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PubMed1992

Effects of violating local independence on IRT parameter estimation for the Binomial Trials Model.

The appropriateness of the Binomial Trials Model for test data that consist of multiple attempts of the same item needs to be determined because the presence of learning or fatigue effects may violate the model's assumption of local independence. The purpose of this study was to determine what effect the severity of the violation of local independence (VLI), coupled with different sample size (SS), test length (TL), and test difficulty (TD) had on the estimation of the model difficulty parameter, b, using computer simulation techniques. Each of the following conditions was replicated 100 times under a completely crossed design: SS (100, 200, 500, 2,000); TL (5, 10, 20, 25 attempts); TD (-1.2, 0.0, 1.2); and VLI (from no violation to complete violation). Examinee ability or latent trait was pseudorandomly drawn from a standard normal distribution, and the b-parameter was estimated using a maximum likelihood procedure on generated test scores. Regardless of SS, TL, and TD, the b-parameter tended to be overestimated for situations in which the VLI condition simulated fatigue and underestimated when the VLI condition simulated late-test learning or practice effect. The findings suggest that violations of local independence, at least as simulated in this study, could seriously bias the difficulty parameter estimates if all examinees tested exhibited the dependency.

Bias↗
PubMed1990

Evaluation of population (NONMEM) pharmacokinetic parameter estimates.

The application of population pharmacokinetic analysis has received increasing attention in the last few years. The main goal of this report is to make investigators aware of the necessity of independent evaluation of the results obtained from a population analysis based on observational studies. We also describe with the help of a specific example (a new synthetic opiate Alfentanil) how such evaluation can be performed for parameter estimates obtained with the software system NONMEM. The method differs depending on the type of serum concentration data that are used for the evaluation. A general method is described, based on the regression model used in NONMEM, that can test for bias in the estimates of fixed and random effects independent of the number of observations per patient and dosing. Since the procedure for testing for statistically significant bias in the prediction of the average concentration and its variability can be relatively complex, we propose that generally available program packages performing estimation of the pharmacokinetic parameters from observational data should contain the necessary software to evaluate the reliability of the parameter estimates on a second data set.

Alfentanil↗
PubMed1990

Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments.

An experiment design procedure is proposed for nonlinear parameter estimation studies that formally incorporates prior parameter uncertainty. The design criterion derives from information theory considerations and involves an asymptotic interpretation of the expected posterior information provided by an experiment. A pharmacokinetic sample schedule design problem is used to illustrate and evaluate this information theoretic design strategy. The model considered is commonly used to describe the plasma concentration of a drug following its oral administration. The limitations and advantages of the proposed design procedure are discussed in relation to other previously reported design techniques for incorporating parameter uncertainty.

Administration, Oral↗
PubMed1990

A comparison of the parameter estimating procedures for the Michaelis-Menten model.

The performance of four parameter estimating procedures for the estimation of the adjustable parameters in the Michaelis-Menten model, the maximum initial rate Vmax, and the Michaelis-Menten constant Km, including Lineweaver & Burk transformation (L-B), Eadie & Hofstee transformation (E-H), Eisenthal & Cornish-Bowden transformation (ECB), and Hsu & Tseng random search (H-T) is compared. The analysis of the simulated data reveals the followings: (i) Vmax can be estimated more precisely than Km. (ii) The sum of square errors, from the smallest to the largest, follows the sequence H-T, E-H, ECB, L-B. (iii) Considering the sum of square errors, relative error, and computing time, the overall performance follows the sequence H-T, L-B, E-H, ECB, from the best to the worst. (iv) The performance of E-H and ECB are on the same level. (v) L-B and E-H are appropriate for pricesly measured data. H-T should be adopted for data whose error level are high. (vi) Increasing the number of data points has a positive effect on the performance of H-T, and a negative effect on the performance of L-B, E-H, and ECB.

Animals↗
PubMed1990

Experimental design and efficient parameter estimation in population pharmacokinetics.

