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At least 109 records · Page 6Linked to original sources

PubMed2005

Pharmacodynamic parameter estimation: population size versus number of samples.

The purpose of this study was to evaluate the effects of population size, number of samples per individual, and level of interindividual variability (IIV) on the accuracy and precision of pharmacodynamic (PD) parameter estimates. Response data were simulated from concentration input data for an inhibitory sigmoid drug efficacy (E(max)) model using Nonlinear Mixed Effect Modeling, version 5 (NONMEM). Seven designs were investigated using different concentration sampling windows ranging from 0 to 3 EC(50) (EC(50) is the drug concentration at 50% of the E(max)) units. The response data were used to estimate the PD and variability parameters in NONMEM. The accuracy and precision of parameter estimates after 100 replications were assessed using the mean and SD of percent prediction error, respectively. Four samples per individual were sufficient to provide accurate and precise estimate of almost all of the PD and variability parameters, with 100 individuals and IIV of 30%. Reduction of sample size resulted in imprecise estimates of the variability parameters; however, the PD parameter estimates were still precise. At 45% IIV, designs with 5 samples per individual behaved better than those designs with 4 samples per individual. For a moderately variable drug with a high Hill coefficient, sampling from the 0.1 to 1, 1 to 2, 2 to 2.5, and 2.5 to 3 EC(50) window is sufficient to estimate the parameters reliably in a PD study.

Humans↗

PubMed2000

Turboprop and rotary-wing aircraft flight parameter estimation using both narrow-band and broadband passive acoustic signal-processing methods.

Flight parameter estimation methods for an airborne acoustic source can be divided into two categories, depending on whether the narrow-band lines or the broadband component of the received signal spectrum is processed to estimate the flight parameters. This paper provides a common framework for the formulation and test of two flight parameter estimation methods: one narrow band, the other broadband. The performances of the two methods are evaluated by applying them to the same acoustic data set, which is recorded by a planar array of passive acoustic sensors during multiple transits of a turboprop fixed-wing aircraft and two types of rotary-wing aircraft. The narrow-band method, which is based on a kinematic model that assumes the source travels in a straight line at constant speed and altitude, requires time-frequency analysis of the acoustic signal received by a single sensor during each aircraft transit. The broadband method is based on the same kinematic model, but requires observing the temporal variation of the differential time of arrival of the acoustic signal at each pair of sensors that comprises the planar array. Generalized cross correlation of each pair of sensor outputs using a cross-spectral phase transform prefilter provides instantaneous estimates of the differential times of arrival of the signal as the acoustic wavefront traverses the array.

Acoustics↗

PubMed1985

Pharmacokinetic parameter estimates from several least squares procedures: superiority of extended least squares.

The precision of pharmacokinetic parameter estimates from several least squares parameter estimation methods are compared. The methods can be thought of as differing with respect to the way they weight data. Three standard methods, Ordinary Least Squares (OLS-equal weighting), Weighted Least Squares with reciprocal squared observation weighting [WLS(y-2)], and log transform OLS (OLS(ln))--the log of the pharmacokinetic model is fit to the log of the observations--are compared along with two newer methods, Iteratively Reweighted Least Squares with reciprocal squared prediction weighting (IRLS,(f-2)), and Extended Least Squares with power function "weighting" (ELS(f-xi)--here xi is regarded as an unknown parameter). The values of the weights are more influenced by the data with the ELS(f-xi) method than they are with the other methods. The methods are compared using simulated data from several pharmacokinetic models (monoexponential, Bateman, Michaelis-Menten) and several models for the observation error magnitude. For all methods, the true structural model form is assumed known. Each of the standard methods performs best when the actual observation error magnitude conforms to the assumption of the method, but OLS is generally least perturbed by wrong error models. In contrast, WLS(y-2) is the worst of all methods for all error models violating its assumption (and even for the one that does not, it is out performed by OLS(ln)). Regarding the newer methods, IRLS(f-2) improves on OLS(ln), but is still often inferior to OLS. ELS(f-xi), however, is nearly as good as OLS (OLS is only 1-2% better) when the OLS assumption obtains, and in all other cases ELS(f-xi) does better than OLS. Thus, ELS(f-xi) provides a flexible and robust method for estimating pharmacokinetic parameters.

