SEARCH · PubMed Health

Results for “parameter estimation”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56Linked to original sources

PubMed1989

Evaluation of a two-compartment Bayesian forecasting program for predicting vancomycin concentrations.

The application of a two-compartment Bayesian forecasting program for vancomycin was tested retrospectively in 45 adult patients with stable renal function. Serial blood samples from 25 of these patients were used to determine population-based parameter estimates. The predictive performance of the Bayesian program was assessed by using both non-steady-state and steady-state vancomycin concentrations as feedback information. Overall, the program tended to underpredict peak and trough steady-state vancomycin serum concentrations. A larger mean prediction error (ME) was seen when non-steady-state feedback serum concentrations were used compared with using population-based parameter estimates (no feedback). In contrast, a marked improvement in ME (peaks: -1.03 versus -2.61; troughs: -1.60 versus -2.07) was seen when steady-state feedback serum concentrations were used compared with no feedback data. Precision improved when either feedback serum concentrations were used to predict steady-state peak and trough vancomycin concentrations. The results from this clinical evaluation demonstrate that the initial pharmacokinetic parameter estimates for a two-compartment Bayesian model provided accurate prediction of steady-state vancomycin concentrations. Prediction bias and precision were improved when steady-state vancomycin concentrations were used to determine individualized pharmacokinetic parameters.

Adult↗

PubMed1992

Segregation analysis of 159 soft tissue sarcoma kindreds: comparison of fixed and sequential sampling schemes.

In this study we compared parameter estimates and model hypotheses in pedigree data collected by fixed sampling with estimates and hypotheses derived by sequential sampling. Employing a fixed sampling scheme, we previously analyzed data on relatives of 159 childhood sarcoma patients. We have now extracted from that data set individuals who would have been included in a sequentially sampled study. We applied segregation analysis to the truncated data, to determine the mode of inheritance and major locus parameter estimates. With data from both sampling schemes we made a family-by-family comparison to determine each family's contribution to a major gene model. The two sampling schemes yielded similar results: we detected segregation of a dominant major gene and obtained similar major locus parameter estimates. However, the sequential sampling scheme derived these conclusions from data on 982 relatives rather than the 2,451 ascertained in the fixed sampling scheme. The sequential sampling scheme failed to identify only one of the kindreds likely to be segregating the gene. For this data set, the sequential sampling scheme would have provided an efficient mechanism to discriminate genetic hypotheses and would have permitted focus of resources on the specific kindreds likely to segregate a major gene.

Adolescent↗

PubMed1993

Real-time identification of parameters of the ARMA model of the human EEG waveforms.

Electroencephalogram (EEG) can provide important information about the functioning of the human brain. In particular, the EEG waveforms manifest certain changes due to application of drugs, such as general anesthetics. Measurement of the changes in the EEG waveforms in real time, may therefore be used to determine the global effects of the administered drug. Among numerous mathematical techniques used in the analysis of the EEG waveforms, perhaps, the fast Fourier transform (FFT) is the most widely used. Recently some researchers have suggested the use of the autoregressive moving average (ARMA) model for the EEG analysis. In this method the coefficients of the ARMA model are identified and used to describe the waveform. We consider a first order ARMA model, and use the Extended Least Squares (ELS) and its recursive version (RELS) for parameter estimation. The identified parameters are then used to describe the time-domain or the frequency-domain properties of the EEG waveforms. Since the parameters of the model may change with time, a forgetting factor is incorporated in the RELS algorithm to allow for tracking of time varying parameters. The advantage of recursive estimation of the coefficients of the ARMA model over the non-recursive estimation and the FFT method, is substantial reduction in computation as well as its capability to track the time varying process.

Algorithms↗

PubMed1998

Estimating equations with incomplete categorical covariates in the Cox model.

Incomplete covariate data is a common occurrence in many studies in which the outcome is survival time. When a full likelihood is specified, a useful technique for obtaining parameter estimates is the EM algorithm. We propose a set of estimating equations to estimate the parameters of Cox's proportional hazards model when some covariate values are missing. These estimating equations can be solved by an algorithm similar to the EM algorithm. Because of the computational burden of finding a solution to these estimating equations, we propose obtaining parameter estimates via Monte Carlo methods. Asymptotic variances of the parameter estimates are also derived. We present a clinical trials example with three covariates, two of which have some missing values.

Algorithms↗

PubMed1991

A three-step approach combining Bayesian regression and NONMEM population analysis: application to midazolam.

