of adult and pediatric AIDS cases; a sensitivity analysis of the model showed that the confidence intervals on these prediction estimates were extremely wide. This prediction variability was due to the uncertainty in estimating the values of the models' thirty variables (twenty biological-behavioural transmission parameters and the initial sizes of ten subgroups). However, the sensitivity analysis revealed that only a few key variables were significant in contributing to the AIDS case prediction variability; partial rank correlation coefficients were calculated and used to identify and to rank the importance of these key variables. The results suggest that long-term precise estimates of the future number of AIDS cases will only be possible once the values of these key variables have been evaluated accurately.     

Imputation approaches for estimating diagnostic accuracy for multiple tests from partially verified designs

Interest often focuses on estimating sensitivity and specificity of a group of raters or a set of new diagnostic tests in situations in which gold standard evaluation is expensive or invasive. Various authors have proposed semilatent class modeling approaches for estimating diagnostic accuracy in this situation. This article presents imputation approaches for this problem. I show how imputation provides a simpler way of performing diagnostic accuracy and prevalence estimation than the use of semilatent modeling. Furthermore, the imputation approach is more robust to modeling assumptions and, in general, there is only a moderate efficiency loss relative to a correctly specified semilatent class model. I apply imputation to a study designed to estimate the diagnostic accuracy of digital radiography for gastric cancer. The feasibility and robustness of imputation is illustrated with analysis, asymptotic results, and simulations.