A computer simulation technique used to evaluate the influence of several aspects of sampling designs on the efficiency of population pharmacokinetic parameter estimation is described. Although the simulations are restricted to the one-compartment one-exponential model, they provide the basis for a discussion of the structural aspects involved in designing a population study. These aspects include number of subjects required, number of samples per subject, and timing of these samples. Parameter estimates obtained from different sampling schedules based on two- and three-point designs are evaluated in terms of accuracy and precision. These simulated data sets include noise terms for both inter- and intraindividual variability. The results show that the population fixed-effect parameters (mean clearance and mean volume of distribution) for this simple pharmacokinetic model are efficiently estimated for most of the sampling schedules when two or three points are used, but the random-effect parameters (describing inter- and intraindividual variability) are inaccurate and imprecise for most of the sampling schedules when only two points are used. This drawback was remedied by increasing the number of data points per individual to three.

Computer Simulation↗
PubMed1991

Genetic and environmental growth trait parameter estimates for Brahman and Brahman-derivative cattle.

Beefmaster, Brahman, Brangus, and Santa Gertrudis field data records were used to determine genetic and environmental parameter estimates using a multiple-trait, pseudo-expectation approach. Adjusted birth weight, 205-d weight, and postweaning gain records were analyzed for each breed. Also, Brangus weaning sheath and navel scores were both analyzed using a single-trait, pseudo-expectation method to determine genetic parameter estimates. Additive birth weight heritability (h2A) estimates ranged from .22 to .37 and maternal birth weight heritability (h2M) estimates ranged from .12 to .55. Estimates for 205-d weight h2A for the four breeds varied from .21 to .25, and 205-d weight h2M estimates ranged from .15 to .21. Postweaning gain h2A estimates ranged from .16 to .56. The genetic correlation between direct and maternal portions of birth weight was negative for all breeds. This was also true for the genetic correlation between direct and maternal portions of 205-d weight, except in Brahman cattle, for which it was .15. The genetic correlation between additive portions of birth weight and 205-d weight was large and positive in all breeds. A moderately positive correlation between 205-d weight and postweaning gain was found for all breeds except Santa Gertrudis, whereas the environmental correlation between these two traits was a small to moderately negative estimate in all breeds. Brangus weaning sheath and navel score heritabilities indicated that genetic change for the size and shape of the sheath and navel area is possible.

Analysis of Variance↗
PubMed1991

Identification of compartmental models for perturbed cell populations using state-space parameter estimation techniques.

Multiple compartment models for describing synchronous cell kinetics in which cell populations are characterized by DNA content are reviewed. These models are useful for understanding and predicting a cell population's dynamic response to perturbations induced by drugs or radiation. A practical approach is proposed for determining the parameters of these models from empirical cell-cycle data. Specifically, a state-space parameter estimation algorithm based on the maximum likelihood method--developed and coded primarily for engineering applications and commercially available for personal computers and minicomputers--can be applied to DNA specific cell-cycle measurements from synchronized cell populations to produce model parameter estimates. This is demonstrated using published data from a cell-cycle experiment. The results show that the procedure works well, and that with careful experimental planning even better results should be possible. Since the compartmental model is often used to represent biological systems, this approach is widely applicable.

Algorithms↗
PubMed1979

Selection of optimal model for the DNA histogram by analysis of error of estimated parameters.

The ability of four different mathematical models of the DNA histogram to give accurate estimates for the fractions of cells in G1, S, and G2 + M has been investigated. The models studied differ in the form and number of parameters of the function used to represent cells in S-phase. Results obtained from simulated DNA histograms suggest that the standard deviations of the model parameters increase exponentially with the width of the G1 and G2 + M peaks of the histogram. Error analysis is presented as a method to select a model of optimal complexity in relation to the resolution provided by the data in a given set of DNA histograms. Introduction of additional parameters improves the agreement between model and data but may result in a less well-posed model. A model with an optimal number of parameters can therefore be found that will yield parameter estimates with the smallest possible standard deviations.

Cell Cycle↗
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↗