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PubMed2004

Cross-comparison of time- and frequency-domain methods for monitoring the myoelectric signal during a cyclic, force-varying, fatiguing hand-grip task.

Various conventional methods to estimate the mean and median power spectral frequencies, and amplitude of the surface electromyogram during 30-90 min, cyclic, force-varying, constant-posture contractions were cross-compared in an experimental trial. The aim was to determine the most appropriate algorithm implementations and reduce the total number of algorithms that need to be considered when monitoring time trends. Subjects produced hand-grip contractions in a repeated intermittent pattern until exhaustion. For all estimated parameters: analysis of contraction levels below 25% maximum voluntary contraction produced poor estimates due to high relative measurement noise; parameter reproducibility was best when comparisons were aligned to the actual force produced rather than the target force and when the biomechanics of the contraction were more consistent; and estimates were not greatly influenced by the rate of change of the force trajectory. For frequency parameters: estimates based on the short-time Fourier transform were similar to those based on time-varying autoregressive methods; longer duration analysis windows exhibited better repeatability; and simple frequency-domain noise filters were not effective in reducing the impact of measurement noise. For amplitude estimates: whitening reduced the variance of the amplitude estimate; and the best analysis window duration was a trade-off between bias (decreased with a short duration window) and variance (decreased with a long duration window).

Adult↗

PubMed1996

Implementation of OSPOP, an algorithm for the estimation of optimal sampling times in pharmacokinetics by the ED, EID and API criteria.

The most common approach to optimize the sampling schedule in parameter estimation experiments is the D-optimality criterion, which consists in maximizing the determinant of the Fisher information matrix (max det F). In order to incorporate prior parameter uncertainty in the optimal design, other criteria have been proposed: The ED = max E (det F), EID = min E (l/det F) and API = max E (log det F) criteria, where the expectation is with respect to the given prior distribution of the parameters. Previously described algorithm for the estimation of optimal sampling times according to these criteria are adaptive random search (ARS), a robust and global but slow optimizer for API, and stochastic gradient (SG), a fast but local optimizer for ED and EID. We implemented an algorithm named OSPOP 1.0, based on non-adaptive random search (RS) followed by stochastic gradient to determine optimal sampling times for parameter estimation in various pharmacokinetic models according to ED, EID and API criteria. Prior distributions are allowed to be uniform, normal or lognormal. This algorithm combines the robustness of RS and the speediness of SG (convergence is obtained in a few minutes on a microcomputer). The results of the SG algorithm have been compared to those described in the literature using the ARS algorithm on a one compartment model with first- order absorption and were very similar. Also, the CPU time needed by SG and ARS algorithms were compared and the former proved to be much faster. Then, it has been applied to a five parameters stochastic model with zero-order absorption rate and Weibull-distributed residence times which was shown to describe adequately the kinetics of metacycline in humans. Population pharmacokinetic parameters of metacycline were estimated from a six subject pilot study, by the iterative two-staged method, using ADAPT II repeatedly. Optimal sampling times were determined with each criterion (ED, EID, API) with a multivariate normal prior parameter distribution. Six to seven distinct sampling times could be estimated. Higher numbers of samples revealed coalescing of design points.

Algorithms↗

PubMed2001

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.

Algorithms↗

PubMed2004

Simulation of the release from a multiparticulate system validated by single pellet and dose release experiments.

A previously described single-pellet release model has been simplified and modified to give predictions of the release from multiple-pellet systems, besides describing the release from single pellets. The simplified single-pellet model has been verified using single-pellet data and has been used to estimate three release-controlling parameters, namely the pellet core radius, the overall mass transfer coefficient, and the lag time. Single-pellet release experiments showed that the release from the individual film-coated drug cores resulted in a wide distribution of release profiles, a phenomenon not observed on the dose level. Therefore, the parameter estimations resulted in distributions of these parameter values. The core radius and the lag times compared well with the experimental data. The distributions were used as input data for the multiple pellet model, in order to predict the release profiles on the dose level, showing results consistent with the measured dose release. The dose-predictive ability of the model was demonstrated in simulations by studying the effect of a change in the size of the single subunits (of constant total dose), showing that smaller pellets give an increased release rate with less variation. The model for predicting dose-release profiles could be of great value in optimising the performance of an existing formulation, as well as in the development of a new controlled-release pharmaceutical.

