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PubMed1986

A mathematical model of survival kinetics. II. Parameter estimation.

Procedures for the estimation of the four parameters of a new mathematical model of survival and mortality kinetics are given. A formulation of the model has been found which had the advantage of maintaining three of four parameters independent of the unit chosen for the age; in addition, two of these parameters have values falling in a narrow range, even when the model is applied to rather different curves. Since, in any problem of this type, the initial estimate of the parameters plays a major role in the achievement of good final estimates, some simple methods of estimation are indicated based upon the characteristics of the function. The initial estimates may enter three different types of procedures; the best one can be chosen according to the precision of the initial estimates. The method is capable of fitting both survivorship and dying functions directly to the empirical data. An interactive approach to the computer facilities has been used as at each step the operator has to decide whether or not to apply a corrective factor. Goodness of fit, usually high, is estimated by chi 2 test.

Aging↗
PubMed1988

The Gemini conundrum--a problem of unpairable data: statistical comparison of ratios each derived from two separately estimated parameters.

In biological studies it may be necessary to compare ratios of two separately estimated parameters under test and control conditions. Since it is not always possible technically to obtain paired data for the two parameters, how does one take account of their variances? By extending previously described approximations in a modified t-test we present a BASIC computer program which may be used to solve this problem.

Algorithms↗
PubMed1979

A program package for simulation and parameter estimation in pharmacokinetic systems.

A set of programs is presented which has been developed for parameter estimation and simulation of models arising from pharmacokinetic applications. The programs can accommodate linear and nonlinear models with multiple inputs and multiple outputs. When the model is defined by differential equations, non-uniform repetitive dosage regimens can be handled. The model may also be entered in integrated form when single dose studies or uniform multiple dose studies are being considered. The programs employ a variable-step, variable-order integration routine to solve the model differential equations, and the Nelder-Mead simplex procedure to determine the parameter values which minimize a weighted least squares criterion. The programs have been written for an interactive time-sharing environment with the experimental data and model equations stored in files for future use.

Computers↗
PubMed1992

Analysis of variance of parameter estimates: F tests and t tests.

The problem of comparing and pooling experimentally independent estimates of a parameter such as a Michaelis constant (K) has been treated as a simple analysis of variance of "within" and "between" set deviations from the fitted variable (v). As applied to assessing the reproducibility of multiple estimates of the same K, this is identical to the procedure of Duggleby (Anal. Biochem. 189, 84-87, 1990). However, the theory developed here shows that applying Duggleby's procedure to the comparison of two experiments (each consisting of multiple data sets) depends critically on the assumption of equal errors within and between the individual sets, i.e., Fvb vw = s2wv/s2bv is close to 1. Application of the method when this is not the case will underestimate the common error (s2rv), overestimate its associated degrees of freedom (vr = vb+vw), and may suggest apparently significant differences where there are none. The theory also shows that this situation is an instance of the Fisher-Behrens problem and shows how Welch's solution can be applied. This gives the between set error s2bv as the corrected estimate of the common error and the corrected degrees of freedom as a simple function of vb, vw, and Fvb vw. When the nine prephenate dehydratase data sets which originally showed three apparently significant differences were reanalyzed in this way, all the variations in K were found to be within the range of the experimental error.

Analysis of Variance↗
PubMed1978

ESTRIP, a BASIC computer program for obtaining initial polyexponential parameter estimates.

A new BASIC exponential stripping program, ESTRIP, allows the relatively rapid calculation of initial polyexponential parameter estimates, as does the previously published FORTRAN IV program, CSTRIP. The potential advantages of the new program are that it can be run on microcomputers and minicomputers with BASIC capability and a relatively small core and that it can be easily modified by the user.

Computers↗
PubMed1990

Nonlinear parameter estimation applied to a model of smooth pursuit eye movements.