NONMEM, the only available supported program for population pharmacokinetic analysis, does not provide the analyst with individual subject parameter estimates. As a result, the relationship between pharmacokinetic parameters and demographic factors such as age, gender, and body weight cannot be sought by plotting demographic factors vs. kinetic parameters. To overcome this problem, we devised a three-step approach. In step 1, an initial NONMEM analysis provides the population pharmacokinetic parameters without taking into account the demographic factors. Step 2 consists of individual bayesian regressions using the measured drug concentrations for each subject and the population pharmacokinetic parameters obtained in step 1. The bayesian parameter estimates of the individual subject can be plotted against the demographic factors of interest. From the scatter plots, it can be seen which are the demographic factors that appear to affect the pharmacokinetic parameters. In step 3, the NONMEM analysis is resumed, and the demographic factors found in step 2 are entered into the NONMEM regression model in a stepwise manner. This method was used to analyze the pharmacokinetics of midazolam in 64 subjects from 714 plasma concentrations and 11 demographic factors. CL (elimination clearance) and V1 were found to be a function of body weight. Age and liver disease were found to decrease CL. Of the 11 demographic factors recorded for each patient, none was found to influence VSS or intercompartmental clearance.

Adolescent↗

PubMed2005

Stochastic differential equations in NONMEM: implementation, application, and comparison with ordinary differential equations.

PURPOSE: The objective of the present analysis was to explore the use of stochastic differential equations (SDEs) in population pharmacokinetic/pharmacodynamic (PK/PD) modeling. METHODS: The intra-individual variability in nonlinear mixed-effects models based on SDEs is decomposed into two types of noise: a measurement and a system noise term. The measurement noise represents uncorrelated error due to, for example, assay error while the system noise accounts for structural misspecifications, approximations of the dynamical model, and true random physiological fluctuations. Since the system noise accounts for model misspecifications, the SDEs provide a diagnostic tool for model appropriateness. The focus of the article is on the implementation of the Extended Kalman Filter (EKF) in NONMEM for parameter estimation in SDE models. RESULTS: Various applications of SDEs in population PK/PD modeling are illustrated through a systematic model development example using clinical PK data of the gonadotropin releasing hormone (GnRH) antagonist degarelix. The dynamic noise estimates were used to track variations in model parameters and systematically build an absorption model for subcutaneously administered degarelix. CONCLUSIONS: The EKF-based algorithm was successfully implemented in NONMEM for parameter estimation in population PK/PD models described by systems of SDEs. The example indicated that it was possible to pinpoint structural model deficiencies, and that valuable information may be obtained by tracking unexplained variations in parameters.

Algorithms↗

PubMed2004

Fitting wald and ex-Wald distributions to response time data: an example using functions for the S-PLUS package.

Schwarz (2001, 2002) proposed the ex-Wald distribution, obtained from the convolution of Wald and exponential random variables, as a model of simple and go/no-go response time. This article provides functions for the S-PLUS package that produce maximum likelihood estimates of the parameters for the ex-Wald, as well as for the shifted Wald and ex-Gaussian, distributions. In a Monte Carlo study, the efficiency and bias of parameter estimates were examined. Results indicated that samples of at least 400 are necessary to obtain adequate estimates of the ex-Wald and that, for some parameter ranges, much larger samples may be required. For shifted Wald estimation, smaller samples of around 100 were adequate, at least when fits identified by the software as having ill-conditioned maximums were excluded. The use of all functions is illustrated using data from Schwarz (2001). The S-PLUS functions and Schwarz's data may be downloaded from the Psychonomic Society's Web archive, www. psychonomic.org/archive/.

Humans↗

PubMed1998

Parameterization of inoculum effect via mathematical modeling: aminoglycosides against Staphylococcus aureus and Escherichia coli.

Inoculum effect describes the inoculum size dependent changes in minimum inhibitory concentrations (MIC) exhibited by antibiotic-bacterium combinations demonstrating such effect. Traditionally, inoculum effect has been loosely defined based on the extent of increase in the MIC with respect to the increase in inoculum size. In most studies, assessment of MIC data has relied on the arbitrary selection of a point of reference for both baseline MIC and inoculum size. More importantly, this conventional method of assessment does not permit information conveyed in a complete MIC versus inoculum size profile to be fully explored. To undertake these issues, a mathematical model was developed for the description of the entire inoculum effect profile. With the employment of three key parameter estimates, i.e., the baseline MIC, the threshold inoculum size at which the increase in MIC commences, and the rate of increase in MIC with respect to inoculum size, both the shape and location of the profile could be adequately defined. To verify the application of this model, a series of four aminoglycosides were tested against standard strains of E. coli and S. aureus. Results showed a good degree of organism specificity and antibiotic-class dependency of the inoculum effect profiles. Analysis of the parameter estimates obtained provided further support for these observations. In conclusion, the mathematical model developed in the present study adequately described the inoculum effect exhibited by the various aminoglycoside-bacterium combinations tested. The parameter estimates generated by the modeling approach allowed comparison and quantitative analysis of the inoculum effect profiles with minimal difficulties.