Delayed-Action Preparations↗

PubMed2006

Comparison of case-deletion diagnostic methods for Cox regression.

Case-deletion diagnostics are a routine component of regression analysis since they identify unusual observations that substantially affect parameter estimates. The exact approach is to compute the change in each regression parameter by dropping that individual and refitting the model. Repeating a Cox regression for the removal of each individual is very time consuming and therefore not done in practice. The two methods commonly used to approximate the exact case-deletion change for Cox regression are the empirical influence function approach and the covariate-vector augmentation approach. This paper reports the results of a simulation study on how well these methods estimate the exact change in a parameter estimate when deleting a known outlier or a known non-outlier. Additionally, we investigate how well these methods correctly identify outliers and non-outliers. The covariate augmentation approach clearly outperformed the influence function approach in these simulations.

Adenocarcinoma↗

PubMed1999

Understanding Rasch measurement: estimation methods for Rasch measures.

Rasch parameter estimation methods can be classified as non-interative and iterative. Non-iterative methods include the normal approximation algorithm (PROX) for complete dichotomous data. Iterative methods fall into 3 types. Datum-by-datum methods include Gaussian least-squares, minimum chi-square, and the pairwise (PAIR) method. Marginal methods without distributional assumptions include conditional maximum-likelihood estimation (CMLE), joint maximum-likelihood estimation (JMLE) and log-linear approaches. Marginal methods with distributional assumptions include marginal maximum-likelihood estimation (MMLE) and the normal approximation algorithm (PROX) for missing data. Estimates from all methods are characterized by standard errors and quality-control fit statistics. Standard errors can be local (defined relative to the measure of a particular item) or general (defined relative to the abstract origin of the scale). They can also be ideal (as though the data fit the model) or inflated by the misfit to the model present in the data. Five computer programs, implementing different estimation methods, produce statistically equivalent estimates. Nevertheless, comparing estimates from different programs requires care.

Algorithms↗

PubMed1995

Estimating parametric survival model parameters in gerontological aging studies: methodological problems and insights.

Studies of the biology of aging (both experimental and evolutionary) frequently involve the estimation of parameters arising in various multi-parameter survival models such as the Gompertz or Weibull distribution. Standard parameter estimation methodologies, such as maximum likelihood estimation (MLE) or nonlinear regression (NLR), require knowledge of the actual life spans or their explicit algebraic equivalents in order to provide reliable parameter estimates. Many fundamental biological discussions and conclusions are highly dependent upon accurate estimates of these survival parameters (this has historically been the case in the study of genetic and environmental effects on longevity and the evolutionary biology of aging). In this article, we examine some of the issues arising in the estimation of gerontologic survival model parameters. We not only address issues of accuracy when the original life-span data are unknown, we consider the accuracy of the estimates even when the exact life spans are known. We examine these issues as applied to known experimental data on diet restriction and we fit the frequently used, two-parameter Gompertzian survival distribution to these experimental data. Consequences of methodological misuse are demonstrated and subsequently related to the values of the final parameter estimates and their associated errors. These results generalize to other multiparametric distributions such as the Weibull, Makeham, and logistic survival distributions.

Aging↗

PubMed1980

Evaluation of methods for estimating population pharmacokinetics parameters. I. Michaelis-Menten model: routine clinical pharmacokinetic data.

Individual pharmacokinetic par parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there was no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 micrograms/ml by the naive pooled data, two-stage, and NONMEN approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage approach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEN produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.

Adult↗

PubMed2000

An integrated framework for the inference of viral population history from reconstructed genealogies.

