A Highly Accurate Pixel-Based FRAP Model Based on Spectral-Domain Numerical Methods

We introduce a new, to our knowledge, numerical model based on spectral methods for analysis of fluorescence recovery after photobleaching data. The model covers pure diffusion and diffusion and binding (reaction-diffusion) with immobile binding sites, as well as arbitrary bleach region shapes. Fitting of the model is supported using both conventional recovery-curve-based estimation and pixel-based estimation, in which all individual pixels in the data are utilized. The model explicitly accounts for multiple bleach frames, diffusion (and binding) during bleaching, and bleaching during imaging. To our knowledge, no other fluorescence recovery after photobleaching framework incorporates all these model features and estimation methods. We thoroughly validate the model by comparison to stochastic simulations of particle dynamics and find it to be highly accurate. We perform simulation studies to compare recovery-curve-based estimation and pixel-based estimation in realistic settings and show that pixel-based estimation is the better method for parameter estimation as well as for distinguishing pure diffusion from diffusion and binding. We show that accounting for multiple bleach frames is important and that the effect of neglecting this is qualitatively different for the two estimation methods. We perform a simple experimental validation showing that pixel-based estimation provides better agreement with literature values than recovery-curve-based estimation and that accounting for multiple bleach frames improves the result. Further, the software developed in this work is freely available online.     

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.     

Hyperparameter estimation using stochastic approximation with application to population pharmacokinetics

A stochastic approximation algorithm is proposed for recursive estimation of the hyperparameters characterizing, in a population, the probability density function of the parameters of a statistical model. For a given population model defined by a parametric model of a biological process, an error model, and a class of densities on the set of the individual parameters, this algorithm provides a sequence of estimates from a sequence of individuals' observation vectors. Convergence conditions are verified for a class of population models including usual pharmacokinetic applications. This method is implemented for estimation of pharmacokinetic population parameters from drug multiple-dosing data. Its estimation capabilities are evaluated and compared to a classical method in population pharmacokinetics, the first-order method (NONMEM), on simulated data.     

Estimation of variance components of quantitative traits in inbred populations

Use of variance-component estimation for mapping of quantitative-trait loci in humans is a subject of great current interest. When only trait values, not genotypic information, are considered, variance-component estimation can also be used to estimate heritability of a quantitative trait. Inbred pedigrees present special challenges for variance-component estimation. First, there are more variance components to be estimated in the inbred case, even for a relatively simple model including additive, dominance, and environmental effects. Second, more identity coefficients need to be calculated from an inbred pedigree in order to perform the estimation, and these are computationally more difficult to obtain in the inbred than in the outbred case. As a result, inbreeding effects have generally been ignored in practice. We describe here the calculation of identity coefficients and estimation of variance components of quantitative traits in large inbred pedigrees, using the example of HDL in the Hutterites. We use a multivariate normal model for the genetic effects, extending the central-limit theorem of Lange to allow for both inbreeding and dominance under the assumptions of our variance-component model. We use simulated examples to give an indication of under what conditions one has the power to detect the additional variance components and to examine their impact on variance-component estimation. We discuss the implications for mapping and heritability estimation by use of variance components in inbred populations.     

Mixed-model analysis of a censored normal distribution with reference to animal breeding

A mixed-model procedure for analysis of censored data assuming a multivariate normal distribution is described. A Bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left-censored. The procedure can be extended to right- and two-tailed censoring. The model employed is a generalized linear model, and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models. Estimates of variance components are obtained using expressions similar to those employed in the EM algorithm for restricted maximum likelihood (REML) estimation under normality.     

