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PubMed1980

Estimation and comparison of parameters in stochastic growth models for barn owls.

Alternative methods for parameter estimation and the incorporation of stochasticity into growth models are investigated and compared to the commonly used sampling error model in which error terms are simply added-on to the integrated form of the growth equation. A process error model, in which the process of growth is assumed to have stochastic variation or error incorporated within it, was found to be more appropriate for use with nonlinear estimation procedures based on a minimization of sigma ei2. The process error model tended to minimize and/or eliminate the autocorrelation of residuals, which were characteristic of the sampling error model. These analyses further suggest that while the commonly used sampling error growth model may indeed provide unbiased parameter estimates, the estimated variances of such estimates are likely to be unwarrantedly low, thus raising questions as to the validity of any statistical comparisons based on such analyses. The procedure is illustrated with growth data from captive-reared sibling nestling barn owls, using the Richards' growth curve. These analyses suggest that both growth rate and growth form are subject to a higher degree of genetic control than is asymptotic weight which showed a greater tendency to vary according to the hatching order of the nestlings.

Age Factors↗

PubMed1996

Nonparametric expectation maximization population modeling of ganciclovir.

The use of the nonparametric expectation maximization (NPEM2) program to estimate pharmacokinetic parameters of ganciclovir in a group of patients with human immunodeficiency virus (HIV) and cytomegalovirus (CMV) infection was evaluated. A 10-point data set per patient obtained over 8 hours was analyzed. Mean pharmacokinetic parameters obtained included rate constant from the central to the peripheral compartment (KCP,3.1 hr-1), rate constant from the peripheral to the central compartment (KPC, 0.824 hr-1), slope of the volume of distribution to body weight (VS, 0.246 L/kg), and slope of clearance to creatinine clearance (Cl(cr)) and body weight (CLS,0.222L/hr/kg/100 mL/ min Cl(cr). Use of NPEM2 led to identification of a subset of patients with CMV retinitis who had a more rapid clearance of ganciclovir of 0.51 to 0.54 L/hr/kg/100 mL/min Cl(cr). Use of smaller, optimally timed samples of five, four, and three data points per patient produced mean pharmacokinetic parameter results consistent with the full ten-point data set. When Bayesian-derived parameter estimates using a five-point data set were compared with a traditional, nonlinear, least-square analysis of the entire ten-point data set, estimates of clearance were determined to be relatively unbiased and precise. The ability of NPEM2 to estimate pharmacokinetic parameters and to determine the population distribution of the parameters was demonstrated. By using points in the analysis chosen by D-optimal design theory, NPEM2 was able to give consistent parameter estimates with as few as three data points. Determination of the distribution appeared to have been dependent on the time points used, however. The approach of MAP-Bayesian analysis to derive patient-specific estimates using optimal samples and prior estimates from a previous population pharmacokinetic analysis for inclusion in subsequent pharmacodynamic analyses of drug exposure (area under the concentration-time curve) may enable development of exposure-response and exposure-toxicity relationships.

Antiviral Agents↗

PubMed1993

The importance of modeling interoccasion variability in population pharmacokinetic analyses.

Individual pharmacokinetic parameters may change randomly between study occasions. Analysis of simulated data with NONMEM shows that ignoring such interoccasion variability (IOV) may result in biased population parameter estimates. Particular parameters affected and the extent to which they are biased depend on study design and the magnitude of IOV and interindividual variability. Neglecting IOV also results in a high incidence of statistically significant spurious period effects. Perhaps most important, ignoring IOV can lead to a falsely optimistic impression of the potential value of therapeutic drug monitoring. A model incorporating IOV was developed and its performance in the presence and absence of IOV was evaluated. The IOV model performs well with respect to both model selection and population parameter estimation in all circumstances studied. Analysis of two real data examples using this model reveals significant IOV in all parameters for both drugs and supports the simulation findings for the case that IOV is ignored: predictable biases occur in parameter estimates and previously nonexistent period effects are found.

Computer Simulation↗

PubMed1994

Maximum likelihood estimation of quantitative trait loci parameters with the aid of genetic markers using a standard statistical package.