We describe a unified set of methods for the inference of demographic history using genealogies reconstructed from gene sequence data. We introduce the skyline plot, a graphical, nonparametric estimate of demographic history. We discuss both maximum-likelihood parameter estimation and demographic hypothesis testing. Simulations are carried out to investigate the statistical properties of maximum-likelihood estimates of demographic parameters. The simulations reveal that (i) the performance of exponential growth model estimates is determined by a simple function of the true parameter values and (ii) under some conditions, estimates from reconstructed trees perform as well as estimates from perfect trees. We apply our methods to HIV-1 sequence data and find strong evidence that subtypes A and B have different demographic histories. We also provide the first (albeit tentative) genetic evidence for a recent decrease in the growth rate of subtype B.

Africa South of the Sahara↗

PubMed1981

[Mathematical modelling of glycolysis and adenine nucleotide metabolism of human erythrocytes. I. Reaction-kinetic statements, analysis of in vivo state and determination of starting conditions for in vitro experiments].

A mathematical model of energy metabolism of human red cells is presented, which includes besides the glycolytic reactions the adenine nucleotide metabolism. The model is based on the network of chemical reactions, the thermodynamic equilibrium constants of fast reversible reactions and on the kinetic equations for irreversible enzyme reactions. The model consists of a system of 16 differential equations and allows the mathematical evaluation of metabolic levels in the steady state of energy metabolism corresponding to the in vivo state erythrocytes with the kinetic data for the enzymes derived from in vitro experiments. The dependence of the levels of metabolites in the steady state on the activity of some enzymes is analysed to characterize the regulatory properties of the system. The comparison of the steady state levels of the model with experimental data makes it possible to estimate values of some controversial enzyme parameters. Estimates of the kinetic parameters of the following intracellular processes are presented: 1) rate constant of AMP-phosphatase, 2) maximum rate of adenylate deaminase, 3) activity of adenine phosphoribosylpyrophosphate transferase and 4) adenosine transport through the cell membrane. The simulation of the preparatory phase before incubation of erythrocytes indicates, that the model also permits to compute the time course of changes of levels of metabolites. To solve the initial problem the stiff differential equation system is integrated numerically by an efficient program without the application of the quasi-steady-state approximation.

Adenine Nucleotides↗

PubMed1988

Estimation of binding parameters by kinetic data analysis: differentiation between one and two binding sites.

A method that enables the discrimination between binding models and the estimation of binding parameters, based solely on kinetic data, is described. Experimental data from association and dissociation experiments were fitted simultaneously to models with mono- or biphasic kinetics with the aid of a non-linear maximum likelihood computer program. Discrimination between two models can be performed statistically. The protocol was used to study the binding of the antitussive [3H]noscapine to guinea pig brain homogenate. Two binding processes could be discriminated by their kinetics, despite the fact that [3H]noscapine apparently binds to one homogeneous population of binding sites in equilibrium binding experiments. This method might find general application when two populations of binding sites are suspected from kinetic data, but when selective ligands are lacking. Since parameter estimates are obtained independent of equilibrium binding data, our approach could also serve as an independent control of such experiments, with respect to both Kd and Bmax.

Animals↗

PubMed1991

Optimal design of experiments to estimate LDL transport parameters in arterial wall.

To quantify transport processes in atherosclerosis, the arterial wall is often exposed to labeled lipoproteins. In vivo experiments are desirable for estimation of transport parameters, but they are technically difficult. A dynamic mass transfer model has been developed to describe experimental transmural profiles of lipoprotein accumulation as a function of luminal permeability, diffusion, convection, and degradation. To avoid extraneous experiments and to assure successful parameter estimation, an optimal design of experiments is needed. For our purposes a design was considered optimal when it maximized the sensitivity of the model output to changes in parameter values as indicated by the determinant of the Hessian matrix of the objective function. A comparison was made between two designs: dual-time designs prescribing unequal circulation times for two distinguishable injections of labeled low-density lipoprotein (LDL) and dual-species designs requiring simultaneous circulation of LDL and tyramine-cellobiose-modified LDL. Circulation time was optimized for both designs. Although both were heavily dependent on the circulation times, dual-time designs required better preliminary knowledge of parameter values. Because labeled degradation products of the modified tracer become anchored in the arterial tissue, information about the degradation process is retained in the dual-species study. For this reason, dual-species designs were generally superior to dual-time designs.

