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PubMed2000

Localization of a quantitative trait locus via a Bayesian approach.

A Bayesian approach to the direct mapping of a quantitative trait locus (QTL), fully utilizing information from multiple linked gene markers, is presented in this paper. The joint posterior distribution (a mixture distribution modeling the linkage between a biallelic QTL and N gene markers) is computationally challenging and invites exploration via Markov chain Monte Carlo methods. The parameter's complete marginal posterior densities are obtained, allowing a diverse range of inferences. Parameters estimated include the QTL genotype probabilities for the sires and the offspring, the allele frequencies for the QTL, and the position and additive and dominance effects of the QTL. The methodology is applied through simulation to a half-sib design to form an outbred pedigree structure where there is an entire class of missing information. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.

Algorithms↗

PubMedDate not supplied

Model-based analysis of clinical fluorescence spectroscopy for in vivo detection of cervical intraepithelial dysplasia.

We present a mathematical model to calculate the relative concentration of light scatterers, light absorbers, and fluorophores in the epithelium and stroma. This mathematical description is iteratively fit to the fluorescence spectra measured in vivo, yielding relative concentrations of each molecule. The mathematical model is applied to a total of 493 fluorescence measurements of normal and dysplastic cervical tissue acquired in vivo from 292 patients. The estimated parameters are compared with histopathologic diagnosis to evaluate their diagnostic potential. The mathematical model is validated using fluorescence spectra simulated with known sets of optical parameters. Subsequent application of the mathematical model to in vivo fluorescence measurements from cervical tissue yields fits that accurately describe measured data. The optical parameters estimated from 493 fluorescence measurements show an increase in epithelial flavin adenine dinucleotide (FAD) fluorescence, a decrease in epithelial keratin fluorescence, an increase in epithelial light scattering, a decrease in stromal collagen fluorescence, and an increase in stromal hemoglobin light absorption in dysplastic tissue compared to normal tissue. These changes likely reflect an increase in the metabolic activity and loss of differentiation of epithelial dysplastic cells, and stromal angiogenesis associated with dysplasia. The model presented here provides a tool to analyze clinical fluorescence spectra yielding quantitative information about molecular changes related to dysplastic transformation.

Computer Simulation↗

PubMed2003

Remote sensing of sediment characteristics by optimized echo-envelope matching.

A sediment geoacoustic parameter estimation technique is described which compares bottom returns, measured by a calibrated monostatic sonar oriented within 15 degrees of vertical and having a 10 degree-21 degree beamwidth, with an echo envelope model based on high-frequency (10-100 kHz) incoherent backscatter theory and sediment properties such as: mean grain size, strength, and exponent of the power law characterizing the interface roughness energy density spectrum, and volume scattering coefficient. An average echo envelope matching procedure iterates on the reflection coefficient to match the peak echo amplitude and separate coarse from fine-grain sediments, followed by a global optimization using a combination of simulated annealing and downhill simplex searches over mean grain size, interface roughness spectral strength, and sediment volume scattering coefficient. Error analyses using Monte Carlo simulations validate this optimization procedure. Moderate frequencies (33 kHz) and orientations normal with the interface are best suited for this application. Distinction between sands and fine-grain sediments is demonstrated based on acoustic estimation of mean grain size alone. The creation of feature vectors from estimates of mean grain size and interface roughness spectral strength shows promise for intraclass separation of silt and clay. The correlation between estimated parameters is consistent with what is observed in situ.

Models, Theoretical↗

PubMed2005

Identifying ultrasonic scattering sites from three-dimensional impedance maps.

Ultrasonic backscattered signals contain frequency-dependent information that is usually discarded to produce conventional B-mode images. It is hypothesized that parametrization of the quantitative ultrasound frequency-dependent information (i.e., estimating scatterer size and acoustic concentration) may be related to discrete scattering anatomic structures in tissues. Thus, an estimation technique is proposed to extract scatterer size and acoustic concentration from the power spectrum derived from a three-dimensional impedance map (3DZM) of a tissue volume. The 3DZM can be viewed as a computational phantom and is produced from a 3D histologic data set. The 3D histologic data set is constructed from tissue sections that have been appropriately stained to highlight specific tissue features. These tissue features are assigned acoustic impedance values to yield a 3DZM. From the power spectrum, scatterer size and acoustic concentration estimates were obtained by optimization. The 3DZM technique was validated by simulations that showed relative errors of less than 3% for all estimated parameters. Estimates using the 3DZM technique were obtained and compared against published ultrasonically derived estimates for two mammary tumors, a rat fibroadenoma and a 4T1 mouse mammary carcinoma. For both tumors, the relative difference between ultrasonic and 3DZM estimates was less than 10% for the average scatterer size.