The equilibrium assumption in estimating the parameters of metapopulation models

1.  The construction of a predictive metapopulation model includes three steps: the choice of factors affecting metapopulation dynamics, the choice of model structure, and finally parameter estimation and model testing.
2.  Unless the assumption is made that the metapopulation is at stochastic quasi-equilibrium and unless the method of parameter estimation of model parameters uses that assumption, estimates from a limited amount of data will usually predict a trend in metapopulation size.
3.  This implicit estimation of a trend occurs because extinction-colonization stochasticity, possibly amplified by regional stochasticity, leads to unequal numbers of observed extinction and colonization events during a short study period.
4.  Metapopulation models, such as those based on the logistic regression model, that rely on observed population turnover events in parameter estimation are sensitive to the implicit estimation of a trend.
5.  A new parameter estimation method, based on Monte Carlo inference for statistically implicit models, allows an explicit decision about whether metapopulation quasi-stability is assumed or not.
6. Our confidence in metapopulation model parameter estimates that have been produced from only a few years of data is decreased by the need to know before parameter estimation whether the metapopulation is in quasi-stable state or not.
7. The choice of whether metapopulation stability is assumed or not in parameter estimation should be done consciously. Typical data sets cover only a few years and rarely allow a statistical test of a possible trend. While making the decision about stability one should consider any information about the landscape history and species and metapopulation characteristics.     

A semiparametric odds ratio model for measuring association

We propose a semiparametric odds ratio model to measure the association between two variables taking discrete values, continuous values, or a mixture of both. Methods for estimation and inference with varying degrees of robustness to model assumptions are studied. Semiparametric efficient estimation and inference procedures are also considered. The estimation methods are compared in a simulation study and applied to the study of associations among genital tract bacterial counts in HIV infected women.     

Use of the Multinomial Dirichlet Model for Analysis of Subdivided Genetic Populations

The distribution found by compounding the multinomial distribution with the Dirichlet distribution has been suggested as a basis for the estimation of parameters in subdivided populations, in particular of the "correlation between genotypes" within subpopulations. It is shown that the estimators deriving from these procedures perform poorly when the data are generated by the classical Wright drift model of subdivided populations. This conclusion suggests that the compound distribution estimation approach does not provide a good estimation procedure for real populations which are reasonably described by the Wright model.     

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

MOTIVATION: Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. RESULTS: In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing.     

Estimation of Respiratory Nasal Pressure and Flow Rate Signals Using Different Respiratory Sound Features

BackgroundRespiratory sounds are associated with the flow rate, nasal flow pressure, and physical characteristics of airways. In this study, we aimed to develop the flow rate and nasal flow pressure estimation models for the clinical application, and find out the optimal feature set for estimation to achieve the optimal model performance.MethodsRespiratory sounds and flow rate were acquired from nine healthy volunteers. Respiratory sounds and nasal flow pressure were acquired from twenty-three healthy volunteers. Four types of respiratory sound features were extracted for flow rate and nasal flow pressure estimation using different estimation models. Effects of estimations using these features were evaluated using Bland-Altman analysis, estimation error, and respiratory sound feature calculation time. Besides, expiratory and inspiratory phases divided estimation errors were compared with united estimation errors.ResultsThe personalized logarithm model was selected as the optimal flow rate estimation model. Respiratory nasal flow pressure estimation based on this model was also performed. For the four different respiratory sound features, there is no statistically significant difference in flow rate and pressure estimation errors. LogEnvelope was, therefore, chosen as the optimal feature because of the lowest computational cost. In addition, for any type of respiratory sound feature, no statistically significant difference was observed between divided and united estimation errors (flow rate and pressure).ConclusionRespiratory flow rate and nasal flow pressure can be estimated accurately using respiratory sound features. Expiratory and inspiratory phases united estimation using respiratory sounds is a more reasonable estimation method than divided estimation. LogEnvelope can be used for this united respiratory flow rate and nasal flow pressure estimation with minimum computational cost and acceptable estimation error.     

Quantile regression models with multivariate failure time data

As an alternative to the mean regression model, the quantile regression model has been studied extensively with independent failure time data. However, due to natural or artificial clustering, it is common to encounter multivariate failure time data in biomedical research where the intracluster correlation needs to be accounted for appropriately. For right-censored correlated survival data, we investigate the quantile regression model and adapt an estimating equation approach for parameter estimation under the working independence assumption, as well as a weighted version for enhancing the efficiency. We show that the parameter estimates are consistent and asymptotically follow normal distributions. The variance estimation using asymptotic approximation involves nonparametric functional density estimation. We employ the bootstrap and perturbation resampling methods for the estimation of the variance-covariance matrix. We examine the proposed method for finite sample sizes through simulation studies, and illustrate it with data from a clinical trial on otitis media.     