Animals↗

PubMed2004

Ascertainment-adjusted maximum likelihood estimation for the additive genetic gamma frailty model.

The additive genetic gamma frailty model has been proposed for genetic linkage analysis for complex diseases to account for variable age of onset and possible covariates effects. To avoid ascertainment biases in parameter estimates, retrospective likelihood ratio tests are often used, which may result in loss of efficiency due to conditioning. This paper considers when the sibships are ascertained by having at least two affected sibs with the disease before a given age and provides two approaches for estimating the parameters in the additive gamma frailty model. One approach is based on the likelihood function conditioning on the ascertainment event, the other is based on maximizing a full ascertainment-adjusted likelihood. Explicit forms for these likelihood functions are derived. Simulation studies indicate that when the baseline hazard function can be correctly pre-specified, both approaches give accurate estimates of the model parameters. However, when the baseline hazard function has to be estimated simultaneously, only the ascertainment-adjusted likelihood method gives an unbiased estimate of the parameters. These results imply that the ascertainment-adjusted likelihood ratio test in the context of the additive genetic gamma frailty may be used for genetic linkage analysis.

Age of Onset↗

PubMed2004

Estimation of neurophysiological parameters from the waking EEG using a biophysical model of brain dynamics.

This paper presents the results from using electroencephalographic (EEG) data to estimate the values of key neurophysiological parameters using a detailed biophysical model of brain activity. The model incorporates spatial and temporal aspects of cortical function including axonal transmission delays, synapto-dendritic rates, range-dependent connectivities, excitatory and inhibitory neural populations, and intrathalamic, intracortical, corticocortical and corticothalamic pathways. Parameter estimates were obtained by fitting the model's theoretical spectrum to EEG spectra from each of 100 healthy human subjects. Statistical analysis was used to infer significant parameter variations occurring between eyes-closed and eyes-open states, and a correlation matrix was used to investigate links between the parameter variations and traditional measures of quantitative EEG (qEEG). Accurate fits to all experimental spectra were observed, and both inter-subject and between-state variability were accounted for by the variance in the fitted biophysical parameters, which were in turn consistent with known independent experimental and theoretical estimates. These values thus provide physiological information regarding the state. transitions (eyes-closed vs. eyes-open) and phenomena including cortical idling and alpha desynchronization. The parameters are also consistent with traditional qEEG, but are more informative, since they provide links to underlying physiological processes. To our knowledge, this is the first study where a detailed biophysical model of the brain is used to estimate neurophysiological parameters underlying the transitions in a broad range (0.25-50 Hz) of EEG spectra obtained from a large set of human data.

Awareness↗

PubMed1991

Quantification of human opiate receptor concentration and affinity using high and low specific activity [11C]diprenorphine and positron emission tomography.

[11C]Diprenorphine, a weak partial opiate agonist, and positron emission tomography were used to obtain noninvasive regional estimates of opiate receptor concentration (Bmax) and affinity (Kd) in human brain. Different compartmental models and fitting strategies were compared statistically to establish the most reliable method of parameter estimation. Paired studies were performed in six normal subjects using high (769-5,920 Ci/mmol) and low (27-80 Ci/mmol) specific activity (SA) [11C]diprenorphine. Two subjects were studied a third time using high SA [11C]diprenorphine after a pretreatment with 1-1.5 mg/kg of the opiate antagonist naloxone. After the plasma radioactivity was corrected for metabolites, the brain data were analyzed using a three-compartment model and nonlinear least-squares curve fitting. Linear differential equations were used to describe the high SA (low receptor occupancy) kinetics. The k3/k4 ratio varied from 1.0 +/- 0.2 (occipital cortex) to 8.6 +/- 1.6 (thalamus). Nonlinear differential equations were used to describe the low SA (high receptor occupancy) kinetics and the curve fits provided the konf2 product. The measured free fraction of [11C]diprenorphine in plasma (f1) was 0.30 +/- 0.03, the average K1/k2 ratio from the two naloxone studies was 1.1 +/- 0.2, and the calculated free fraction of [11C]diprenorphine in the brain (f2) was 0.3. Using the paired SA studies, the estimated kinetic parameters, and f2, separate estimates of Bmax and Kd were obtained. Bmax varied from 2.3 +/- 0.5 (occipital cortex) to 20.6 +/- 7.3 (cingulate cortex) nM. The average Kd (eight brain regions) was 0.85 +/- 0.17 nM.