We present a procedure that optimally adjusts specified parameters of a mathematical model to describe a set of measured data. The technique integrates a dynamic systems-simulation language with a robust algorithm for nonlinear parameter estimation, and it can be implemented on a microcomputer. Sensitivity functions are generated that indicate how the operation of the model is affected by each updated parameter. This procedure offers a greater resolution of optimal parameter values than other, less rigorous methods. To illustrate this technique we have applied it to the model of human smooth pursuit eye movements proposed by D.A. Robinson and colleagues (1986).

Eye Movements↗
PubMed1990

A method for binding parameters estimation of A1 adenosine receptor subtype: a practical approach.

Working with pig brain striatum in which A1 and A2 adenosine receptor subtypes coexist, we describe an uncomplicated method for unequivocally obtaining the equilibrium parameters (KD and binding capacity) of A1 receptor without interference from ligand binding to A2 receptor. Also, the equilibrium parameter estimation method we propose avoids the experimental determination of nonspecific binding by the inclusion of the corresponding unknown parameter in the function. This not only saves time but also avoids the use of expensive radioligands in saturation experiments. The method is suitable for any system with two different receptor subtypes for the same physiological ligand, and good estimates of the equilibrium parameters corresponding to the subtype displaying the higher affinity for the ligand can be obtained.

Adenosine↗
PubMed1977

Kinetic parameter estimation by numerical algorithms and multiple linear regression: theoretical.

A new method is presented for the determination of kinetic parameters based on a functional relationship among experimental data derived from the postulated model. The data, even though containing errors, are manifestations of this relationship, which should be satisfied by parameters fitted to the system. The procedure involves the use of numerical integration and/or differentiation of the data, followed by multiple linear regression. It does not require initial estimates or repetitive iteration for linear systems and can be applied to nonlinear models. The accuracy of estimated parameter depends on the goodness of the particular numerical approximation method used.

Computers↗
PubMedDate not supplied

Nonlinear gradient isotherm parameter estimation for proteins with consideration of salt competition and multiple forms.

Salt gradients in ion-exchange chromatography are routinely used to speed separation of proteins and to concentrate products, but systematic optimization of these gradients requires protein equilibrium data as a function of salt concentration. An understanding of conformational changes, aggregation, and salt effects, which include both competition and affinity modulation, is important for equilibrium isotherm parameter estimation. In this study, gradient elution of bovine serum albumin (BSA) in anion exchange was well predicted by a salt-modulated nonlinear isotherm which considers salt competition. The isotherm was able to predict BSA gradient elution from batch equilibrium data. The same isotherm was also able to predict elution for various gradient slopes when fitted to an intermediate slope gradient experiment. If multiple forms due to aggregation or denaturation exist, isotherm parameters are readily averaged in batch experiments because of the long equilibration times. Similarly, gradient experiments yield averaged parameters because the salt gradient tends to merge the closely eluting forms. However, in isocractic elution, if the reaction rate is not rapid enough to give a merged peak, the estimated isotherm parameters are only fair predictors of gradient behavior and vice versa. Slower flow rates in isocratic elution can help reduce the discrepancy by allowing forms to merge through interconversion. As an alternative to determining averaged parameters, consideration of two binding forms, using VERSE-LC, an advanced rate model, gave good agreement with experimental data over the entire range of salt gradient durations.

Animals↗
PubMed1990

Evaluation of six gentamicin nomograms using a bayesian parameter estimation program.

A new set of guidelines for the administration of gentamicin was developed by estimating steady-state peak and trough gentamicin concentrations for simulated patients with known weights and creatinine clearances. The most appropriate doses to achieve target peak concentrations of 5-10 mg/L and troughs of less than 2 mg/L were then tabulated. The performance of these new guidelines was assessed using data collected from 60 patients who had received gentamicin and had at least two serum concentration measurements. Individual estimates of clearance and volume of distribution were obtained using a Bayesian parameter estimation program and these estimates were used to predict the steady-state peak and trough concentrations that would arise from the new guidelines and five other previously published nomograms (Mawer, Chan, Hull-Sarubbi, Rule of Eight, and Dettli). The new guidelines, the Dettli nomogram, and the Hull-Sarubbi table achieved similar percentages (52-57%) of patients within the target ranges (5-10 mg/L for peak and less than 2 mg/L for trough), although 28% of patients had predicted peak concentrations below 5 mg/L with the new method compared to 15% with the other two. Only 38% of patients were within both ranges when the Mawer nomogram and the Rule of Eight methods were used. Since a large percentage of patients would have achieved concentrations outside of the target ranges no matter which nomogram was used, serum concentration monitoring is still recommended to confirm dose requirements.

