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PubMed1984

Statistical prediction of drug stability based on nonlinear parameter estimation.

The classical approach in Arrhenius prediction of drug stability uses two sequential steps of linear regression involving (a) a function of drug content versus time to obtain the rate constants (k) at several elevated temperatures and (b) the relationship of logarithm of mean k versus reciprocal temperature to predict the room temperature rate constant and hence the shelf-life of the drug. Uncertainties in drug content determinations are often neglected in the second regression. The classical approach also provides a wide and unsymmetrical 95% confidence interval for the predicted shelf-life. We have developed equations which allow for direct statistical prediction of shelf-life using observed values of drug content, time, and temperature. Nonlinear regression analysis was employed to provide parameter estimates of drug shelf-life and the energy of activation. The developed approach was shown to provide good estimates of shelf-life with meaningful statistics of reactions over a wide range of stability and energetics, with various kinetic orders, with different levels of noise in the data, and with different types of data structure. Comparison between the nonlinear approach and the classical approach showed that the nonlinear approach provided better mean estimates of shelf-life with much smaller and more symmetrical 95% confidence intervals than the classical approach. The method appears sufficiently robust and wide-ranging as to be potentially applicable for the prediction of the drug stability of pharmaceutical products.

Chemistry, Pharmaceutical↗
PubMed1992

Arm function after axillary dissection for breast cancer: a pilot study to provide parameter estimates.

Sixty-three women participated in a study in Calgary, Alberta to assess the rate of arm recovery and factors affecting it up to one year after axillary node dissection for breast cancer. Outcomes included objective measures of swelling, mobility, and strength, and subjective assessments of pain (at rest and with movement) and stiffness. Approximately 42% of women had residual impairment of at least one type one year after surgery, the most common problems being pain (16%) and reduced grip strength (16%). Except for lymphedema, measurements one year after surgery showed little change from measurements at 6 months, suggesting that the shorter follow-up may be appropriate for assessing the long term effects of axillary dissection. Lymphedema was the only sequela which increased over time. The results provide parameter estimates for designing studies to evaluate the role of physiotherapy after axillary dissection.

Arm↗
PubMed1995

Parameter estimation of labial movements in speech production: implications for speech motor control.

Central to theories of speech motor control are estimates on magnitudes of lip activity expressed in terms of central tendency, variability, and interrelatedness. In fact, the tenability of each of two competing theories of motor control for speech production rests solely on the observation of the predicted direction of the correlation coefficient (one positive and one negative) that indexes the relationship of concurrent lip activity. Each theory, however, predicts a relationship that is the complete opposite of the relationship predicted by the other. That is, one theory proposes that the labial system functions on the basis of complementary variation, whereas the other assumes positive covariation, or complementary modulation. In apparent contradiction, each prediction has been observed under laboratory conditions. The explanation for this apparent contradiction resides in the small sample sizes upon which each estimate was based. The minimum number of observations that are necessary to achieve accurate estimates of lip displacement parameters has remained unclear. This paper addresses three fundamental questions: (a) how many observations of on-task behavior are necessary to accurately estimate mean and variance values for the magnitude of upper lip displacement in a speech production experiment?, (b) what is the analogous number of observations for estimating the same values of lower lip displacement (together with the mandible) in the same context?, and (c) how many observations are necessary to accurately estimate the correlation coefficient indexing the relationship of lip displacements during the production of speech? Answers to these questions are accomplished through a review of estimator properties, a Monte Carlo computer simulation, and through laboratory observations.(ABSTRACT TRUNCATED AT 250 WORDS)

Humans↗
PubMed1992

Parameter estimation for carcass traits including growth information of Simmental beef cattle using restricted maximum likelihood with a multiple-trait model.

(Co)variance component estimates were computed for retail cuts per day of age (kilograms per day), cutability (percentage of carcass weight), and marbling score (1 through 11) using a multiple-trait sire model. Restricted maximum likelihood estimates of (co)variance components were obtained via an expectation-maximization algorithm. Carcass data consisted of 8,265 progeny records collected by U.S. Simmental producers. Growth trait information (birth weight, weaning weight, and[or] postweaning gain) for those progeny with carcass data and an additional 5,405 contemporaries formed the complete data set for analysis. A total of 420 sires were represented. Three models differing in number of traits were investigated: 1) carcass traits with growth traits, 2) carcass traits only, and 3) single trait. The final models did not include postweaning gain because of convergence problems. Parameter estimates for all three models were essentially the same. Heritability estimates were .30, .18, and .23 for retail cuts per day, cutability, and marbling score, respectively. Correlations between growth and carcass traits were low except for those with retail cuts per day, which were moderate and positive. The additional information gained by adding growth traits to the carcass-traits-only evaluation lowered prediction error variances most for retail cuts per day. Little change in prediction error variances was found for cutability and marbling score. Inclusion of growth traits in future sire evaluations for carcass traits will benefit the evaluation of retail cuts per day but have considerably less effect on cutability and marbling score.