Adult↗

PubMed1988

Compartment models for estimating attributes of digesta flow in cattle.

1. The basic assumptions involved in one- and two-compartment models with age-independent distributed residence times (exponential, G1) for describing digesta flow are reviewed as the bases for describing families of one- and two-compartment models which assume age-dependent distributions (Gn) of residence times. 2. The two-compartment, age-independent model with exponentially distributed residence times (G1G1) yielded estimates of essentially equal rate parameters when fitted to faecal values for all four cows receiving a diet of 500 g coarsely chopped, sodium hydroxide-treated straw/kg and one of four cows receiving the same diet but with ground and pelleted straw. The incorporation of progressively higher orders of age dependency (G2-G6, Gn) into the faster turnover compartment of two-compartment models (GnG1) resulted in a resolution of equal rate parameters estimated by the G1G1 model and a reduction in standard errors for the rate and the initial concentration parameters. 3. The occurrence of equal rate parameters in two-compartment models indicated an age-dependent process; a process which could equally well be described by a one-compartment, age-dependent compartment having an order of age dependency equal to the sum of these orders in the two-compartment model with equal rate parameters. 4. The age-independent models overestimated time of first appearance in the faeces of a meal's particles. The association of age dependency with the faster turnover compartment resulted in earlier estimates for first appearance of the marked particles; estimates which were more consistent with observed first appearance. 5. The faecal excretion pattern from cows fed on the ground and pelleted straw diet exhibited an age-independent distribution of longer residence times which dominated approximately 80% of the later residence times. Age-dependent, one-compartment models gave a poor fit to such data from these cows fed on ground and pelleted straw. In contrast, age-dependent, one-compartment models provided an excellent fit to data from cows fed on chopped straw; data which indicated that age-independent distributions of residence times were much delayed in appearing or were totally absent. 6. The mean residence time for the slower turnover, age-independent compartment estimated from faecal excretional of stained particles from either diet was similar to that estimated from duodenal concentrations of the stained particles. This suggests that the slower turnover model compartment was confined to preduodenal sites.(ABSTRACT TRUNCATED AT 250 WORDS)

Age Factors↗

PubMed2005

Evaluation of uncertainty of the comprehensive interpretation of borehole logs by the multiple re-run statistical method.

Measurements of various physical quantities in a borehole by geophysical well logging tools are designed to determine these quantities for underground geological formations. Then, the raw data (logs) are combined in a comprehensive interpretation to obtain values of geological parameters. Estimating the uncertainty of calculated geological parameters, interpreted in such a way, is difficult, often impossible, when classical statistical methods are used. The method presented here permits an estimate of the uncertainty of a quantity to be obtained. The discussion of the dependence between the uncertainty of nuclear and acoustic tool responses, and the estimated uncertainty of the interpreted geological parameters (among others: porosity, water saturation, clay content) is presented.

Journal Article↗

PubMed1991

Effects of tracer blood measurement noise on glucose metabolic rate estimation.

Tracer kinetic modeling with Positron Emission Tomography (PET) requires measurements of the time-activity curves in both plasma (PTAC) and tissue (TTAC) to estimate physiological parameters. However, the estimation usually ignores the measurement noise in plasma tracer activity curves. The accuracy and reliability of the physiological parameters estimated by ignoring such noise are not well understood. In this paper, computer simulations were performed to investigate the influence of input measurement noise on the accuracy of estimates. The results show that input measurement noise causes considerable variability in the parameter estimates.

Blood Glucose↗