Estimation of the probability parameters for a model of radiation inactivation of cells from experimental survival curves

A simple method is proposed for estimation of a and b parameters of the probability model of radiation inactivation of cells with a reference to the experimental survival curves. The examples of such an estimation for bacteria, yeast, and mammalian cells are discussed.     

Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process

Online estimation of unknown state variables is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The extended Kalman filter (EKF) algorithm has been widely applied for wastewater treatment processes. However, the series approximations in the EKF algorithm are not valid, because biological wastewater treatment processes are highly nonlinear with a time-varying characteristic. This work proposes an alternative online estimation approach using the sequential Monte Carlo (SMC) methods for recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. SMC is an algorithm that makes it possible to recursively construct the posterior probability density of the state variables, with respect to all available measurements, through a random exploration of the states by entities called ‘particle’. In this work, the simplified and modified Activated Sludge Model No. 3 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic state-space model applied to the SMC method. The performance of the SMC method for online state estimation applied to a biological sequencing batch reactor with online and offline measured data is encouraging. The results indicate that the SMC method could emerge as a powerful tool for solving online state and parameter estimation problems without any model linearization or restrictive assumptions pertaining to the type of nonlinear models for biological wastewater treatment processes.     

Efficient parameter estimation for spatio-temporal models of pattern formation: case study of Drosophila melanogaster

MOTIVATION: Diffusable and non-diffusable gene products play a major role in body plan formation. A quantitative understanding of the spatio-temporal patterns formed in body plan formation, by using simulation models is an important addition to experimental observation. The inverse modelling approach consists of describing the body plan formation by a rule-based model, and fitting the model parameters to real observed data. In body plan formation, the data are usually obtained from fluorescent immunohistochemistry or in situ hybridizations. Inferring model parameters by comparing such data to those from simulation is a major computational bottleneck. An important aspect in this process is the choice of method used for parameter estimation. When no information on parameters is available, parameter estimation is mostly done by means of heuristic algorithms. RESULTS: We show that parameter estimation for pattern formation models can be efficiently performed using an evolution strategy (ES). As a case study we use a quantitative spatio-temporal model of the regulatory network for early development in Drosophila melanogaster. In order to estimate the parameters, the simulated results are compared to a time series of gene products involved in the network obtained with immunohistochemistry. We demonstrate that a (mu,lambda)-ES can be used to find good quality solutions in the parameter estimation. We also show that an ES with multiple populations is 5-140 times as fast as parallel simulated annealing for this case study, and that combining ES with a local search results in an efficient parameter estimation method.     

Estimation of protein secondary structure and error analysis from circular dichroism spectra

The estimation of protein secondary structure from circular dichroism spectra is described by a multivariate linear model with noise (Gauss-Markoff model). With this formalism the adequacy of the linear model is investigated, paying special attention to the estimation of the error in the secondary structure estimates. It is shown that the linear model is only adequate for the alpha-helix class. Since the failure of the linear model is most likely due to nonlinear effects, a locally linearized model is introduced. This model is combined with the selection of the estimate whose fractions of secondary structure summate to approximately one. Comparing the estimation from the CD spectra with the X-ray data (by using the data set of W.C. Johnson Jr., 1988, Annu. Rev. Biophys. Chem. 17, 145-166) the root mean square residuals are 0.09 (alpha-helix), 0.12 (anti-parallel beta-sheet), 0.08 (parallel beta-sheet), 0.07 (beta-turn), and 0.09 (other). These residuals are somewhat larger than the errors estimated from the locally linearized model. In addition to alpha-helix, in this model the beta-turn and "other" class are estimated adequately. But the estimation of the antiparallel and parallel beta-sheet class remains unsatisfactory. We compared the linear model and the locally linearized model with two other methods (S. W. Provencher and J. Gl?ckner, 1981, Biochemistry 20, 1085-1094; P. Manavalan and W. C. Johnson Jr., 1988, Anal. Biochem. 167, 76-85). The locally linearized model and the Provencher and Gl?ckner method provided the smallest residuals. However, an advantage of the locally linearized model is the estimation of the error in the secondary structure estimates.     