Consistent parameter estimates of quantitative trait loci linked to genetic markers can be derived by maximum likelihood methodology. For many experimental designs of interest, parameter estimates and their standard errors can be obtained by program LE of BMDP, which uses the Newton-Raphson method of iteration. Program LE was tested on data simulated for a backcross between two inbred lines. A single quantitative trait locus linked to either one or two genetic markers was simulated. Convergence was rapid, and computing and programming time were insignificant. All parameter estimates were within the expected bounds. Many different designs can be readily analyzed.

Algorithms↗

PubMed2004

Subspace-based MRS data quantitation of multiplets using prior knowledge.

Accurate quantitation of Magnetic Resonance Spectroscopy (MRS) signals is an essential step before converting the estimated signal parameters, such as frequencies, damping factors, and amplitudes, into biochemical quantities (concentration, pH). Several subspace-based parameter estimators have been developed for this task, which are efficient and accurate time-domain algorithms. However, they suffer from a serious drawback: they allow only a limited inclusion of prior knowledge which is important for accuracy and resolution. In this paper, a new method is presented: KNOB-SVD and its improved variant KNOB-TLS. KNOB-SVD is a recently proposed method, based on the Singular Value Decomposition (SVD), which allows the use of more prior knowledge about the signal parameters than previously published subspace-based methods. We compare its performance in terms of robustness and accuracy with the performance of three commonly used methods for signal parameter estimation: HTLS, a subspace-based method which does not allow any inclusion of prior knowledge, except for the model order; HTLSPK(Delta fd(eq)), a subspace-based method obtained by incorporating in HTLS the prior information that the frequency differences between doublet components are known and the damping factors are equal; and AMARES, an interactive maximum likelihood method that allows the inclusion of a variety of prior knowledge. Extensive simulation and in vivo studies, using (31)P as well as proton MRS signals, show that the new method outperforms HTLS and HTLSPK(Delta fd(eq)) in robustness, accuracy, and resolution, and that it provides parameter estimates comparable to the AMARES ones.

Journal Article↗

PubMed2005

On the modeling of breath-by-breath oxygen uptake kinetics at the onset of high-intensity exercises: simulated annealing vs. GRG2 method.

Modeling in the time domain, the non-steady-state O2 uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG2 algorithm (a gradient-descent method known for its robustness). Forty simulated Vo2 on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG2 significantly biased two estimated kinetic parameters of the first exponential (the time delay td1 and the time constant tau1) and impaired the precision (i.e., standard deviation) of the baseline A0, td1, and tau1 compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A2, the time delay td2, and the time constant tau2). Nevertheless, td2 was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O2 uptake on a cycle ergometer and O2 uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG2 for A1 although better with SA for A2 and tau2. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.

Algorithms↗

PubMed1991

Least-squares estimation of enzyme parameters.

The estimation of the enzyme parameters Km and Vmax from initial velocity data, or of analogous parameters in binding or transport experiments may be accomplished by transformation of the data, or by a direct weighted least-squares fit. Although the latter makes better use of the data, the method is complex and may be sensitive to initial parameter estimates. We develop a method which reduces the problem to finding the zero of a continuous function of a single variable.

Computer Simulation↗

PubMed2006

Faithful estimation of dynamics parameters from CPMG relaxation dispersion measurements.

This work examines the robustness of fitting of parameters describing conformational exchange (k(ex), p(a/b), and Deltaomega) processes from CPMG relaxation dispersion data. We have analyzed the equations describing conformational exchange processes for the intrinsic inter-dependence of their parameters that leads to the existence of multiple equivalent solutions, which equally satisfy the experimental data. We have used Monte-Carlo simulations and fitting to the synthetic data sets as well as the direct 3-D mapping of the parameter space of k(ex), p(a/b), and Deltaomega to quantitatively assess the degree of the parameter inter-dependence. The demonstrated high correlation between parameters can preclude accurate dynamics parameter estimation from NMR spin-relaxation data obtained at a single static magnetic field. The strong parameter inter-dependence can readily be overcome through acquisition of spin-relaxation data at more than one static magnetic field thereby allowing accurate assessment of conformational exchange properties.

Algorithms↗

PubMed1983

A comparison of methods for estimating the kinetic parameters of two simple types of transport process.