Analysis of Variance↗

PubMed2006

A successive parameter estimation algorithm for chirplet signal decomposition.

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, and object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation.

Algorithms↗

PubMed1999

The effect of collinearity on parameter estimates in nonlinear mixed effect models.

PURPOSE: To demonstrate how correlations among predictor variables in a population pharmacokinetic model affect the ability to discern which covariates should enter into the structural pharmacokinetic model. METHODS: Monte Carlo simulation was used to generate multiple-dose concentration-time data similar to that seen in a Phase III clinical trial. The drugs' pharmacokinetics were dependent on two covariates. Five data sets were simulated with increasing correlation between the two covariates. All data sets were analyzed using NONMEM both with and without inclusion of the covariates in the structural pharmacokinetic model. Summary measures for ill-conditioning and sensitivity analysis were used to examine how increasing correlation among covariates affects the accuracy and precision of the parameter estimates. RESULTS: When covariates were included in the structural pharmacokinetic model and the correlation between covariates increased, the standard error of the parameter estimates increased and the value of parameter estimates themselves became increasingly biased. When the correlation between predictor variables was 0.75, the standard errors of the parameter estimates were too large to declare statistical significance. CONCLUSIONS: Correlations among predictor variables greater than 0.5 when entered into the model simultaneously should be a warning to researchers because the (1) the accuracy of the parameter estimates themselves may be biased and (2) the precision of the estimates may be inflated due to ill-conditioning.

Clinical Trials, Phase III as Topic↗

PubMed2006

A biphasic parameter estimation method for quantitative analysis of dynamic renal scintigraphic data.

Dynamic renal scintigraphy is an established method in nuclear medicine, commonly used for the assessment of renal function. In this paper, a biphasic model fitting method is proposed for simultaneous estimation of both vascular and parenchymal parameters from renal scintigraphic data. These parameters include the renal plasma flow, vascular and parenchymal mean transit times, and the glomerular extraction rate. Monte Carlo simulation was used to evaluate the stability and confidence of the parameter estimates obtained by the proposed biphasic method, before applying the method on actual patient study cases to compare with the conventional fitting approach and other established renal indices. The various parameter estimates obtained using the proposed method were found to be consistent with the respective pathologies of the study cases. The renal plasma flow and extraction rate estimated by the proposed method were in good agreement with those previously obtained using dynamic computed tomography and magnetic resonance imaging.

Computer Simulation↗

PubMed1987

Three-element model for total systemic circulation: emphasis on the accuracy of parameter estimates.

In this study, the accuracy achievable in the parameter estimates of a three-element linear model for the systemic vascular bed is considered. The model neglects inertial effects and includes only three elements representing arterial compliance, peripheral resistance and venous compliance, in agreement with recent sensitivity investigations. Parameter estimation starts from arterial and right atrial pressure signals generated by a closed-loop simulator of the cardiovascular circulation and corrupted with normal noise to account for measurement errors. In this way, the influences of a wide variety of circulatory conditions were investigated. The results achieved give evidence that arterial compliance is generally well estimated, while venous compliance is more variable, particularly at high peripheral resistance when measured signals appear to be less sensitive to this parameter. However, presence of cardiac disease, such as heart failure and valvular stenosis has minimal influence on compliance estimates. These results suggest that this simple model can be conveniently applied even under noisy conditions.