Synthesizing secondary data into survival analysis to improve estimation efficiency

The accelerated failure time (AFT) model and Cox proportional hazards (PH) model are broadly used for survival endpoints of primary interest. However, the estimation efficiency from those models can be further enhanced by incorporating the information from secondary outcomes that are increasingly available and highly correlated with primary outcomes. Those secondary outcomes could be longitudinal laboratory measures collected from doctor visits or cross-sectional disease-relevant variables, which are believed to contain extra information related to primary survival endpoints to a certain extent. In this paper, we develop a two-stage estimation framework to combine a survival model with a secondary model that contains secondary outcomes, named as the empirical-likelihood-based weighting (ELW), which comprises two weighting schemes accommodated to the AFT model (ELW-AFT) and the Cox PH model (ELW-Cox), respectively. This innovative framework is flexibly adaptive to secondary outcomes with complex data features, and it leads to more efficient parameter estimation in the survival model even if the secondary model is misspecified. Extensive simulation studies showcase more efficiency gain from ELW compared to conventional approaches, and an application in the Atherosclerosis Risk in Communities study also demonstrates the superiority of ELW by successfully detecting risk factors at the time of hospitalization for acute myocardial infarction.     

On parameter estimation for biaxial mechanical behavior of arteries

This article considers the parameter estimation of multi-fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors. First, the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model. Then, the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data balancing between variance and bias errors.     

Statistical Alignment with a Sequence Evolution Model Allowing Rate Heterogeneity along the Sequence

We present a stochastic sequence evolution model to obtain alignments and estimate mutation rates between two homologous sequences. The model allows two possible evolutionary behaviors along a DNA sequence in order to determine conserved regions and take its heterogeneity into account. In our model, the sequence is divided into slow and fast evolution regions. The boundaries between these sections are not known. It is our aim to detect them. The evolution model is based on a fragment insertion and deletion process working on fast regions only and on a substitution process working on fast and slow regions with different rates. This model induces a pair hidden Markov structure at the level of alignments, thus making efficient statistical alignment algorithms possible. We propose two complementary estimation methods, namely, a Gibbs sampler for Bayesian estimation and a stochastic version of the EM algorithm for maximum likelihood estimation. Both algorithms involve the sampling of alignments. We propose a partial alignment sampler, which is computationally less expensive than the typical whole alignment sampler. We show the convergence of the two estimation algorithms when used with this partial sampler. Our algorithms provide consistent estimates for the mutation rates and plausible alignments and sequence segmentations on both simulated and real data.     

Variable Selection for Semiparametric Mixed Models in Longitudinal Studies

Summary .  We propose a double-penalized likelihood approach for simultaneous model selection and estimation in semiparametric mixed models for longitudinal data. Two types of penalties are jointly imposed on the ordinary log-likelihood: the roughness penalty on the nonparametric baseline function and a nonconcave shrinkage penalty on linear coefficients to achieve model sparsity. Compared to existing estimation equation based approaches, our procedure provides valid inference for data with missing at random, and will be more efficient if the specified model is correct. Another advantage of the new procedure is its easy computation for both regression components and variance parameters. We show that the double-penalized problem can be conveniently reformulated into a linear mixed model framework, so that existing software can be directly used to implement our method. For the purpose of model inference, we derive both frequentist and Bayesian variance estimation for estimated parametric and nonparametric components. Simulation is used to evaluate and compare the performance of our method to the existing ones. We then apply the new method to a real data set from a lactation study.     

Multilevel models for survival analysis with random effects

A method for modeling survival data with multilevel clustering is described. The Cox partial likelihood is incorporated into the generalized linear mixed model (GLMM) methodology. Parameter estimation is achieved by maximizing a log likelihood analogous to the likelihood associated with the best linear unbiased prediction (BLUP) at the initial step of estimation and is extended to obtain residual maximum likelihood (REML) estimators of the variance component. Estimating equations for a three-level hierarchical survival model are developed in detail, and such a model is applied to analyze a set of chronic granulomatous disease (CGD) data on recurrent infections as an illustration with both hospital and patient effects being considered as random. Only the latter gives a significant contribution. A simulation study is carried out to evaluate the performance of the REML estimators. Further extension of the estimation procedure to models with an arbitrary number of levels is also discussed.