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PubMed1993

Comparison of three methods of estimating the parameters of the Naka-Rushton equation.

The Naka-Rushton equation empirically describes the amplitude R of the dark-adapted electroretinogram b-wave, as a function of stimulus luminance L, as R/Rmax = Ln/(Ln + Kn). Estimating the three parameters Rmax, n, and K of this function from electroretinogram data is of both experimental and clinical interest. Several different approaches have been developed to accomplish this analysis, but these approaches may derive different estimates of the three parameters. To examine this possibility, we compared the results of three methods of fitting the Naka-Rushton equation to data sets obtained from 30 normal subjects. Two methods were nonlinear curve-fitting programs; the third method involved fitting a regression line to transformed data. The results indicate that solutions provided by these methods have consistent differences, which may be an important consideration when comparing results reported in studies that used different curve-fitting methods.

Dark Adaptation↗

PubMed1988

Nonlinear estimation of parameters in biphasic Arrhenius plots.

This paper presents a formal procedure for the statistical analysis of data on the thermotropic behavior of membrane-bound enzymes generated using the Arrhenius equation and compares the analysis to several alternatives. Data is modeled by a bent hyperbola. Nonlinear regression is used to obtain estimates and standard errors of the intersection of line segments, defined as the transition temperature, and slopes, defined as energies of activation of the enzyme reaction. The methodology allows formal tests of the adequacy of a biphasic model rather than either a single straight line or a curvilinear model. Examples on data concerning the thermotropic behavior of pig brain synaptosomal acetylcholinesterase are given. The data support the biphasic temperature dependence of this enzyme. The methodology represents a formal procedure for statistical validation of any biphasic data and allows for calculation of all line parameters with estimates of precision.

Acetylcholinesterase↗

PubMed1988

A deep breath method for noninvasive estimation of cardiopulmonary parameters.

A specific ventilation pattern incorporating a single deep breath is used to demonstrate the possibility of estimating six cardiopulmonary parameters by measuring respiratory flow and expired oxygen and carbon dioxide concentrations at the mouth. Equations are derived from both alternating and continuous ventilation models of gas exchange which allow the six parameter estimates to be computed. The results indicate that pulmonary capillary blood flow, functional residual capacity, equivalent lung volume, mixed venous PO2 and PCO2, and pulmonary tissue plus capillary blood volume can be estimated in subjects with normal gas exchange. The use of a mechanical ventilator to provide a uniform ventilation pattern before and after the ventilator induced deep breath is the key to the methods simplicity. This allowed parameter estimates to be obtained which could then be analyzed for accuracy and precision. The feasibility of estimating these parameters, demonstrated by the present study, suggests that a recursive least squares estimation procedure could be used to recover the time variation of each parameter during exercise stress testing of subjects with normal or nearly normal gas exchange.

Blood Volume↗

PubMed1984

Limiting dilution assays for the determination of immunocompetent cell frequencies. III. Validity tests for the single-hit Poisson model.

A statistical method was developed to test the validity of the single-hit Poisson model in limiting dilution assays used to determine immunocompetent cell frequencies. Principles of bioassay, validity tests, and the distinction between model-discrimination experiments and parameter-estimation assays are reviewed in the Introduction. The new test derived and then demonstrated with previously published data is intended to be used for parameter-estimation assays based upon the single-hit Poisson model. It is a family of related chi 2, t, and F tests for deviations from zero of the slopes of weighted least squares regression plots. These plots regress the logarithms of single-dose estimates fi of the frequency phi on the total cell doses lambda i and fi on the total cell dose reciprocals 1/lambda i, that is, Yi = ln fi on Xi = lambda i and Yi = fi on Xi = 1/lambda i. The test discriminates against alternative models with multiple-hit/target response-generation processes, a variable number (dose-dependent) of false negatives, and a constant number (dose-independent) of false positives. Its purpose as a test for parameter-estimation assays, though, is to detect deviations from the single-hit Poisson model and not to select one of these alternative models. Tests for model-discrimination experiments to select or 'prove' an unknown alternative model are considered in light of relevant literature reviewed in the Discussion.

Animals↗

PubMed1990

Pharmacokinetic-pharmacodynamic modeling of the central nervous system effects of heptabarbital using aperiodic EEG analysis.