Blood Circulation↗

PubMed1998

Respirometric assay for biofilm kinetics estimation: parameter identifiability and retrievability

Currently, no fast and accurate methods exist for measuring extant biokinetic parameters for biofilm systems. This article presents a new approach to measure extant biokinetic parameters of biofilms and examines the numerical feasibility of such a method. A completely mixed attached growth bioreactor is subjected to a pulse of substrate, and oxygen consumption is monitored by on-line measurement of dissolved oxygen concentration in the bulk liquid. The oxygen concentration profile is then fit with a mechanistic mathematical model for the biofilm to estimate biokinetic parameters. In this study a transient biofilm model is developed and solved to generate dissolved oxygen profiles in the bulk liquid. Sensitivity analysis of the model reveals that the dissolved oxygen profiles are sufficiently sensitive to the biokinetic parameters-the maximum specific growth rate coefficient (insertion markμ) and the half-saturation coefficient (Ks)-to support parameter estimation if accurate estimates of other model parameters can be obtained. Monte Carlo simulations are conducted with the model to add typical measurement error to the generated dissolved oxygen profiles. Even with measurement error in the dissolved oxygen profile, a pair of biokinetic parameters is always retrievable. The geometric mean of the parameter estimates from the Monte Carlo simulations prove to be an accurate estimator for the true biokinetic values. Higher precision is obtained for insertion markμ estimates than for Ks estimates. In summary, this theoretical analysis reveals that an on-line respirometric assay holds promise for measuring extant biofilm kinetic parameters. Copyright 1998 John Wiley & Sons, Inc.

Journal Article↗

PubMed1989

Nonlinear parameter estimation applied to psychophysically measured impulse responses.

A technique is presented for the estimation of the impulse response, based on data from a psychophysical experiment on threshold vision. A two-step method is used for the estimation of the model parameters. The first step is a Hankel matrix approach, and the second an unweighted least squares method. Results of this estimation technique are presented. The model with the estimated parameters corroborates other psychophysical data. The estimates obtained are adequate for the intended purposes of simulation and modeling.

Mathematics↗

PubMed1994

Equivalent dipole parameter estimation using simulated annealing.

Equivalent-electrical dipole source modeling of evoked potential signals requires complicated non-linear multivariate optimization. Newton and non-linear simplex optimization methods often converge to a local minimum, and their results are affected by the procedure's starting parameter estimates. This paper describes simulated annealing, a more robust and resistant global optimization method. As an illustrative example, both the simplex and simulated annealing algorithms were used for parameter estimation in modeling wave V of the brain-stem auditory evoked potential (BAEP) using a single decaying sinusoid dipole source. Data for a single subject from 3000 responses to stimuli on each of 2 days were recorded, with modeling performed on 1000 response subaverages. Each estimation problem was run with 5 different sets of starting parameters. Simulated annealing always converged to the global minimum regardless of the starting parameter estimates while simplex often converged to markedly different solutions for different starting parameter estimates. No association was apparent between the simplex's converging to a local minimum and the closeness of the starting estimates to the true parameter values. Implementation of simulated annealing is discussed in terms of cooling schedules and other procedure parameters.

Acoustic Stimulation↗

PubMed2006

Parameter estimation of a respiratory control model from noninvasive carbon dioxide measurements during sleep.

A new method for estimating the parameters of a human gas exchange model is presented. Sensitivity analysis is used both to inspect the relative importance of the model parameters and to speed up the par-ameter estimation process. Multistart optimization is used to compensate for the effects of partial and noisy measurements. The validity of the method is first investigated with a test problem for which par-ameter identifiability is shown. The method is then applied to the estimation of sleep-related changes in the respiratory control system from the end-tidal and transcutaneous carbon dioxide measurements on human subjects. The results show that it is possible to gain insight into the behaviour of the rather complex physiological system using only a few noninvasive measurements and tractable computations.

Algorithms↗

PubMed2003

Kinetics of benzene biodegradation by Pseudomonas aeruginosa: parameter estimation.

