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PubMed1976

The comparison of parameters estimated from several different samples by maximum likelihood.

A system of computer programs has been developed to compare the parameters of several samples taken from populations with arbitrary but known distribution functions. The user indicates which of the parameters are assumed to be equal in all populations under the null hypothesis alone or under both the null and the alternative hypotheses. The programs perform maximum likelihood estimation under the general and the restricted model and also calculate the values needed for a likelihood ratio test. The programming language used was PL/I-FORM AC. An illustrative numerical example is given.

Animals↗
PubMed1989

Anaerobic threshold: reproducibility out from ventilatory parameter estimation.

Anaerobic threshold (AT) during exercise is usually noninvasively determined by assuming a two-segment mathematical relationship between two ventilatory parameters. In the literature, all the possible pairs of segments are first considered, and the most appropriate pair is then selected according to at least-squares method. In such a model, the AT is considered to be related to the joining point of the two segments. In order to test the reliability of the model, we compare the results of the least-squares method to those based on maximum probability method in discriminating the two regression coefficients. In order to test the reproducibility of the two different criteria, comparisons have been repeated after data have been filtered. A paired t test was used to carry out comparisons. Ventilatory parameters were collected in 10 healthy subjects during the use of a bicycle ergometer. The required power was increased every 15 s by steps of 30 W, starting from 50 W. Ve, VO2 and VCO2 have been sampled every 15 s, then the three functions--Ve versus VO2, Ve versus VCO2 and VCO2 versus VO2--were considered. Each function was stylized with two linear segments. Each segment was estimated by using a second-kind linear fitting. We verified that: (i) the AT may be reliably appreciated depending on the pair of selected parameters; (ii) only when data are smoothed is no difference between the two criteria documented (Ve vs. VO2, p = 0.99; Ve vs. VCO2, p = 0.54); (iii) no significant difference, related to smoothing, is documented both in using the least-squares method (Ve vs. VO2, p = 0.61; Ve vs. VCO2, p = 0.15) and the maximum p level criterion (Ve vs. VO2, p = 0.59; Ve vs. VCO2, p = 0.19).

Adolescent↗
PubMed1987

PEDA: a microcomputer program for parameter estimation and dosage adjustment in clinical practice.

PEDA, an integrated program in BASIC for implementation on microcomputers, has been developed for use in clinical practice to assist dosage adjustment for individual patients. A parameter optimization for individual patients is based on the principle of Bayes' theory and Maximum Likelihood Estimation, and utilizes a prior information on the distribution of population pharmacokinetic parameters, means and variances, as well as serum drug concentrations. The program can accommodate a one-compartment open linear model and a non-linear model at steady state (Michaelis-Menten model) and handle both uniform and non-uniform multiple dosage regimens mostly arising from clinical settings. Clinical examples which demonstrate the ability and the flexibility of the program are provided. The program may also be used as an aid for instruction in clinical pharmacokinetics.

Adult↗
PubMed1977

Respiratory parameter estimation using forced oscillatory impedance data.

The frequency dependency of the magnitude and phase angle of total respiratory impedance was measured in apneic dogs at functional residual capacity during forced oscillation by a special electronics unit. Regression analysis of these data yielded estimates of total respiratory resistance (RFO), inertance (IFO), and compliance (CFO). After correcting for the effects of the endotracheal tube, mean control values (+/-SE) of RFO, IFO, and CFO for the clinically normal dogs were 1.30+/-0.10 cmH2O-1-1-s, 0.0114+/-0.0022 cmH2O-1-1-s2, and 0.0306+/-0.0009 1-cm H2O-1, respectively. Estimates obtained with added resistance, a less dense gas, and abdominal weighting were consistent with predicted effects. In four dogs with mild respiratory symptoms, mean RFO was significantly elevated with no change in IFO or CFO. Independent measurements of resistance and compliance during tidal ventilation correlated well with RFO (r=0.87) and CFO (r=0.80), but RFO and CFO were, on the average, 71% of the tidal breathing values. Thus, the method provides precise estimates of RFO, IFO, and CFO, and allows detection of small changes in these parameters.

Airway Resistance↗
PubMed1982

Analytical approximations of sensitivities of steady state predictions to errors in parameter estimation.