The concentration EEG effect relationship of heptabarbital was modeled using effect parameters derived from aperiodic EEG analysis. Male Wistar rats (n = 10) received an intravenous infusion of heptabarbital at a rate of 6-9 mg/kg per min until burst suppression with isoelectric periods of 5 sec or longer. Arterial blood samples were obtained and EEG was measured continuously until recovery of baseline EEG and subjected to aperiodic analysis for quantification. Two EEG parameters, the amplitudes per second (AMP) and the total number of waves per second (TNW), in five discrete frequency ranges and for two EEG leads were used as descriptors of the drug effect on the brain. The EEG parameters responded both qualitatively and quantitatively different to increasing concentrations of heptabarbital. Monophasic concentration effect curves (decrease) were found for the frequency ranges greater than 2.5 Hz and successfully quantified with a sigmoidal Emax model after collapsing the hysteresis by a nonparametric modeling approach. For the parameter TNW in the 2.5-30 Hz frequency range the value of the pharmacodynamic parameters EC50, Emax, and n (means +/- SD) were 78 +/- 7 mg/L, 11.4 +/- 1.7 waves/sec and 5.0 +/- 1.5, respectively. For other discrete frequency ranges, differences in EC50 were observed, indicating differences in sensitivity to the effect of heptabarbital. In the 0.5 +/- 2.5 Hz frequency range biphasic concentration effect relationships (increase followed by decrease) were observed. To fully account for the hysteresis in these concentration effect relationships, postulation of two effect compartments was necessary. To characterize these biphasic effect curves two different pharmacodynamic models were evaluated. Model 1 characterized the biphasic concentration effect relationship as the summation of two sigmoidal Emax models, whereas Model 2 assumed the biphasic effect to be the result of only one inhibitory mechanism of action. With Model 1 however realistic parameter estimation was difficult because the maximal increase could not be measured, resulting in high correlations between parameter estimates. This seriously limits the value of Model 1. Model 2 involves besides estimation of the classical pharmacodynamic parameters Emax, EC50, and n also estimation of the maximal disinhibition Amax. This model is a new approach to characterize biphasic drug effects and allows, in principle, reliable estimation of all relevant pharmacodynamic parameters.

Animals↗

PubMed1994

A DeFries and Fulker regression model for genetic nonadditivity.

Parameter estimates from the DeFries and Fulker [(DF) Behav. Genet. 15:462-473, 1985] regression method can be greater than unity or less than zero. This occurs when the monozygotic correlation is greater than twice the dizygotic correlation. Sensible values can be obtained in these cases by fitting a constrained DF model that estimates genetic and nonshared environmental variance components only. In this article I demonstrate that the original Df model yields positively biased heritability estimates and negatively biased estimates of shared environmentality when data are significantly influenced by genetic nonadditivity. The magnitude of the bias is algebraically expressed. I then describe a simple regression equation that provides unbiased estimates of the standardized additive and dominance genetic variance components. Results of a study of 6 million twin pairs from the Monte Carlo Twin Registry demonstrate that the DF additive and dominance genetic parameter estimates are virtually identical to those obtained by maximum-likelihood procedures. Finally, I derive the expectations for the constrained DF model and show that the genetic parameter estimates from this model are negatively biased estimates of broad-sense heritability.

Genes, Dominant↗

PubMed2005

A comparison of different bivariate correlated frailty models and estimation strategies.

Frailty models are becoming increasingly popular in multivariate survival analysis. Shared frailty models in particular are often used despite their limitations. To overcome their disadvantages numerous correlated frailty models were established during the last decade. In the present study, we examine bivariate correlated frailty models, and especially the behavior of the parameter estimates when using different estimation strategies. We consider three different bivariate frailty models: the gamma model and two versions of the log-normal model. The traditional maximum likelihood procedure of parameter estimation in the gamma case with an explicit available likelihood function is compared with maximum likelihood methods based on numerical integration and a Bayesian approach using MCMC methods with the help of a comprehensive simulation study. We detected a strong dependence between the two parameter estimates (variance and correlation of frailties) in the bivariate correlated frailty model and analyzed this dependence in detail.

Bayes Theorem↗

PubMed1990

Quantification of aortic regurgitation by Doppler echocardiography: a new method evaluated in pigs.