This study determined the model parameters describing biodegradation of benzene by conducting kinetic microcosm batch tests in both pure solution and saturated aquifer material conditions for various initial benzene (100-700 mg/L) and microbial concentrations (10(7)-10(9) colony-forming units [CFU]/ml) using Pseudomonas aeruginosa as benzene-degrading bacteria. In both tests, benzene and microbial concentrations were monitored over time in order to investigate which of two Monod kinetic equations, the Monod-with-growth or the Monod-no-growth model, was more suitable for describing benzene biodegradation and to estimate the associated model parameters. Parameter estimation was performed by fitting the numerical solution of each model obtained by the fourth-order Runge-Kutta integration to the measured data of benzene and/or microbial concentrations. For the Monod-with-growth model, the best fit of the numerical solution was significantly different than the measured benzene concentrations, especially at early times, because of the gradual increase of microbial population in the growth curve. In contrast, the solution based on the Monod-no-growth model produced reasonable agreement with the measured benzene data. The estimated parameters of maximum substrate utilization rate (kmax) and half-saturation constant (Kc) were in the range of 61 to 105 mg/L/d and about 270 mg/L, respectively, which differ significantly from values previously reported in the literature. We attribute the differences observed in our study to our experimental conditions of initial substrate and bacterial concentrations and oxygen and nutrient supply. Our results imply that an appropriate model type and reasonable values of kinetic parameters should be chosen to model the biodegradation of hydrocarbons in the subsurface environment.

Benzene↗

PubMed1982

A simulation study of parameter estimation in the one and two compartment models.

Few attempts have been made to examine the statistical problems that the user of compartmental models must face. Some properties of the estimators of parameters for one and two compartmental models based on nonlinear estimation were studied through simulation. Of particular interest were the effect of the experimental design and the effect of different error structures on the empirical sampling distribution for the estimators. For the one compartment model it was found that nonlinear estimation yielded essentially unbiased estimators that were normally distributed unless the random error for the model was large. In the two compartment model simulations, bias appeared in the estimators to the extent that bimodal sampling distributions of the estimators were observed as the random error for the model was increased.

Humans↗

PubMed1995

Accuracy of numerical inversion of Laplace transforms for pharmacokinetic parameter estimation.

Numerical inversion of the Laplace transform is a useful technique for pharmacokinetic modeling and parameter estimation when the model equations can be solved in the Laplace domain but the solutions cannot be inverted back to the time domain. The accuracy of numerical inversion of the Laplace transform using an infinite series approximation due to Hosono was systematically studied by reference to 17 widely differing functions having known inverse transforms. The error of inversion was found to be very sensitive to the details of the computer implementation of the method; for example, double-precision artihmetic is essential. The method used to sum the series in the least-squares program Multi(Filt) was often unable to achieve a relative error of less than 10(-4), and a Monte Carlo simulation showed that this method is insufficiently accurate for reliable least-squares parameter estimation. Improvements to the algorithm are described whereby a better method of applying Euler's transformation is used and the number of terms summed is determined automatically by the rate of convergence of the series. The improved algorithm is more efficient in inverting easy functions and more reliable in inverting difficult functions, especially those involving a time lag. With its use, pharmacokinetic parameter estimation can be performed with essentially the same accuracy as when the function is defined in the time domain.

Algorithms↗

PubMed1983

Parameter estimation in linear functional relationships.

We present the application of a weighted least-squares technique to extract parameter estimates in linear models when all variables are subject to error and the goal of the investigation is the value of the parameters themselves. We assume that the relative variances of the variables are known and that the errors between variables are independent. The method of parameter estimation for linear functional relationships is presented, and we describe its differences from linear regression. We discuss how to obtain confidence intervals for the parameter estimates with an emphasis on computer Monte Carlo simulations. An explicit example related to measurements of lung volume changes is presented. An eigenvalue analysis of the data pertaining to the number of independent variables and a physical interpretation of the data space are also discussed.

Abdomen↗

PubMed1997

Parameter estimability of biphasic response models.