Sets of experimental data, with known characteristics and error structures, have been simulated for the Michaelis-Menten equation plus a second term, either for linear transport or for competitive inhibition. The Michaelis-Menten equation plus linear term was fitted by several methods and the accuracy and the precision of the parameter estimates from the several methods were compared. The model-fitting methods were: three for least-squares non-linear regression, computer versions of two graphical methods and of two non-parametric methods. The most precise and accurate method was that of D.W. Marquardt (J. Soc. Ind. Appl. Math. 11 (1963) 431--441). The Michaelis-Menten equation with competitive inhibition was also fitted by several methods, viz., two for least-squared non-linear regression, non-parametric method and four variants of the Preston-Schaeffer-Curran plot (Preston, R.L. et al. (1974) J. Gen. Physiol. 64, 443--467). The most precise and accurate of these was the non-linear regression method of W.W. Cleland (Adv. Enzymol. 29 (1967) 1--32). For both these models, the various graphical methods and non-parametric methods gave poor results and are not recommended.

Binding, Competitive↗

PubMed1992

EMSA: a SAAM service for the estimation of population parameters based on model fits to identically replicated experiments.

This paper presents a new technique for the aggregation of models to produce population parameter estimates based on a set of identically replicated experiments. After describing the theoretical basis for the technique we discuss tactical and strategic issues associated with its implementation in the SAAM software. Finally, we demonstrate its utility in the aggregation of models fitted to four simulated experiments.

Algorithms↗

PubMed2005

On-line estimation of concentration parameters in fermentation processes.

It has long been thought that bioprocess, with their inherent measurement difficulties and complex dynamics, posed almost insurmountable problems to engineers. A novel software sensor is proposed to make more effective use of those measurements that are already available, which enable improvement in fermentation process control. The proposed method is based on mixtures of Gaussian processes (GP) with expectation maximization (EM) algorithm employed for parameter estimation of mixture of models. The mixture model can alleviate computational complexity of GP and also accord with changes of operating condition in fermentation processes, i.e., it would certainly be able to examine what types of process-knowledge would be most relevant for local models' specific operating points of the process and then combine them into a global one. Demonstrated by on-line estimate of yeast concentration in fermentation industry as an example, it is shown that soft sensor based state estimation is a powerful technique for both enhancing automatic control performance of biological systems and implementing on-line monitoring and optimization.

Algorithms↗

PubMed1989

Estimation of genetic parameters among breeding soundness examination components and growth traits in yearling bulls.

Data on breeding soundness examinations (BSE) and performance traits were obtained on 549 yearling beef bulls at the San Juan Basin Research Center, Hesperus, Co from 1976 to 1984. Genetic parameters estimated for components of BSE included percent motility (PMOT), percent primary abnormalities (PPRIM), percent secondary abnormalities (PSEC), percent normal sperm (PNOR), scrotal circumference (SC) and BSE score (BSESC). Performance traits included birth weight, weaning weight, yearling weight and average daily gain. The least squares model included birth year, age of dam and breed as fixed effects, sire/breed as a random variable, and age and percent inbreeding as covariates. Paternal half-sib estimates of heritability were PMOT, .08 +/- .07; PPRIM, .31 +/- .09; PSEC, .02 +/- .05; PNOR, .07 +/- .06; BSESC, .10 +/- .06 and SC, .40 +/- .09. Phenotypic correlations among BSE components and growth traits were generally favorable. Genetic correlations involving percent secondary abnormalities were highly variable with large standard errors. Seminal traits improved as age increased and became poorer as inbreeding increased.

Age Factors↗

PubMed2006

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data.

BACKGROUND: Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made. RESULTS: We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogeneous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations. CONCLUSION: We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

Bayes Theorem↗

PubMed1985

[Improved estimation of parameters of blood pressure regulation in anesthetized dogs].

Estimation of parameters was based on tilting table tests in anaesthetized mongrel dogs. The registered variables were the carotid sinus pressure, aortic and superior vena cava pressure as well as the e.c.g. An orthostatic loading series after experimental designs of first order of Plackett and Burman served as an additional disturbance, which is necessary for a model in a closed loop system. Systemic parameters were estimated from measured data by means of recursive regression and generalized recursive regression. A discrepancy between the excellent animal tests and the quality of the model of subsequent estimation of parameters suggested a filtration of measured data, and a non-linear model (Hammerstein model) was selected for comparison. Contrary to the Hammerstein model, filtration of data led to a considerable improvement of the estimated parameters in the present study.