We have developed a method to quantify aortic regurgitant orifice and volume, based on measurements of the velocity of the regurgitant jet, aortic systolic flow, the systolic and diastolic arterial pressures, a Windkessel arterial model, and a parameter estimation technique. In six pigs we produced aortic regurgitant flows between 2.1 and 17.8 ml per beat, i.e. regurgitant fractions from 0.06 to 0.58. Pulmonary and aortic flows were measured with electromagnetic flow probes, aortic pressure was measured invasively, and the regurgitant jet velocity was obtained with continuous-wave Doppler. The parameter estimation procedure was based on the Kalman filter principle, resulting primarily in an estimate of the regurgitant orifice area. The area was multiplied by the velocity integral of the regurgitant jet to estimate regurgitant volume. A strong correlation was found between the regurgitant volumes obtained by parameter estimation and the electromagnetic flow measurement. These results from our study in pigs suggest that it may be possible to quantify regurgitant orifice and volume in patients completely noninvasively from Doppler and blood pressure measurements.

Animals↗

PubMed2000

Direct least-squares estimation of spatiotemporal distributions from dynamic SPECT projections using a spatial segmentation and temporal B-splines.

Artifacts can result when reconstructing a dynamic image sequence from inconsistent, as well as insufficient and truncated, cone beam single photon emission computed tomography (SPECT) projection data acquired by a slowly rotating gantry. The artifacts can lead to biases in kinetic model parameters estimated from time-activity curves generated by overlaying volumes of interest on the images. However, the biases in time-activity curve estimates and subsequent kinetic parameter estimates can be reduced significantly by first modeling the spatial and temporal distribution of the radiopharmaceutical throughout the projected field of view, and then estimating the time-activity curves directly from the projections. This approach is potentially useful for clinical SPECT studies involving slowly rotating gantries, particularly those using a single-detector system or body contouring orbits with a multidetector system. We have implemented computationally efficient methods for fully four-dimensional (4-D) direct estimation of spatiotemporal distributions from dynamic SPECT projection data. Temporal B-splines providing various orders of temporal continuity, as well as various time samplings, were used to model the time-activity curves for segmented blood pool and tissue volumes in simulated cone beam and parallel beam cardiac data acquisitions. Least-squares estimates of time-activity curves were obtained quickly using a workstation. Given faithful spatial modeling, accurate curve estimates were obtained using cubic, quadratic, or linear B-splines and a relatively rapid time sampling during initial tracer uptake. From these curves, kinetic parameters were estimated accurately for noiseless data and with some bias for noisy data. A preliminary study of spatial segmentation errors showed that spatial model mismatch adversely affected quantitative accuracy, but also resulted in structured errors (projected model versus raw data) that were easily detected in our simulations. This suggests iterative refinement of the spatial model to reduce structured errors as an area of future research.

Algorithms↗

PubMed2004

The effect of strain rate on the viscoelastic response of aortic valve tissue: a direct-fit approach.

Knowledge of strain-rate sensitivity of soft tissue viscoelastic and nonlinear elastic properties is important for accurate predictions of biomechanical behavior and for quantitative assessment of the effects of disease or surgical/pharmaceutical intervention. Soft tissues are known to exhibit mild rate sensitivity, but experimental artifacts related to testing system control can confound estimation of these effects. "Perfect" ramp-and-hold stress-relaxation tests become difficult at high strain rates because of problems related to undershoot/overshoot error and vibrations. These errors can introduce unwanted bias into parameter estimation methods that rely on idealizations of the applied ramp-and-hold displacement. To address these problems, we describe a new method for estimating quasilinear viscoelastic (QLV) parameters that directly fits the QLV constitutive model to the actual point-wise stress-time history of the test, using an adaptive grid refinement (AGR) global optimization algorithm. This new method significantly improves the accuracy and predictivity of QLV parameter estimates for heart valve tissues, compared to traditional methods that use idealized displacement data. We estimated QLV parameters for aortic valve tissue over a range of physiologic displacement rates, finding that the viscoelastic content parameter (C) increased slightly with increasing strain rate, but the fast (tau1) and slow (tau2) time constants were strain rate insensitive.

Algorithms↗

PubMed2003

Bayesian estimation of parameters of a structural model for genetic covariances between milk yield in five regions of the United States.