Amikacin↗

PubMed2003

Considerations in analyzing single-trough concentrations using mixed-effects modeling.

The purpose of this study was to assess the effect of trial design and data analysis choices on the bias and precision of pharmacokinetic (PK) parameter estimation. NONMEM was used to simulate and analyze plasma concentrations collected according to a dense (five samples) or sparse (single-trough samples) sampling scheme for a one-compartment open model with intravenous administration. The results indicated that the bias on estimates of CL with only single-trough data was 17% compared to less than 1% for only dense data. The estimates of CL were improved by fixing all other parameters and estimating only mean and variance of CL (-11% to 1.4%, depending on the estimation method). Adding dense data led to further improvements (-2.3% to 0.3%, depending on further improvements). In these cases, first-order conditional estimation (FOCE) methods resulted in better estimates of CL than first-order (FO) methods. These steps also improved the Bayesian estimates of CL. These studies support the following recommendations: (1) avoid collecting single-trough concentrations unless there is reasonable knowledge about the PK of the drug; (2) if collecting single-trough concentrations is inevitable, avoid estimating all parameters when modeling single-trough concentration data; (3) use prior information by modeling the single-trough concentration data along with dense data from other studies; and (4) use Bayes estimates if the PK model and its parameters are known with reasonable certainty.

Bayes Theorem↗

PubMed1988

Estimated mechanical properties of synergistic muscles involved in movements of a variety of human joints.

One of the most challenging aspects of biomechanical modelling is parameter estimation. Parameter values that define the nonlinear relations within the classic Hill-based muscle model structure have been estimated for a large number of muscles involved in movements of a number of joints. The technique used to estimate these parameters is based on combining information on muscle as a material with geometrical data on muscle-joint anatomy. The resulting relations are compatible with available human experimental data and with past modelling estimates. An estimation of the relative importance of the various synergistic muscle properties during dynamic movement tasks is also provided, aided by examples of muscle load-sharing as a function of optimization criteria including measures of position error, muscle stress and neural effort.

Algorithms↗

PubMed1999

Estimating kinetic parameters from dynamic contrast-enhanced T(1)-weighted MRI of a diffusable tracer: standardized quantities and symbols.

We describe a standard set of quantity names and symbols related to the estimation of kinetic parameters from dynamic contrast-enhanced T(1)-weighted magnetic resonance imaging data, using diffusable agents such as gadopentetate dimeglumine (Gd-DTPA). These include a) the volume transfer constant K(trans) (min(-1)); b) the volume of extravascular extracellular space (EES) per unit volume of tissue v(e) (0 < v(e) < 1); and c) the flux rate constant between EES and plasma k(ep) (min(-1)). The rate constant is the ratio of the transfer constant to the EES (k(ep) = K(trans)/v(e)). Under flow-limited conditions K(trans) equals the blood plasma flow per unit volume of tissue; under permeability-limited conditions K(trans) equals the permeability surface area product per unit volume of tissue. We relate these quantities to previously published work from our groups; our future publications will refer to these standardized terms, and we propose that these be adopted as international standards.

Contrast Media↗

PubMed1996

Pedigree analysis package vs. MIXD: fitting the mixed model on a large pedigree.

Results of a simulation study with two methods of analysis of data simulated under the mixed model on a 232-member pedigree are presented. The programs Pedigree Analysis Package (PAP), which approximate the likelihoods needed in a complex segregation analysis, and MIXD, which uses Monte Carlo Markov chain (MCMC), to estimate likelihoods were used. PAP obtained unbiased estimates of the major locus genotype means and the gene frequency, but biased estimates of the environmental variance component, and thus the heritability. A substantial fraction of the runs did not converge to an internal set of parameter estimates when analyzed with PAP. MIXD, which uses the Gibbs sampler to perform the MCMC sampling, produced unbiased estimates of all parameters with considerably more accuracy than obtained with PAP, and did not suffer from convergence of estimates to the boundary of the parameter space. The difference in behavior and accuracy of parameter estimates between PAP and MIXD was most apparent for models with either high or low residual additive genetic variance. Thus in situations where accuracy of the model is important, use of MCMC methods may be useful. In situations where less accuracy is needed, approximation methods may be adequate. Practical issues in using MCMC as implemented in MIXD to fit the mixed model are also discussed. Results of the simulations indicate that, unlike PAP, the starting configurations of most parameter estimates do not substantially influence the final parameter estimates in analysis with MIXD.