Analysis of Variance↗
PubMed1998

Error structure for the HPLC analysis for atenolol, metoprolol and propranolol: a useful weighting method in parameter estimation.

Three reversed-phase high performance liquid chromatography (HPLC) methods with UV detection were developed and fully validated for the quantification of three beta-blockers: atenolol, metoprolol and propranolol. After validation, error structures for the HPLC analysis were established using a convenient and practical procedure. The mean percentage of relative standard deviation (RSD) of the experimental concentrations (C), were less than 4.29% for proportionality and less than 3.68% for precision for any of the drugs, which allowed the quantitation of beta-blockers assayed at concentrations in the range 25-0.78 micrograms.ml-1. The error structures for the HPLC analysis were: SD (micrograms.ml-1) = 5.02 x 10(-2) C for atenolol, SD (micrograms.ml-1) = 4.55 x 10(-2) + 0.63 x 10(-2) C - 7.58 x 10(-6) C3 for metoprolol and SD (micrograms.ml-1) = 2.73 x 10(-2) C - 3.49 x 10(-4) C2 for propranolol. The reciprocal of the square of the SD of the drug concentrations measured within the calibration curve could be used as weighting methods in parameter estimation by non-linear regression.

Adrenergic beta-Antagonists↗
PubMed1997

Similarity or discrepancy in pharmacokinetic parameter estimation between bolus and infusion studies.

A recent study by Heatherington and Rowland showing discrepancies in steady-state volume of distribution (Vss) estimation of two barbiturates between bolus and infusion studies in rat hindlimb preparations was reviewed. Their rationale is that increasing the duration of administration may increase the accessibility for tissue distribution and thus increase Vss for compounds showing slow tissue uptake. Such a dosing-duration-dependent distribution concept is, however, inconsistent with the principle in linear kinetics that the fate or disposition function of any drug molecules is independent of time of administration and presence of other molecules. When their well-designed bolus studies were reanalyzed by including extrapolated outflow data from the last sampling time to infinity, the Vss values for the two barbiturates were found to be very similar to those obtained by the infusion method. Our analysis seems to validate a theoretical concept that parameter estimation is independent of the duration of administration in linear kinetics. A potential complication of using the bolus method to study Vss is presented.

Animals↗
PubMed1988

Effect of blood curve smearing on the accuracy of parameter estimates obtained for 82Rb/PET studies of blood-brain barrier permeability.

82Rb in conjunction with positron emission tomography (PET) has been used to estimate the blood to brain transport rate constant (K1) for Rb and the regional brain/tumour blood volume (Vb). Errors in K1 and Vb depend upon the accuracy of the measured arterial blood radioactivity and PET-monitored brain radioactivity. Arterial blood is usually sampled by placing a catheter in the radial artery and measuring the radioactivity in blood passing continuously in front of a detector or by counting discrete blood samples in a well scintillation detector. In either case, the passage of blood through catheter/pump tubing produces a smearing of the waveform as well as a delay in the arrival of radioactivity at the blood sampling site. The change in shape of the blood curve is significant for bolus-type injections and results in large errors in those model parameters which contribute substantially to the initial phase of the brain activity curve. We report here the results of computer simulations and an analysis of patient data which suggest that parameter estimation errors due to smearing and time shift may be large (greater than 50%) but that these errors can be minimised by the use of deconvolution techniques.

Blood-Brain Barrier↗
PubMed1985

Parameter estimation and sensitivity analysis of a nonlinearly elastic static lung model.