Inference about genetic covariance matrices using multiple-trait models is often hindered by lack of information. This leads to imprecise estimates of genetic parameters and of breeding values. Patterns in a genetic covariance matrix can be exploited to reduce the number of parameters and to increase quality of inferences. A structural model for genetic covariances was developed and fitted to milk yield data in five regions of the United States. This was compared with a standard multiple-trait analysis using a deviance information criterion, a measure of quality of fit. Data consisted of 3,465,334 Holstein first-lactation records from daughters of 43,755 sires in five regions of the United States (Midwest, Northeast, Northwest, Southeast, Southwest). Parameters of the structural model included an intercept and effects of measures of genetic and of management similarity on genetic covariances. Genetic similarity depended on the number of records contributed by sires that were common to a pair of regions. Management similarity was a function of the quantity of concentrate used to produce 1000 kg of milk in each pair of regions. The structural and the multiple-trait models gave similar estimates of genetic covariances, but the number of parameters was 8 in the former vs. 15 in the latter. Hence, estimates of genetic covariances were more precise with the structural model. A deviance information criterion suggested a slight superiority of the multiple-trait model, although probably within sampling error. For both models, genetic correlations between milk yield in five regions of the United States were larger than 0.93.

Analysis of Variance↗

PubMed2003

Calibration and inverse modelling of soil physical and biological parameters of a nitrate leaching model with the pest programme.

This paper reports on experiences with the use of the PEST (Parameter ESTimation) programme to calibrate the soil physical parameters of a nitrate leaching model (the Burns alpha model) and to determine the N mineralization rate by inverse modelling. Parameter estimation was much more efficient and accurate with the PEST programme than with a built in "trial and error" calibration module. The determination of the N mineralization rate by inverse modelling with PEST using measured nitrate concentrations was not possible, and several reasons for this are given. With more suitable experimental fields (lighter soil texture and/or deeper groundwater level), more replications in the nitrate measurements and a one-step calibration of the alpha parameter and the N mineralization rate, determination of the N mineralization rate may become possible.

Calibration↗

PubMedDate not supplied

[Procedures for estimating transmission parameters from influenza epidemics: use of serological data].

A maximum likelihood procedure is given for estimating household and community transmission parameters from observed influenza infection data. The mathematical model used does not require the specification of infection onset times and, therefore, can be used with serological data which detect asymptomatic infections. Infection data was derived by serology and virus isolation from the Tecumseh Respiratory Illness Study and the Seattle Flu Study for the years 1975-1979. Influenza A (H1N1), A (H3N2), and B viruses were found to be in descending order both in terms of ease of spread in the household and intensity of the epidemic in the community except when two strains co-circulate. Children are found to be the main introducers of influenza into households.

Adult↗

PubMed1995

A Nonparametric Alternative to Modeling Population Pharmacokinetics in Patients with Spinal Cord Injury: Comparison with the Standard Two-Stage Method.

The estimation of population-specific pharmacokinetic parameters from sparse of fragmentary data obtained during routine patient care is a powerful analytical tool in drug development and therapeutic drug monitoring. The Nonparametric Expectation Maximization program (NPEM) performs this function and generates robust parameter estimates which are distribution-free and unconstrained by assumption-rich parametric, for example, Gaussian, analyses. We compared standard two-stage method (STS) estimates of amikacin pharmacokinetic parameters (V, CL) derived from a sampling rich strategy (11 patients with spinal cord injury, SCI; 7 able-bodied controls) to estimates of pharmacokinetic parameters obtained from an NPEM one-compartment analysis incorporating the 11 optimally sampled SCI patients and 8 sparse data sets (19 patients with SCI; 7 controls). The STS (n = 11) and NPEM (n = 19) analyses provided similar V and CL parameter estimates in patients with SCI: 0.20 plus minus 0.04 L kg(minus sign1), 0.93 plus minus 0.24 ml min(minus sign1) kg(minus sign1) and 0.20 plus minus 0.06 L kg(minus sign1), 1.12 plus minus 0.26 ml min(minus sign1) kg(minus sign1), respectively. NPEM is a useful, user-friendly, distribution-free computational program for estimating the central tendency and interindividual variability of amikacin pharmacokinetic parameters in spinal cord injured humans.

Journal Article↗

PubMed2003

A Bayesian method of estimating kinetic parameters for the inactivation of Cryptosporidium parvum oocysts with chlorine dioxide and ozone.

The main objective of this paper is to use Bayesian methods to estimate the kinetic parameters for the inactivation kinetics of Cryptosporidium parvum oocysts with chlorine dioxide or ozone which are characterized by the delayed Chick-Watson model, i.e., a lag phase or shoulder followed by pseudo-first-order rate of inactivation. As the length of the lag phase (CT(lag)) is not known, Bayesian statistics provides a more accurate approach than traditional statistical methods to fitting the delayed Chick-Watson kinetics. Markov Chain Monte Carlo method is used to estimate CT(lag) and first-order rate constant values. This method is also used to estimate the minimum CT requirement (with safety factor) for 99% inactivation of C. parvum oocysts.