Acoustics↗

PubMed1979

Kinetic model for production and metabolism of very low density lipoprotein triglycerides. Evidence for a slow production pathway and results for normolipidemic subjects.

A model for the synthesis and degradation of very low density lipoprotein triglyceride (VLDL-TG) in man is proposed to explain plasma VLDL-TG radioactivity data from studies conducted over a 48-h interval after injection of glycerol labeled with 14C, 3H, or both. The curve describing the radioactivity of plasma VLDL triglycerides reaches a maximum at about 2 h, after which the decay is biphasic in all cases; the late curvature becoming evident only after 8--12 h. To fit the complex curve, it was necessary to postulate two pathways for the incorporation of plasma glycerol into VLDL-TG, one much slower than the other. A process of stepwise delipidation of VLDL in the plasma compartment, previously proposed for VLDL apoprotein models, was also necessary. Predicted VLDL-TG synthesis rates calculated with this model can differ significantly from those based on experiments of shorter duration in which the slow VLDL-TG component is not apparent. The results of these studies strongly support the interpretation that the late, slow component of the VLDL-TG activity curve is predominantly due to the slowly turning-over precursor compartment in the conversion pathway and is not due either to a slow compartment in the labeled precursor, plasma free glycerol, or to an exchange of plasma VLDL-TG with an extravascular compartment. It also cannot, in these studies, be attributed to a slowly turning-over VLDL-TG moiety in the plasma. The model was tested with data from 59 studies including normal subjects and patients with obesity and(or) various forms of hyperlipoproteinemia. Good fits were obtained in all cases, and the estimated parameter values and their uncertainties for 13 normolipemic nonobese subjects are presented. Sensitivty testing was carried out to determine how critical various parameter estimations are to the assumptions introduced in the modeling.

Glycerol↗

PubMed2005

Comparison of basic assumptions embedded in learning models for experience-based decision making.

The present study examined basic assumptions embedded in learning models for predicting behavior in decisions based on experience. In such decisions, the probabilities and payoffs are initially unknown and are learned from repeated choice with payoff feedback. We examined combinations of two rules for updating past experience with new payoff feedback and of two choice rule assumptions for mapping experience onto choices. The combination of these assumptions produced four classes of models that were systematically compared. Two methods were employed to evaluate the success of learning models for approximating players' choices: One was based on estimating parameters from each person's data to maximize the prediction of choices one step ahead, conditioned by the observed past history of feedback. The second was based on making a priori predictions for the entire sequence of choices using parameters estimated from a separate experiment. The results indicated the advantage of a class of models incorporating decay of previous experience, whereas the ranking of choice rules depended on the evaluation method used.

Adult↗

PubMed1985

A new physiologic model for dynamic process of creatine kinase activity after acute myocardial infarction and estimation of infarct size.

A new physiologic model for dynamic process of Creatine Kinase (CK) after acute myocardial infarction is proposed. The fundamental hypotheses are tested. The new model is better than the log-normal model in goodness of fit. With this new model, the infarct size of complicated cases with double or multiple peak CK curve can be estimated as well as that of uncomplicated cases. To estimate parameters, a nomographic algorithm and a computer program have been designed. In most cases, the initial values for parameters estimated with Marquardt's method can be determined from individual CK data.

Creatine Kinase↗

PubMed1986

Sequential estimation of genetic and phenotypic parameters in multitrait mixed model analysis.

Single-trait and multitrait (2-, 3-, 4-, and 5-trait) restricted maximum likelihood methods were applied to the same set of data with complete information on all traits. Results suggest that parameter estimates from a data set vary depending upon the type of analysis (single- or multitrait model) and upon the other traits included in multitrait analysis. The choice of parameter estimation method for a breeding design should be based on the breeding goal. In parameter estimation or sire evaluation, traits included in a multitrait analysis should correspond to the traits of interest in the breeding goal. Multitrait analysis explores all intercorrelations simultaneously in parameter estimation and thus provides a complete picture of all interrelationships among traits. In contrast, single-trait analysis produces pairwise (simple) correlations and ignores the possible contribution of other related traits under study to the pairwise correlation. The 5-trait model analysis through canonical transformation was about 300% more efficient in terms of computer time than single-trait model analysis of the same 5 traits. In this study, parameter estimates converged faster under multitrait analysis through canonical transformation than under single-trait analysis.