A model for the static pressure-volume behavior of the lung parenchyma based on a pseudo-elastic strain energy function was tested. Values of the model parameters and their variances were estimated by an optimal least-squares fit of the model-predicted pressures to the corresponding data from excised, saline-filled dog lungs. Although the model fit data from twelve lungs very well, the coefficients of variation for parameter values differed greatly. To analyze the sensitivity of the model output to its parameters, we examined an approximate Hessian, H, of the least-squares objective function. Based on the determinant and condition number of H, we were able to set formal criteria for choosing the most reliable estimates of parameter values and their variances. This in turn allowed us to specify a normal range of parameter values for these dog lungs. Thus the model not only describes static pressure-volume data, but also uses the data to estimate parameters from a fundamental constitutive equation. The optimal parameter estimation and sensitivity analysis developed here can be widely applied to other physiologic systems.

Animals↗
PubMed1989

Sensitivity analysis of the systemic circulation with a view to computer simulation and parameter estimation.

A sensitivity analysis study has been performed on a seven-parameter model of the systemic vascular bed in order to obtain structure reductions appropriate for simulation and estimation. This analysis considers separately the systolic and diastolic transfer functions between arterial and venous pressures in order to divide a non-linear problem in two distinct linear problems. The results obtained refer to nominal parameter values corresponding to normal circulatory conditions in man and supply guide-lines for an application-oriented selection of reduced models. Simple resistance-compliance models are preferred because the inertial effects appear to have only slight influence. In particular, the choice of a five-parameter model seems to be convenient for simulation purposes. An additional structure reduction is suggested to reach reliable results in parameter estimation problems. The resulting model is characterized by three elements: peripheral resistance, arterial compliance and venous compliance.

Blood Circulation↗
PubMed1985

Parameter estimates for a QALY utility model.

This paper discusses a utility model for quality adjusted life years (QALY). According to this model, the utility of Y years of survival in health state Q is bYrH(Q), where b is a scaling constant and r and H(Q) are parameters. The parameter r is shown to be interpretable as a representation of a patient's risk attitude with respect to survival duration. The parameter H(Q) represents the proportionate reduction in the utility of survival when health state Q prevails. Methods are described for estimating these parameters from the results of an individual patient utility assessment. Results are then reported for empirical estimation of parameters r and H(Q) from the preference judgments of a sample of 46 coronary artery disease patients. In this empirical study, health state Q takes on two values--survival with angina pectoris and survival free from angina pectoris. Estimated values of parameters r and H(Q) are discussed in relation to the decision analysis of coronary artery bypass graft surgery. Finally, it is argued that the model deserves consideration as a medical utility model, despite some preliminary evidence that assumptions of the model are descriptively false, because it provides a simple representation of the utility of survival duration and health quality. These aspects of health outcomes are known to be critically important in the expected utility analysis of health decisions.

Angina Pectoris↗
PubMed1995

Misclassification of a prognostic dichotomous variable: sample size and parameter estimate adjustment.

Under general conditions, Lagakos showed that for an explanatory variable observed with error, the asymptotic relative efficiency (ARE) when using the observed rather than the true values in linear models, logistic models and proportional hazards models for survival is the square of the correlation between the true and observed variables. The result is useful for sample size adjustment when this correlation is estimable. Often, one cannot observe correct values of the explanatory variable under any circumstances. We show, however, that under the models considered by Lagakos for a dichotomous explanatory variable, the ARE equals the kappa statistic in a read-reread protocol. Consequently, one need not know 'truth' in this situation to estimate the ARE and to adjust sample size to maintain desired power; divide the estimated sample size obtained with the assumption of no measurement error by the consistent estimate of the kappa statistic (which is unlikely to be zero or negative). We then develop heuristically an adjusted estimate of the beta parameter in a proportional hazards survival model. The work was motivated by analyses of the Childhood Brain Tumour Consortium database. Examples from this database illustrate the method.

Brain Neoplasms↗
PubMed1997

Multiple Parameter Estimation in an Adaptive Psychometric Method: MUEST, an Extension of the QUEST Method

An extension of the so-called QUEST method of Watson and Pelli (1979, 1983) is proposed. In contrast to the traditional QUEST method, the new method, the MUEST method, offers the possibility of simultaneously estimating more than one parameter of a parametric representation of the psychometric function. Knowledge about more parameters gives a higher guarantee of obtaining correct threshold values. The basic extension itself is analytically quite modest and can be explained in a few sentences. However, the involved additional techniques, like the placing of stimulus levels, require a more extensive description, which is presented here. Copyright 1997 Academic Press. Copyright 1997 Academic Press

Journal Article↗
PubMed1992

A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

The Akaike minimum information criterion provides a means to determine the appropriate number of lags in a linear autoregressive model of a time series. We show that the Akaike criterion is closely related to the reliability estimates of successively determined parameters of a linear autoregressive (LAR) model. A similar criterion may be applied to determine whether the addition of a nonlinear term to an LAR model provides a statistically significant improvement in the description of the time series. As an example, we use this method to identify quadratic contributions to a nonlinear autoregressive characterization of a typical 3/s spike and wave seizure discharge.