Pharmacodynamics of general anesthetic agents generally exhibit biphasic concentration-effect relationships (i.e., an activation phase at low concentrations and inhibition at higher concentrations). These relationships are usually characterized with biphasic models constructed from various combinations and modifications of the nonlinear sigmoid E(MAX) model. We tested and quantified the parameter estimability of the simplest additive biphasic pharmacodynamic models by a Monte Carlo method. The estimated model parameters were used to calculate descriptors of the concentration-effect data. Parameters and descriptors were compared with their true values. When the IC50/EC50 ratio was low (<10), E(MAX), EC50, and IC50 were poorly estimated (high coefficient of variation and pronounced bias). However, the fit to the data was excellent, and the data descriptors calculated from the estimated model parameters demonstrated high precision and accuracy. Baseline effect (E0) was estimated with good precision and accuracy. As the IC50/EC50 ratio was increased, the estimability of model parameters and data descriptors improved, with the data descriptors continuing to be more estimable than model parameters. Thus, model parameters become estimable when there is sufficient separation between EC50 and IC50 to produce a plateauing of peak effect (activation), which can be observed directly from the data signature. Data descriptors are not subject to this limitation and thus may serve as better metrics for summarizing concentration-effect relationships.

Anesthetics↗

PubMed2002

Influence of arterial vs. venous sampling site on nicotine tolerance model selection and parameter estimation.

In this modeling study we utilize previously published nicotine pharmacokinetic (PK) and pharmacodynamic (PD, heart rate) data to investigate the influence of PK sampling site (venous vs. arterial) on the selection of a specific PD tolerance model and estimation of its parameters. We describe a general model for tolerance which includes as special cases feedback (TF), and kinetic based tolerance (TK) models. A TK model has arterial plasma drug concentrations (Ca) driving (hypothetical) effect (Ce) and antagonist (Cm) site concentrations, which drive a non-feedback effect (Enf): tolerance depends on the relative rate of equilibration of Ce and Cm with Ca. The TF model adds feedback which makes tolerance depend on Enf, not just on drug kinetics for nicotine. The arterial-sampling-analysis (PKPDa) has Ca driving Ce and Cm. The venous-sampling-analysis (PKPDv) does the same but estimates Ca from venous data by means of deconvolution. A TF model (with Cm = Ce) was always selected in the PKPDa. According to this model tolerance developed rapidly with a median half-life of 6.6 min, and median decrease of effect due to tolerance of 31%. Different variants of the TF or TK models were selected in the PKPDv. Parameter estimates for PKPDv show higher variability, and, for the TF model, lower rate and extent of tolerance development and threefold increase in EC50. The study shows that (i) TF models are more appropriate than TK models to describe nicotine effect data, (ii) venous sampling may lead to incorrect model selection and inaccurate and imprecise parameter estimation in respect to arterial sampling, and (iii) arterial sampling should be preferred for accurate (non-steady-state) PD modeling.

Arteries↗

PubMed2003

Wolbachia and cytoplasmic incompatibility in the California Culex pipiens mosquito species complex: parameter estimates and infection dynamics in natural populations.

Before maternally inherited bacterial symbionts like Wolbachia, which cause cytoplasmic incompatibility (CI; reduced hatch rate) when infected males mate with uninfected females, can be used in a program to control vector-borne diseases it is essential to understand their dynamics of infection in natural arthropod vector populations. Our study had four goals: (1) quantify the number of Wolbachia strains circulating in the California Culex pipiens species complex, (2) investigate Wolbachia infection frequencies and distribution in natural California populations, (3) estimate the parameters that govern Wolbachia spread among Cx. pipiens under laboratory and field conditions, and (4) use these values to estimate equilibrium levels and compare predicted infection prevalence levels to those observed in nature. Strain-specific PCR, wsp gene sequencing, and crossing experiments indicated that a single Wolbachia strain infects Californian Cx. pipiens. Infection frequency was near or at fixation in all populations sampled for 2 years along a >1000-km north-south transect. The combined statewide infection frequency was 99.4%. Incompatible crosses were 100% sterile under laboratory and field conditions. Sterility decreased negligibly with male age in the laboratory. Infection had no significant effect on female fecundity under laboratory or field conditions. Vertical transmission was >99% in the laboratory and approximately 98.6% in the field. Using field data, models predicted that Wolbachia will spread to fixation if infection exceeds an unstable equilibrium point above 1.4%. Our estimates accurately predicted infection frequencies in natural populations. If certain technical hurdles can be overcome, our data indicate that Wolbachia can invade vector populations as part of an applied transgenic strategy for vector-borne disease reduction.

Animals↗