Bayes Theorem↗
PubMed1992

Transport parameter estimation from lymph measurements and the Patlak equation.

Two methods of estimating protein transport parameters for plasma-to-lymph transport data are presented. Both use IBM-compatible computers to obtain least-squares parameters for the solvent drag reflection coefficient and the permeability-surface area product using the Patlak equation. A matrix search approach is described, and the speed and convenience of this are compared with a commercially available gradient method. The results from both of these methods were different from those of a method reported by Reed, Townsley, and Taylor [Am. J. Physiol. 257 (Heart Circ. Physiol. 26): H1037-H1041, 1989]. It is shown that the Reed et al. method contains a systematic error. It is also shown that diffusion always plays an important role for transmembrane transport at the exit end of a membrane channel under all conditions of lymph flow rate and that the statement that diffusion becomes zero at high lymph flow rate depends on a mathematical definition of diffusion.

Animals↗
PubMed1989

The influence of assay variability on pharmacokinetic parameter estimation.

The impact of assay variability on pharmacokinetic modeling was investigated. Simulated replications (150) of three "individuals" resulted in 450 data sets. A one-compartment model with first-order absorption was simulated. Random assay errors of 10, 20, or 30% were introduced and the ratio of absorption rate (Ka) to elimination rate (Ke) constants was 2, 10, or 20. The analyst was blinded as to the rate constants chosen for the simulations. Parameter estimates from the sequential method (Ke estimated with log-linear regression followed by estimation of Ka) and nonlinear regression with various weighting schemes were compared. NONMEM was run on the 9 data sets as well. Assay error caused a sizable number of curves to have apparent multicompartmental distribution or complex absorption kinetic characteristics. Routinely tabulated parameters (maximum concentration, area under the curve, and, to a lesser extent, mean residence time) were consistently overestimated as assay error increased. When Ka/Ke = 2, all methods except NONMEM underestimated Ke, overestimated Ka, and overestimated apparent volume of distribution. These significant biases increased with the magnitude of assay error. With improper weighting, nonlinear regression significantly overestimated Ke when Ka/Ke = 20. In general, however, the sequential approach was most biased and least precise. Although no interindividual variability was included in the simulations, estimation error caused large standard deviations to be associated with derived parameters, which would be interpreted as interindividual error in a nonsimulation environment. NONMEM, however, acceptably estimated all parameters and variabilities. Routinely applied pharmacokinetic estimation methods do not consistently provide unbiased answers. In the specific case of extended-release drug formulations, there is clearly a possibility that certain estimation methods yield Ka and relative bioavailability estimates that would be imprecise and biased.

Biometry↗
PubMed1991

In vivo NMR spectral parameter estimation: a comparison between time and frequency domain methods.

We have compared various methods of in vivo NMR spectral parameter estimation, namely a nonlinear fit of the free induction decay signal in the time domain (NLTD), a nonlinear fit of the fast Fourier transform of the FID data in the frequency domain using either a continuous Lorentzian model (NLLM) or a Fourier-sampled model (NLFM), and a time-domain linear prediction method using singular value decomposition (LPSVD). Monte Carlo simulations of 31P and 13C in vivo experiments were used to assess the bias and statistical uncertainties of spectral parameters obtained with each method. In the 31P case, all methods appear to be equivalent except the LPSVD method that led to significantly biased peak amplitudes (up to 28%). In the 13C case, the only methods able to recover the glycogen peak were the NLTD method and its equivalent in the frequency domain (NLFM). In both the 31P and the 13C cases simulations demonstrated that 256 data points were sufficient. These results demonstrate the feasibility and the robustness of a nonlinear fit of the FID data in the time domain, and we illustrate this on 31P and 13C data sets obtained in humans.