Animals↗

PubMed2004

Estimating bias in population parameters for some models for repeated measures ordinal data using NONMEM and NLMIXED.

The application of proportional odds models to ordered categorical data using the mixed-effects modeling approach has become more frequently reported within the pharmacokinetic/pharmacodynamic area during the last decade. The aim of this paper was to investigate the bias in parameter estimates, when models for ordered categorical data were estimated using methods employing different approximations of the likelihood integral; the Laplacian approximation in NONMEM (without and with the centering option) and NLMIXED, and the Gaussian quadrature approximations in NLMIXED. In particular, we have focused on situations with non-even distributions of the response categories and the impact of interpatient variability. This is a Monte Carlo simulation study where original data sets were derived from a known model and fixed study design. The simulated response was a four-category variable on the ordinal scale with categories 0, 1, 2 and 3. The model used for simulation was fitted to each data set for assessment of bias. Also, simulations of new data based on estimated population parameters were performed to evaluate the usefulness of the estimated model. For the conditions tested, Gaussian quadrature performed without appreciable bias in parameter estimates. However, markedly biased parameter estimates were obtained using the Laplacian estimation method without the centering option, in particular when distributions of observations between response categories were skewed and when the interpatient variability was moderate to large. Simulations under the model could not mimic the original data when bias was present, but resulted in overestimation of rare events. The bias was considerably reduced when the centering option in NONMEM was used. The cause for the biased estimates appears to be related to the conditioning on uninformative and uncertain empirical Bayes estimate of interindividual random effects during the estimation, in conjunction with the normality assumption.

Bias↗

PubMed1990

[Study on the estimation theory of genetic parameters--the estimation method when the parents were relative].

By decomposing the expected mean squares in variance analysis, the estimation methods of genetic parameters are suggested in sib analysis when the parents of the sibs are relatives. Two estimation examples are also given. The results indicate that the estimation values are greater than those estimated by supposing that the parents are not relatives. The closer relative the parents are, the bigger the biased would be. The computer programme PARESTH and PARESTF made it easy to apply the methods. Furthermore, the methods can also be used in variance analysis when the relationships between the levels of each factors are determined.

Analysis of Variance↗

PubMedDate not supplied

Fast estimation of arterial vascular parameters for transient and steady beats with application to hemodynamic state under variant gravitational conditions.

Numerous parameter estimation techniques exist for characterizing the arterial system using electrical circuit analogs. These techniques are often limited by requiring steady-state beat conditions and can be computationally expensive. Therefore, a new method was developed to estimate arterial parameters during steady and transient beat conditions. A four-element electrical analog circuit was used to model the arterial system. The input impedance equations for this model were derived and reduced to their real and imaginary components. Next, the physiological input impedance was calculated by computing fast Fourier transforms of physiological aortic pressure (AoP) and aortic flow. The approach was to reduce the error between the calculated model impedance and the physiological arterial impedance using a Jacobian matrix technique which iteratively adjusted arterial parameter values. This technique also included algorithms for estimating physiological arterial parameters for nonsteady physiological AoP beats. The method was insensitive to initial parameter estimates and to small errors in the physiological impedance coefficients. When the estimation technique was applied to in vivo data containing steady and transient beats it reliably estimated Windkessel arterial parameters under a wide range of physiological conditions. Further, this method appears to be more computationally efficient compared to time-domain approaches.

Animals↗

PubMed2005

Using geometric control and chaotic synchronization to estimate an unknown model parameter.

We present a new parameter estimation procedure for nonlinear systems. Such technique is based on the synchronization between the model and the system whose unknown parameter is wanted. Synchronization is accomplished by controlling the model to make it follow the system. We use geometric nonlinear control techniques to design the control system. These techniques allow us to derive sufficient conditions for synchronization and hence for proper parameter estimation. As an example, this procedure is used to estimate a parameter of an example serving as a model.

Journal Article↗

PubMed1982

Impact of numbers and frequency of weighings on bovine weight-age curve parameters.