Analysis of Variance↗

PubMed1985

Mathematical models of arterial transmural transport.

A finite-element model (FEM) and corresponding five-parameter analytical model (AM) were derived to study the one-dimensional transport of chemically reactive macro-molecules across (x) arterial tissue. Derivations emphasize chemical activity [a(x)], its gradient, and water flux as driving forces for chemical reactions and transport. The AM was fitted to 28 measured 125I-albumin transmural concentration [c(x)] curves giving parameter estimates of diffusivity (DA), convective velocity (nu A), and so on as functions of pressure (P), location (z) along the vessel, etc. The FEM was used to study 1) intimal-medial a(x) associated with molecular sieving and medial edema, 2) reversible binding, and 3) errors of AM in analysis of c(x). Results are as follows. Average relative error for the 28 AM fits was 5.3%. Only estimates of DA and nu A had acceptable coefficients of variation. DA (approximately 0.10 X 10(-7) cm2 X s-1) decreased with P, increased with z to a maximum, and then decreased; nu A was approximately proportional to P (approximately 0.12 X 10(-7) cm X s-1 X mmHg-1) and decreased slightly with z; distribution coefficient (epsilon F) decreased with z and was smaller for serum than for simple albumin reagent. Assumed boundary conditions for AM were associated with approximately 1.4% error in AM c(x). Parameter estimates were sensitive to wall inhomogeneity, e.g., approximately 15% error. In conclusion, the AM and FEM simulated measured c(x) well; the FEM is useful for study of mechanisms, experimental designs, and AM errors; trends of AM parameter estimates suggest dependence on P, z, and composition of reagent for further FEM and experimental study.

Arteries↗

PubMed1992

Estimation of unbound concentrations of morphine from microdialysate concentrations by use of nonlinear regression analysis in vivo and in vitro during steady state conditions.

The unbound concentration of morphine in striatum of rats was estimated during a constant rate infusion of morphine 14 mumol/h*kg, by use of the microdialysis technique and nonlinear regression analysis. The concentrations in plasma of morphine and its metabolite, morphine-3-glucuronide, were 4.2 +/- 1.4 microM and 7.7 +/- 4.0 microM, respectively, during the constant rate infusion. The corresponding estimated unbound concentrations of morphine in striatum varied between 0.06 and 0.11 microM. No morphine-3-glucuronide was detected in the brain dialysates. The unbound concentration in striatum was lower than expected based on unbound plasma concentrations and could be an indication of active transport from the brain. Five different equations were tested to find the best empirical description of the relationship between microdialysate concentration and perfusion rate by nonlinear regression analysis. The equations were validated by a serum in vitro study, where three unbound concentrations of morphine estimated from microdialyis were compared to estimates obtained from equilibrium dialysis. The precision of the parameter estimates obtained from the five equations was tested by Monte Carlo simulations. One of the equations (Eq. 4) was selected in preference to the others, because of the good agreement with the estimated unbound concentration obtained by equilibrium dialysis in vitro, and good precision of the parameter estimates. The method described in this paper is valuable when estimating the unbound concentration of drug from microdialysate concentrations during steady state conditions. Furthermore, the method is easily accessible when working in the pharmacokinetic and pharmacodynamic field.

Animals↗

PubMed2000

Evaluation and extensions of a structural equation modeling approach to the analysis of survival data.

Recently a new method for the analysis of survival data using a structural equation modeling approach has been suggested by Pickles and colleagues using twin data they demonstrated the application of this model to study the correlation in age of onset. The purpose of the current research is twofold: 1) to evaluate the statistical performance of the model as presented by Pickles and colleagues, and 2) to expand and evaluate the model in more applications, including both genetically informative data and other multivariate examples. Results evaluated from this study involve three areas of method performance: Type-I error rates, power, and parameter estimates under four different distributions (normal, Gamma-2, Gamma-6 and g-and-h) and four different sample sizes (n = 125, 250, 500 and 750). Results based on the original Pickles model indicated that in all sample size and distribution conditions the Type-I error rate was adequate, in fact below the nominal level of .05. Additionally, power was greater than .80 for sample sizes of 500 or more for all distribution conditions. Parameter estimates were upwardly biased when the population value was rho = .20. This bias varied across distributions; the g-and-h distribution showed the largest bias. Results from the expanded model indicated that Type-I error rates were adequate. Power results were not affected by distribution type; sample sizes of 500 were above the .80 level. Parameter estimates continued to be upwardly biased in this more general model, although the degree of bias was smaller.