Anesthesia, General↗

PubMed2004

A computer program for Spearman-Kärber and probit analysis of psychometric function data.

PMETRIC is a computer program for the analysis of observed psychometric functions. It can estimate the parameters of these functions, using either probit analysis (a parametric technique) or the Spearman-Kärber method (a nonparametric one). For probit analysis, either a maximum likelihood or a minimum chi 2 criterion may be used for parameter estimation. In addition, standard errors of parameter estimates can be estimated via bootstrapping. The program can be used to analyze data obtained from either yes-no or m-alternative forced-choice tasks. To facilitate the use of PMETRIC in simulation work, an associated program, PMETGEN, is provided for the generation of simulated psychometric function data. Use of PMETRIC is illustrated with data from a duration discrimination task.

Computer Simulation↗

PubMed2001

Analysis of toxicokinetic data using NONMEM: impact of quantification limit and replacement strategies for censored data.

The purpose of this study was to examine how best to incorporate plasma samples which fall below an assay's lower limit of quantification into the process of toxicokinetic data modeling. Secondly to establish what proportion of data can be below the quantification limit without compromising NONMEM's parameter estimates. Using pharmacokinetic parameters determined in a rat toxicokinetic study we simulated datasets that might emerge from similar experiments in which only one sample was obtained per individual. A number of quantification limits were used which resulted in increasing proportions of data values being treated as if they were below the limit of quantification (BQL). For each quantification level we incorporated BQL data into our analyses in number of ways. We compared these analysis methods with respect to how well the underlying parameter values were retrieved. Omitting BQL data values or entering them as zero led to inaccurate and biased study results. We found that incorporating BQL values using more complex substitution methods via a mixed effects model produced more reliable and less biased parameter estimates. The four substitution methods that we investigated performed similarly. Parameter estimates became less reliable and more biased as the quantification level was increased depending on the method of BQL value incorporation. Naive methods of BQL data handling can produce unreliable and biased parameter estimates. An alternative is to incorporate BQL values into a population-type model, our results showed this method to be preferable. We found it advisable that the proportion of BQL data should not exceed one third and, if possible should be less than one quarter.

Animals↗

PubMed1996

A novel extravascular input function for the assessment of drug absorption in bioavailability studies.

PURPOSE: Flexible parametric models describing the input process after extravascular drug administration are needed for the assessment of absorption rate and the use of population methods in bioavailability and bioequivalence studies. METHODS: The oral concentration-time curve modeled as the product of the input and disposition function in the Laplace domain was obtained by numerical inversion methods for parameter estimation. The utility of the inverse Gaussian input density was examined using bioavailability data of an extended-release dosage form. Measures of rate of absorption and the cumulative absorbed amount profile were defined in terms of the estimated model parameters. RESULTS: Accurate estimation of absorption parameters was achieved by simultaneous fitting of the extravascular and intravascular data (describing the latter by a triexponential function). The new input function allowed a direct estimation of both extent of absorption and mean absorption time. CONCLUSIONS: The findings suggest that the inverse Gaussian density is a useful input function. Its flexibility may reduce the effect of model misspecification in parameter estimation. All parameters can be readily interpreted in terms of the absorption process.

Absorption↗

PubMed1987

Extended least squares (ELS) for pharmacokinetic models.

An important part of pharmacokinetic research is fitting models to observed data and estimating the parameters in the model. In general, parameter estimation in pharmacokinetics is a subset of the general problem of nonlinear regression or parameter estimation in nonlinear regression models. The same criteria, algorithms, and software used in other areas of science have been used in pharmacokinetics. Nonlinear modeling is a difficult mathematical and statistical task, often presenting problems. Any proposed new tool is of interest, and extended least squares (ELS) has been suggested as being better than the methods usually used. This suggestion and the evidence supporting it are examined; additional simulations are reported. With the evidence presently available, ELS does not seem to be superior to traditional least squares methods.

Biometry↗