Estimates of mature weight (A) and maturing rate (K), determined by asymptotic regression, were studied to evaluate the effects of using quarterly weights taken in different seasons of the year for estimating growth curve parameters. Quarterly weights of 102 Angus cows were used to calculate eight sets of weight-age curves. Four sets of estimates were calculated from weights from birth to 5 yr of age (FIVE-YEAR curves) and four sets were calculated from all weights collected throughout the life of each cow (LIFETIME curves). Within each age group, one set of parameters was estimated from all weights up to the respective ages (FIVE-YEAR and LIFETIME). The other three sets, within each age, were based on quarterly weights from birth to 1 yr of age plus one weight/year taken during the summer, fall or winter. The symbols A and K were used with the following subscripts: 0 or 5 as a first digit to represent weight-age parameters estimated from all weights taken during the life of the cow and from weights taken before the cow was 5 yr old, respectively; and 0, 2, 3, or 4 as a second digit to represent all quarterly weight, summer, fall or winter weights, respectively. Mean estimates of mature weight were 496, 492, 492, 522, 483, 478, 487 and 508 kg for A00, A02, A03, A04, A50, A52, A53, and A54, respectively. Season of weighing affected both A and K. Coefficients of correlation among the estimates of mature weights were all positive and larger than .70. Coefficients of correlation among estimates of rate of maturing were larger than .50, except those involving the correlation of K00 and FIVE-YEAR estimates. This study indicates that weight-age characteristics estimated from quarterly weights from birth to 1 yr of age and a single annual weight from 1 to 5 yr are adequate for estimating practical weight-age parameters at an early cow age. However, in FIVE-YEAR estimates, the effect of a cow's being nonpregnant at 2, 3 or 5 yr of age and, in LIFETIME estimates, any open year, especially the terminal year, may result in serious bias.

Aging↗

PubMed1992

An empirical test for the reliability of quantal analysis based on Pascal statistics.

We have previously shown that amplitude distributions of excitatory postsynaptic potentials (EPSPs) can be better described by Pascal distribution when the mean quantal content (m) is not stationary but fluctuating according to gamma distribution. We have developed the procedure of estimating quantal parameters by the method of maximum likelihood. In this study, we examined empirically the reliability of this quantal parameter estimation procedure by using Monte Carlo simulations. The reliability was evaluated by absolute values of error (magnitude of error) of estimated parameters relative to the known 'true' parameters. The mean values of relative magnitude of error were relatively small unless the probability of failures was too large (greater than 0.7) or too small (less than 0.1). The values of relative magnitude of error became smaller in association with increases in the sample size. When the probability of failure was between 0.1 and 0.7, the sample size was 1000, coefficient of variation of quantal size was 0.45, the values of relative magnitude of error of estimated parameters were below 0.1. These results mean that this procedure gives relatively reliable estimates of quantal parameters with the limitation that the probability of failure is neither too large (greater than 0.7) nor too small (less than 0.1); it is preferable that the sample size is as large as 1000.

Evoked Potentials↗

PubMed1996

Population pharmacokinetics of ceftazidime in cystic fibrosis patients analyzed by using a nonparametric algorithm and optimal sampling strategy.

Postinfusion data obtained from 17 patients with cystic fibrosis participating in two clinical trials were used to develop population models for ceftazidime pharmacokinetics during continuous infusion. Determinant (D)-optimal sampling strategy (OSS) was used to evaluate the benefits of merging four maximally informative sampling times with population modeling. Full and sparse D-optimal sampling data sets were analyzed with the nonparametric expectation maximization (NPEM) algorithm and compared with the model obtained by the traditional standard two-stage approach. Individual pharmacokinetic parameter estimates were calculated by weighted nonlinear least-squares regression and by maximum a posteriori probability Bayesian estimator. Individual parameter estimates obtained with four D-optimally timed serum samples (OSS4) showed excellent correlation with parameter estimates obtained by using full data sets. The parameters of interest, clearance and volume of distribution, showed excellent agreement (R2 = 0.89 and R2 = 0.86). The ceftazidime population models were described as two-compartment kslope models, relating elimination constants to renal function. The NPEM-OSS4 model was described by the equations kel = 0.06516+ (0.00708.CLCR) and V1 = 0.1773 +/- 0.0406 liter/kg where CLCR is creatinine clearance in milliliters per minute per 1.73 m2, V1 is the volume of distribution of the central compartment, and kel is the elimination rate constant. Predictive performance evaluation for 31 patients with data which were not part of the model data sets showed that the NPEM-ALL model performed best, with significantly better precision than that of the standard two-stage model (P < 0.001). Predictions with the NPEM-OSS4 model were as precise as those with the NPEM-ALL model but slightly biased (-2.2 mg/liter; P < 0.01). D-optimal monitoring strategies coupled with population modeling results in useful and cost-effective population models and will be of advantage in clinical practice, as it allows pharmacokinetic-pharmacodynamic modeling with sparse data, thus describing the relationship between ceftazidime exposure and response in the treatment of acute exacerbations in patients with cystic fibrosis.