Bias↗

PubMed1995

An indicator quantitatively comparing two treatment effect sizes on responder and non-responder groups--exponential of estimated interaction parameter.

Sometimes a specific treatment is effective in one subgroup but not in another. An indicator allowing quantitative comparison of treatment effect in two subgroups would be useful in clinical medicine. We have developed such an indicator. It is obtained by calculations using Cox's proportional hazard or logistic model with therapy, subgroup, and confounding explanatory variables. The parameter of the interaction between therapy and subgroup can be estimated and tested statistically. The exponential value of the interaction parameter is what we tentatively call the "hazard ratio ratio", meaning the ratio between the treatment effects in two subgroups. The 95% confidence interval of the indicator can also be calculated. As a numerical example, the hazard ratio between the survival times of postoperative gastric cancer patients treated by adjuvant immunochemotherapy and patients without adjuvant immunochemotherapy in a subgroup with high serum glycosidically bound sialic acid (SA) level was lower than that in a low-SA subgroup using an estimate for hazard ratio ratio of less than 0.5 with statistical significance. We propose this indicator be used as a "responder/non-responder ratio" of therapy effect.

Antibiotics, Antineoplastic↗

PubMed1988

Parameter identification of the human lower limb under dynamic, transient torsional loading.

The response of the lower limb to dynamic, transient torsional loading applied at the foot has been measured for a male test subject. The dynamic loading was provided by a computer controlled pneumatic system which applied single haversine (i.e. half cycle of a sine wave) axial moment pulses of variable amplitude (0-100 Nm) and duration (50-600 ms). Potentiometers measured the absolute rotations of the three leg segments. Test variables included rotation direction, weight bearing and joint flexion. Two approaches were explored for specifying parameters (i.e. inertia, damping, stiffness) of a three degree-of-freedom dynamic system model which best duplicated the measured response. One approach involved identification of linear parameters by means of optimization while the other approach entailed estimation. Parameter estimates, which included non-linear, asymmetric stiffness functions, were derived from the literature. The optimization was undertaken so as to identify parameter dependence on test variables. Results indicate that parameter values are influenced by test variables. Results also indicate that the non-linear, estimated model better approximates the experimental data than the linear, identified model. In addition to identifying parameters of a three degree-of-freedom model, parameters were also identified for a single degree-of-freedom model where the motion variable was intended to indicate the rotation of the in vivo knee. It is concluded that the simpler model offers good accuracy in predicting both magnitude and time of occurrence of peak knee axial rotations. Model motion fails to track the measured knee rotation subsequent to the peak, however.

Ankle Joint↗

PubMed2006

Characterizing phase-only fMRI data with an angular regression model.

FMRI voxel time series are complex-valued with real and imaginary parts that are usually converted to magnitude-phase polar coordinates. Magnitude-only data models that discard the phase portion of the data have dominated fMRI analysis. However, when such analyses are performed, the data that is discarded may contain valuable biologic information that is not in the magnitude data. This biologic information from BOLD fMRI data may be vascular [Menon RS. Postacquisition suppression of large-vessel BOLD signals in high-resolution fMRI. Magn Reson Med 2002;47(1):1-9] or neuronal [Bodurka J, Jesmanowicz A, Hyde JS, Xu H, Estowski L, Li S-J. Current-induced magnetic resonance phase imaging. J Magn Reson 1999;137(1):265-71] in origin. When phase-only time series that discard the magnitude portion of the data have been analyzed, ordinary least squares (OLS) regression has been the technique of choice. However, OLS models may fit poorly when phase-wrap or low signal-to-noise ratio (SNR) is present. We have explored alternatives to the OLS model which will account for the angular response of the phase while also allowing us the flexibility to develop similar hypothesis tests. We adopt an angular regression model by Fisher and Lee [Fisher NI, Lee AJ. Regression models for an angular response. Biometrics 1992;48:665-77] for our analysis and show its improvement over the OLS model at low SNR in terms of both parameter estimation and inferences. We found an improvement in parameter estimation along with modeling for the Fisher and Lee method in simulated data while detailing potential benefits when used with experimentally acquired data. Finally, we look at a map of the statistics testing the association of the observed voxel phase time course and the reference function in our acquired data. This shows the possible detection of biological information in the generally discarded phase.

Algorithms↗