The sensitivity theory is applied to derive a linear approximation to the functional dependence of some steady state quantities of therapeutic significance on pharmacokinetic parameters obtained from the biexponential response to a single drug dose. The error of a steady state prediction depends in general on two terms. The first one may be viewed as an approximate sensitivity of the prediction to the parameter errors, and this depends solely on the algebraic relation between the prediction and the parameters. The second term is the relative error in parameters, and this may be affected by experimental design and the method of data analysis. Comparisons are made with Monte Carlo simulations and "a posteriori" estimates of variance of a prediction.

Kinetics↗
PubMed1984

Estimating parameters of the family-size distribution in ascertainment sampling schemes: numerical results.

It is argued that, in any ascertainment sampling scheme using data from families of various sizes, there is never any need to assume a particular form for the (unknown) family-size distribution. There exists a simple conditional method, making no assumptions about the family-size distribution, that is always preferable to the assumption of any particular distributional form. Furthermore, the simplicity of the conditional method gives insights into properties of estimates of genetic and ascertainment parameters, which are not available when a particular form for the family-size distribution is assumed.

Biometry↗
PubMed1994

Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism.

An important step in understanding a metabolic pathway is to identify its structure, in terms of the flow of material and information. In pursuing this goal, the available information for a given system is usually obtained from experiments in vitro and comes from different sources. Frequently, the final set of regulatory signals acting in the system in vivo is unclear, and some kind of test is needed on the intact system. Besides defining an appropriate experimental approach, identification of the regulatory pattern needs a theoretical framework in which the different experimental measurements can be evaluated and a final picture can be agreed on. Mathematical approaches based on sensitivity coefficients provide a useful tool for addressing this problem. Within this framework, the appropriate parameters are related to both the structure of the reaction network and the signals that regulate the target system. Thus the identification of the regulatory structure can be related to the estimation of the appropriate set of parameters. In pursuing this goal, we will show the limitations of using steady-state measurements and the usefulness of using dynamic data. We suggest a way to test the regulatory pattern in a given metabolic pathway by combining both kinds of data, and we show, by using a reference system, the potential of the method suggested.

Metabolism↗
PubMedDate not supplied

Logistic growth curve of chickens: a comparison of techniques to estimate parameters.

Parameters of a mathematical function of growth, fit to the body weight curve of two randombred control populations of each sex of chickens from hatching through 45 weeks of age, were estimated. The logistic function was chosen from among growth formulae that express rate of gain as a function of weight at a given time and gain to be made. Two logistic parameters, growth-rate constant and age at the point of inflection, were estimated by the methods of sample quantiles and nonlinear regression from weekly mean body weights of 225 males and 281 females of the Rhode Island Red (RIR) line, and 164 males and 239 females of the White Leghorn (WL) line. Males had a larger growth-rate constant than females of the same line. The RIR line had a larger rate constant than the WL line, for each sex. Age at the point of inflection was similar for males and females in the RIR line, but smaller for males than females in the WL line. Sample quantiles yielded larger, less precise estimates of the growth-rate constant than nonlinear regression. Estimates of age at the point of inflection were usually smaller using sample quantiles.

Aging↗
PubMed1983

The amino acid requirements of growing turkeys. 1. Model construction and parameter estimation.

A model has been formulated to calculate the protein and amino acid requirements for growing turkeys. A requirement was taken as the sum of the needs for maintenance, for gain in carcass weight without feathers, and for the feathers. Parameters used in the model were obtained from a study of carcass composition along the growth period and from two balance trials with adult turkeys. The maintenance requirement was considered to be the sum of the needs for replacing skin and intestinal protein losses and for the obligatory creatinine excretion in the urine. Nitrogen retention was determined at 2.3 g/day in protein-fed adult (17 kg) male turkeys as an estimate for the replacement needs for skin protein loss. Creatinine excretion in these birds was 123 mg/day. When fed an N-free diet, 16.5 kg adult turkeys excreted a total of 3.5 g/day amino acids as a result of intestinal losses. The protein requirement for maintenance was estimated at 32 mg/day/g2/3 of body weight by summing up the different needs and dividing by .85, the coefficient of protein absorption. Protein and amino acid analyses of nude carcass and feathers and the growth curve were used to calculate the requirements for growth. These were then related to energy intake predicted by equations, which included previously determined coefficients for maintenance and growth (Hurwitz et al., 1980a), and the results of carcass lipid analysis. The calculated amino acid requirements were similar to those of the National Research Council (1977).