Adult↗

PubMedDate not supplied

Estimation of respiratory parameters via fuzzy clustering.

The results of monitoring respiratory parameters estimated from flow-pressure-volume measurements can be used to assess patients' pulmonary condition, to detect poor patient-ventilator interaction and consequently to optimize the ventilator settings. A new method is proposed to obtain detailed information about respiratory parameters without interfering with the expiration. By means of fuzzy clustering, the available data set is partitioned into fuzzy subsets that can be well approximated by linear regression models locally. Parameters of these models are then estimated by least-squares techniques. By analyzing the dependence of these local parameters on the location of the model in the flow-volume-pressure space, information on patients' pulmonary condition can be gained. The effectiveness of the proposed approaches is demonstrated by analyzing the dependence of the expiratory time constant on the volume in patients with chronic obstructive pulmonary disease (COPD) and patients without COPD.

Airway Resistance↗

PubMed2002

Optimal temperature input design for estimation of the square root model parameters: parameter accuracy and model validity restrictions.

As part of the model building process, parameter estimation is of great importance in view of accurate prediction making. Confidence limits on the predicted model output are largely determined by the parameter estimation accuracy that is reflected by its parameter estimation covariance matrix. In view of the accurate estimation of the Square Root model parameters, Bernaerts et al. have successfully applied the techniques of optimal experiment design for parameter estimation [Int. J. Food Microbiol. 54 (1-2) (2000) 27]. Simulation-based results have proved that dynamic (i.e., time-varying) temperature conditions characterised by a large abrupt temperature increase yield highly informative cell density data enabling precise estimation of the Square Root model parameters. In this study, it is shown by bioreactor experiments with detailed and precise sampling that extreme temperature shifts disturb the exponential growth of Escherichia coli K12. A too large shift results in an intermediate lag phase. Because common growth models lack the ability to model this intermediate lag phase, temperature conditions should be designed such that exponential growth persist even though the temperature may be changing. The current publication presents (i) the design of an optimal temperature input guaranteeing model validity yet yielding accurate Square Root model parameters, and (ii) the experimental implementation of the optimal input in a computer-controlled bioreactor. Starting values for the experiment design are generated by a traditional two-step procedure based on static experiments. Opposed to the single step temperature profile, the novel temperature input comprises a sequence of smaller temperature increments. The structural development of the temperature input is extensively explained. High quality data of E. coli K12 under optimally varying temperature conditions realised in a computer-controlled bioreactor yield accurate estimates for the Square Root model parameters. The latter is illustrated by means of the individual confidence intervals and the joint confidence region.

Bioreactors↗

PubMed1989

Estimation of ligand binding parameters by simultaneous fitting of association and dissociation data: a Monte Carlo simulation study.

A new procedure for analysis of ligand binding kinetics was evaluated by Monte Carlo simulations. In this, all association and dissociation data were fitted simultaneously to a set of nonlinear equations. This should have several advantages over more conventional methods; data are better used in a single fitting procedure in which the degrees of freedom are maximized and the error term is spread over more observations; all relevant parameters (Bmax, k1, and k-1) are obtained directly; values obtained from measurements are not treated as errorless; and it yields a single residual term that can be used for statistical comparison among binding models and/or experiments. We have compared this approach with the common practice of analyzing the association and dissociation phases separately, either by nonlinear regression or by linear regression after suitable transformations. With respect to both the precision and accuracy of parameter estimates, the simultaneous procedure was superior to the other two methods. The properties of the simultaneous procedure were further investigated, concerning both parameter estimation and the probability of reliably detecting a second binding site. For the latter, the relative density of receptor subtypes and the dissociation rate constants were found to be of major importance, whereas association rate constants and ligand concentration were of minor importance in this respect. The probability of resolving two sites by kinetic or equilibrium data under similar conditions with the aid of a single labeled ligand was examined. When the selectivity of the ligand was low, the resolution was found to be more probable when based on kinetic, rather than equilibrium, data. This was true at higher selectivities as well, provided kinetic data were obtained at two different ligand concentrations.

Binding Sites↗