Algorithms↗
PubMed1987

A note on confidence intervals with extended least squares parameter estimates.

It has previously been shown that the extended least squares (ELS) method for fitting pharmacokinetic models behaves better than other methods when there is possible heteroscedasticity (unequal error variance) in the data. Confidence intervals for pharmacokinetic parameters, at the target confidence level of 95%, computed in simulations with several pharmacokinetic and error variance models, using a theoretically reasonable approximation to the asymptotic covariance matrix of the ELS parameter estimator, are found to include the true parameter values considerably less than 95% of the time. Intervals with the ordinary least squares method perform better. Two adjustments to the ELS confidence intervals, taken together, result in better performance. These are: (i) apply a bias correction to the ELS estimate of variance, which results in wider confidence intervals, and (ii) use confidence intervals with a target level of 99% to obtain confidence intervals with actual level closer to 95%. Kineticists wishing to use the ELS method may wish to use these adjustments.

Kinetics↗
PubMed1991

Investigation of parameter estimator and adaptive controller for assist pump by computer simulation.

The multi-output adaptive controller of a left ventricular assist device (LVAD) was studied by computer simulation. The controller regulated two outputs--mean aortic pressure (mAoP) and mean atrial pressure (mLAP)--by regulating vacuum pressure (input). The autoregressive models were used to describe the circulatory system. The parameters of the models were estimated by the recursive least squares method. Based on the autoregressive models, the vacuum pressure minimizing a performance index was searched. The index used was the weighted summation of the square errors. Responses of the adaptive controller were simulated when the contractility of the left ventricle was decreased at various rates and the peripheral resistance was changed. Both the mAoP and mLAP were controlled to their predicted values in the steady state. The steady-state errors of the mAoP were less than a few mm Hg, and those of the mLAP were lower than 1 mm Hg. Consequently, the estimated parameters can be regarded as true parameters, and the adaptive controller has the potential to control more than two outputs. The multioutput adaptive controller studied is useful in controlling the LVAD according to the change in circulatory condition.

Aorta, Thoracic↗
PubMed1976

CSTRIP, a fortran IV computer program for obtaining initial polyexponential parameter estimates.

A new exponential stripping program, CSTRIP, has been developed. This program overcomes the problems associated with the use of previously published techniques and enables the rapid economical calculation of initial polyexponential parameter estimates. Values for the coefficients and exponents of the exponential terms are calculated as well as estimates of lag times. An exhaustive search procedure ensures that the results are comparable to, or better than, those obtained by manual residual methods.

Computers↗
PubMed1992

Model parameters estimation when the evoked potential recordings are affected by a random scale factor.

In many situations an important source of the average evoked potentials (EPs) variability is a random scale factor affecting each recording. As a result, the outcome of any EP detection method may be greatly affected. However, using an appropriate probabilistic model these scale factor can be estimated, and the performance of any available detection index improved by data rescaling. In this paper the Maximum Likelihood Estimators of the waveform of the response and the scale factor affecting both background noise and this waveform are obtained. Also, an iterative algorithm for model parameters estimation is presented and its convergence is examined in a simulation study. The Linear Discriminant function is computed using simulated test data in both situations, before and after rescaling of recordings. The performance of these statistics is evaluated by mean of ROC curves.

Algorithms↗
PubMed1989

Source parameter estimation in inhomogeneous volume conductors of arbitrary shape.

In this paper it is demonstrated that the use of a direct matrix inverse in the solution of the forward problem in volume conduction problems greatly facilitates the application of standard, nonlinear parameter estimation procedures for finding the strength as well as the location of current sources inside an inhomogeneous volume conductor of arbitrary shape from potential measurements at the outer surface (inverse procedure). This, in turn, facilitates the inclusion of a priori constraints. Where possible, the performance of the method is compared to that of the Gabor-Nelson method. Applications are in the fields of bioelectricity (e.g., electrocardiography and electroencephalography).

Electric Conductivity↗