Amino Acids↗
PubMed1990

Mechanical impedance of the canine diaphragm. Part 2. Theoretical model and parameter estimation.

In the paper the equation of motion of the small amplitude transverse forced vibration of a radially prestressed and circularly clamped thin membrane has been developed. The material of the membrane is considered to be homogeneous, isotropic, incompressible and viscoelastic. From the analytical solution of this equation the incremental mechanical impedance of the membrane was derived as a function of frequency, geometrical parameters and incremental viscoelastic coefficients of the material. The parameters of the model were fitted to experimental impedance data using a global optimisation procedure to obtain the incremental viscoelastic moduli of the canine diaphragm. The estimated quasi-static behaviour of the model is shown to be consistent with the results of experimental quasi-static measurements. It is concluded that the incremental viscoelastic moduli of a soft tissue and the stress dependence of these material coefficients can be determined by fitting the parameters of the model to the impedance data of that particular tissue.

Animals↗
PubMed1991

Influence of method of model fitting and gender on estimated parameters for the relationship between starvation heat production and body size in the domestic fowl.

The relationship between starvation heat production (SHP) in kJ/d and body weight (W) in kg for domestic fowl was examined with compiled calorimetric data for 294 fowls (Johnson and Farrell, 1985). Linear regression analyses using ordinary least squares methods were performed before and after transformation of the data to a logarithmic scale (base = 10). Coefficients of determination (R2) were similar for untransformed and log-transformed data (R2's = .56 and .53, respectively). The slopes for untransformed data of males and females were different (P less than 0.033). When the model parameters for: SHP = b0 Wb1 were derived from log-transformed data, there were no significant differences in exponents for males vs. females (P greater than .95). However, when the coefficients were estimated using non-linear regression techniques, a difference was detected at the level of P = 0.072. It was determined that there is no advantage in describing the relationship of SHP as a non-linear function of W, nor is it appropriate to express physiological variables as a ratio of weight raised to some mass exponent without statistical justification. Using W or W2 as a covariable for the statistical analysis of physiological data would produce equally acceptable determinations of significance.

Animals↗
PubMedDate not supplied

A simple steady state kinetic model for alcohol dehydrogenase. Use of reaction progress curves for parameters estimation at pH 7.4.

A simple rate equation for alcohol dehydrogenase was obtained by assuming independent binding sites for ethanol and NAD+ and fully competitive inhibition by the products of the reaction, acetaldehyde and NADH. A random binding order was also assumed. The rate equation is described by six parameters: four association constants (two for the substrates and two for the products of the reaction), Vf for the forward direction, and the equilibrium constant of the reaction. The six parameters were determined at pH 7.4 by numerical analysis of progress curves of reactions started with different concentrations of ethanol and NAD+. The parameters for alcohol dehydrogenase partially purified from rat liver were: Km for ethanol = 0.746 mM, Km for NAD+ = 0.0563 mM, Km for acetaldehyde = 7.07 microM, Km for NADH = 4.77 microM and Keq = 2.36 X 10(-4). The computed values allowed a very good simulation of the experimental progress curves and little variation was observed in the kinetic parameters when the reactions were started in the presence of either NADH or acetaldehyde.

Alcohol Dehydrogenase↗
PubMed1992

Confidence limits for the parameter estimation in the dipole localization method on the basis of spatial correlation of background EEG.

A new residual function in the inverse problem of equivalent dipole localization methods is proposed which is based on the spatial correlation of the background EEG. This residual has the advantage that it allows the calculation of confidence limits for dipole model parameters. The method was applied to VEP data, and it was studied how the localization precision depends on the recording time of the EEG. It was found that the tangential position of an equivalent dipole can be located at 99% confidence in a region of the order 7 x 7mm for a head radius of 10cm, while the 99% confidence interval of the depth estimate is approximately 1cm, with a recording time of 20 minutes. It was also observed that an EEG recording time of more than 10-15 minutes is needed to obtain stable localization precision estimates.

Brain↗
PubMed1984

Analytical approximations of sensitivities of steady state predictions to errors in parameter estimation: II. Michaelis-Menten kinetics.