Animals↗

PubMedDate not supplied

Parameter identification in dynamical models of anaerobic waste water treatment.

Biochemical reactions can often be formulated mathematically as ordinary differential equations. In the process of modeling, the main questions that arise are concerned with structural identifiability, parameter estimation and practical identifiability. To clarify these questions and the methods how to solve them, we analyze two different second order models for anaerobic waste water treatment processes using two data sets obtained from different experimental setups. In both experiments only biogas production rate was measured which complicates the analysis considerably. We show that proving structural identifiability of the mathematical models with currently used methods fails. Therefore, we introduce a new, general method based on the asymptotic behavior of the maximum likelihood estimator to show local structural identifiability. For parameter estimation we use the multiple shooting approach which is described. Additionally we show that the Hessian matrix approach to compute confidence intervals fails in our examples while a method based on Monte Carlo Simulation works well.

Anaerobiosis↗

PubMed2002

Pharmacokinetic and pharmacodynamic modeling of humanized anti-factor IX antibody (SB 249417) in humans.

BACKGROUND: SB 249417 is a humanized anti-factor IX/IXa antibody that, on administration to rats and monkeys, produces an immediate suppression of factor IX activity and prolongation of activated partial thromboplastin times (aPTT). OBJECTIVE: Our objective was to establish the pharmacokinetics of SB 249417 and to explore its effects on factor IX activity levels and aPTT in humans. METHODS: In this phase I, single-blind, randomized, placebo-controlled, parallel-group, single intravenous infusion study, individual and mean data from a total of 26 healthy volunteers at 5 dosing levels were analyzed. A 2-compartment pharmacokinetic model was used in the analysis of total SB 249417 concentration-time profiles. A modified indirect-response model was used, with the total concentration indirectly serving as the driving force for the suppression of free factor IX concentration (as assessed by factor IX activity). The aPTT was related to factor IX activity with a biexponential equation, and a population approach was used to generate posterior parameter estimates for the individual fittings. RESULTS: Mean parameter estimates from individual fittings are 0.092 L/kg for volume of distribution, 0.15 L/kg for steady-state volume of distribution, and 0.0021 L/kg per hour for systemic clearance. The model described well the factor IX activity and aPTT time course in response to SB 249417 at 5 dose levels. The estimated half-life of factor IX in blood was 21 hours. CONCLUSIONS: This model was stable and robust in fitting both mean and individual data. Endogenous factor IX baseline levels and dose were the major determinants of the decline in factor IX activity during the infusion period. Thereafter the recovery of factor IX activity was governed solely by the endogenous factor IX turnover rate.

Adult↗

PubMed2002

Serum creatinine patterns in coronary bypass surgery patients with and without postoperative cognitive dysfunction.

UNLABELLED: Renal dysfunction is common after coronary artery bypass graft (CABG) surgery. We have previously shown that CABG procedures complicated by stroke have a threefold greater peak serum creatinine level relative to uncomplicated surgery. However, postoperative creatinine patterns for procedures complicated by cognitive dysfunction are unknown. Therefore, we tested the hypothesis that postoperative cognitive dysfunction is associated with acute perioperative renal injury after CABG surgery. Data were prospectively gathered for 282 elective CABG surgery patients. Psychometric tests were performed at baseline and 6 wk after surgery. Cognitive dysfunction was defined both as a dichotomous variable (cognitive deficit [CD]) and as a continuous variable (cognitive index). Forty percent of patients had CD at 6 wk. However, the association between peak percentage change in postoperative creatinine and CD (parameter estimate = -0.41; P = 0.91) or cognitive index (parameter estimate = -1.29; P = 0.46) was not significant. These data indicate that postcardiac surgery cognitive dysfunction, unlike stroke, is not associated with major increases in postoperative renal dysfunction. IMPLICATIONS: We previously noted that patients with postcardiac surgery stroke also have greater acute renal injury than unaffected patients. However, in the same setting, we found no difference in renal injury between patients with and without cognitive dysfunction. Factors responsible for subtle postoperative cognitive dysfunction do not appear to be associated with clinically important renal effects.

Aged↗