Data Interpretation, Statistical↗
PubMed2000

Nonlinear regression in parameter estimation from polarographic signals

In this work we describe a detailed treatment of polarographic data curves, including error analysis, by means of nonlinear least-squares in its standard form (or resorting to the errors in variables model). Error estimates for the related parameters are additionally verified by Monte-Carlo simulation and resampling techniques.

Journal Article↗
PubMed1998

A Metropolis Monte Carlo implementation of bayesian time-domain parameter estimation: application to coupling constant estimation from antiphase multiplets.

The Bayesian perspective on statistics asserts that it makes sense to speak of a probability of an unknown parameter having a particular value. Given a model for an observed, noise-corrupted signal, we may use Bayesian methods to estimate not only the most probable value for each parameter but also their distributions. We present an implementation of the Bayesian parameter estimation formalism developed by G. L. Bretthorst (1990, J. Magn. Reson. 88, 533) using the Metropolis Monte Carlo sampling algorithm to perform the parameter and error estimation. This allows us to make very few assumptions about the shape of the posterior distribution, and allows the easy introduction of prior knowledge about constraints among the model parameters. We present evidence that the error estimates obtained in this manner are realistic, and that the Monte Carlo approach can be used to accurately estimate coupling constants from antiphase doublets in synthetic and experimental data.

Algorithms↗
PubMedDate not supplied

Arterial windkessel parameter estimation: a new time-domain method.

We developed and validated a new, more accurate, and easily applied method for calculating the parameters of the three-element Windkessel to quantitate arterial properties and to investigate ventriculoarterial coupling. This method is based on integrating the governing differential equation of the three-element Windkessel and solving for arterial compliance. It accounts for the interaction between characteristic impedance and compliance, an important phenomenon that has been ignored by previously implemented methods. The new integral method was compared with four previously published methods as well as a new independent linear least-squares analysis, using ascending aortic micromanometric and volumetric flow measurements from eight dogs. The parameters calculated by the new integral method were found to be significantly different from those obtained by the previous methods but did not differ significantly from maximum likelihood estimators obtained by a linear least-squares approach. To assess the accuracy of parameter estimation, pressure and flow waveforms were reconstructed in the time domain by numerically solving the governing differential equation of the three-element Windkessel model. Standard deviations of reconstructed waveforms from the experimental ensemble-averaged waveforms, which solely reflect the relative accuracy of the Windkessel parameters given by the various methods, were calculated. The new integral method invariably yielded the smallest error. These results demonstrate the improved accuracy of our new integral method in estimating arterial parameters of the three-element Windkessel.

Animals↗
PubMed1978

Program to estimate parameters of linear systems without numerical differentiation.

This paper describes a computer program for estimating the parameters of a linear differential equation systen with constant coefficients by use of a nonlinear least-squares method. For minimization the sum of squares of an existing standard program, the Gauss-Newton gradient procedure, is employed. The differential equation system is solved by the Taylor expansion method. The advantage of this approach is that the derivatives with respect to the parameters are available without numerical differentiation. Therefore the inaccuracy inherent in numerical differentiation and the problem of choosing the modification of the parameters are eliminated. The given procedure is applicable for all the first order gradient methods. The presented method was tested with generated data from a four-compartmental model.

Computers↗
PubMed1981

Twin-family studies of perceptual speed ability. II. Parameter estimation.

Offspring of monozygotic (MZ) twins form half-ships that permit a direct test of maternal effects and differentiate several sources of between-family environmental variance. Combined with conventional twin data, these genetic half-sibships provide a unique data set for estimating sources of variation in quantitative traits. To illustrate, genetic and environmental parameters were estimated for Identical Pictures Test data obtained from children of MZ twin parents and an (approximate) age-matched cohort of like-sex twins. Analyses of variance of the data, standardized for age and sex, yield 12 mean squares to which gene-environment models were fit. Maximum-likelihood estimation revealed a complete absence of maternal influences and shared environmental effects; a simple two-parameter model, assuming random mating and attributing variation in test scores to additive genes and within-family environment, adequately accounts for the familial data.

Adolescent↗