Linear sensitivity theory is used to estimate the reliability of predictions of the minimum and maximum concentrations at steady state in the Michaelis-Menten model with i.v. bolus. The dependence of the relative errors in the predictions on the errors in the pharmacokinetic parameters is derived in an analytical form. It is shown that the quality of the predictions is not equally sensitive to all errors in parameters, and that the sensitivity factors vary with the degree of saturation of the system. An example of application for a drug, such as phenytoin, is discussed. It is suggested that sensitivity analysis may be useful in design of pharmacokinetic experiments aimed at the control of steady state levels for drugs with Michaelis-Menten kinetics.

Kinetics↗
PubMed1990

Determination of a constitutive relation for passive myocardium: II. Parameter estimation.

In the first paper of this series, we proposed a new transversely isotropic pseudostrain-energy function W for describing the biomechanical behavior of excised noncontracting myocardium. The specific functional form of W was inferred directly from biaxial data to be a polynomial function of two coordinate invariant measures of the finite deformation and five material parameters. In this paper, best-fit values of the material parameters are determined from biaxial data using a nonlinear least-squares regression. These values of the parameters are shown to be well-determined, and the final constitutive relation is shown to have good predictive capabilities. Since the proposed constitutive relation describes much broader classes of in-vitro biaxial data than previously proposed relations, it may be better applicable to analyses of stress in the passive heart.

Animals↗
PubMed1985

Discrimination of the isozymes of human placental hexosaminidase by kinetic parameter estimation.

Human placental beta-N-acetylhexosaminidase (EC 3.2.1.52) (HEX) is a lysosomal glycosyl hydrolase with an acidic pH optimum. Four isozymes (HEX B, HEX I1, HEX I2, and HEX A) have been isolated from human placenta. HEX BA derived from the subunit rearrangement of HEX A was also prepared. To determine if the isozymes of hexosaminidase differ in their kinetic parameters, the conditions for 4-methylumbelliferyl-beta-D-N-acetylglucosaminide hydrolysis were optimized for each isozyme. The Km values were essentially similar and varied from 0.64 +/- 0.06 for HEX BA to 0.85 +/- 0.13 for HEX I1. The Vmax values were similar only for HEX I1 (3.90 +/- 0.28 kat kg-1) and HEX I2 (4.40 +/- 0.17). Vmax values varied significantly between HEX A (9.68 +/- 0.52), HEX B (8.00 +/- 0.75), HEX BA (4.81 +/- 0.17), and the HEX I values.

Electrophoresis, Polyacrylamide Gel↗
PubMed1979

Dynamic evaluation of human vestibulo-ocular function using white noise rotation stimulus and linear system parameter estimation techniques.

White noise acceleration inputs were used to determine the human VOR transfer function both for normal subjects and for patients falling into two pilot categories: unilateral labyrinthectomy and reduced bilateral responses. The systematic patterns shown in the transfer function of the pilot abnormal categories as compared to the normal data suggests one method of classifying test results (table I). Frequency domain linear systems parameter fits were also made using the same data. The changes in these fit parameters, when pilot abnormal data is compared to normal data, suggests the use of the parameter fits themselves as a second classification scheme (fig. 1). The second scheme is not appropriate in cases where the response is unrelated to the stimulus.

Eye Movements↗
PubMed1990

Two methods for parameter estimation using multiple-trait models and beef cattle field data.

Two methods are presented for estimating variances and covariances from beef cattle field data using multiple-trait sire models. Both methods require that the first trait have no missing records and that the contemporary groups for the second trait be subsets of the contemporary groups for the first trait; however, the second trait may have missing records. One method uses pseudo expectations involving quadratics composed of the solutions and the right-hand sides of the mixed model equations. The other method is an extension of Henderson's Simple Method to the multiple trait case. Neither of these methods requires any inversions of large matrices in the computation of the parameters; therefore, both methods can handle very large sets of data. Four simulated data sets were generated to evaluate the methods. In general, both methods estimated genetic correlations and heritabilities that were close to the Restricted Maximum Likelihood estimates and the true data set values, even when selection within contemporary groups was practiced. The estimates of residual correlations by both methods, however, were biased by selection. These two methods can be useful in estimating variances and covariances from multiple-trait models in large populations that have undergone a minimal amount of selection within contemporary groups.

Analysis of Variance↗