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PubMed1989

Estimation of parameters and missing values under a regression model with non-normally distributed and non-randomly incomplete data.

We carried out a simulation study to compare the performance of three algorithms (complete cases, ALLVALUE, and expectation maximization, EM) in estimating regression parameters and missing values for situations that have varying amounts of missing data, distributions (normal, mixture of normals and lognormal), patterns of incomplete data (random, related and censored), and degrees of correlational structure among the dependent and independent variables. We found that the EM and complete cases algorithms performed equally well regardless of the correlational structure, when the percentage of incomplete data was only 5 per cent. When this percentage increased to 25 per cent, the EM algorithm was generally best for estimation, but the complete cases algorithm was safe and conservative. This finding may be attributed to the study design, which required that the slopes be the same in the population of all cases, and in the population of complete cases. In addition, the one-step imputing method (ALLVALUE) was competitive only for situations with weak correlational structure and/or little missing data. In that situation the bias caused with use of all available information was less than that caused with use of only complete cases. On the other hand, for imputation, the EM algorithm performed optimally, even in situations of censored or log-normally distributed data.

Algorithms↗

PubMed2006

Using nonlinear models in fMRI data analysis: model selection and activation detection.

There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.

Adult↗

PubMed2004

[Comparison of different models for estimating genetic parameters of early growth traits in cashmere goat].

Using data on early growth traits (including birth weight, weaning weight, daily gain, and yearling weight) of cashmere goat from the Aerbasi White Cashmere Goat Breeding Farm in Inner Mongolia, four different animal models for estimating genetic parameters were compared. The four models differ in the way of handling maternal genetic effect and maternal environmental effect: in model I both maternal genetic and environmental effect were excluded, in model II only maternal genetic effect was included, in model III only maternal environmental effect was included, and in model IV both maternal genetic and environmental effect were included. The variance components under different models were estimated with derivative-free restricted maximum likelihood (DFREML) method using the MTDFREML program. The differences between different models were tested by likelihood ratio test. The results show that both maternal genetic and environmental effect have highly significant effect on birth weight. For weaning weight and daily gain the maternal genetic effect is not significant while the maternal environmental effect is highly significant; for yearling weight the maternal genetic effect is significant while the maternal environmental effect is not.

Animals↗

PubMed2004

The importance of proper model assumption in bayesian phylogenetics.

We studied the importance of proper model assumption in the context of Bayesian phylogenetics by examining >5,000 Bayesian analyses and six nested models of nucleotide substitution. Model misspecification can strongly bias bipartition posterior probability estimates. These biases were most pronounced when rate heterogeneity was ignored. The type of bias seen at a particular bipartition appeared to be strongly influenced by the lengths of the branches surrounding that bipartition. In the Felsenstein zone, posterior probability estimates of bipartitions were biased when the assumed model was underparameterized but were unbiased when the assumed model was overparameterized. For the inverse Felsenstein zone, however, both underparameterization and overparameterization led to biased bipartition posterior probabilities, although the bias caused by overparameterization was less pronounced and disappeared with increased sequence length. Model parameter estimates were also affected by model misspecification. Underparameterization caused a bias in some parameter estimates, such as branch lengths and the gamma shape parameter, whereas overparameterization caused a decrease in the precision of some parameter estimates. We caution researchers to assure that the most appropriate model is assumed by employing both a priori model choice methods and a posteriori model adequacy tests.

Bayes Theorem↗

PubMed1990

Bayesian forecasting of serum gentamicin concentrations in intensive care patients.

This study retrospectively evaluated the predictive performance of a 1-compartment Bayesian forecasting program in adult intensive care unit (ICU) patients with stable renal function. A comparison was made of the reliability of 3 sets of population-based parameter estimates and 2 serum concentration monitoring strategies. A larger mean error for prediction of peak gentamicin concentrations was seen with literature-derived parameters than when ICU population-based parameter estimates were used. Bias and precision improved when non-steady-state peak and trough concentrations were used to predict those at steady-state; the addition of steady-state values did not provide additional information for predictions once non-steady-state feedback concentrations were incorporated. The addition of 4 serial gentamicin concentrations obtained at both non-steady-state and steady-state did not noticeably improve the predictive performance. The results demonstrate that initial ICU pharmacokinetic parameter estimates for a 1-compartment Bayesian model provide accurate prediction of steady-state gentamicin concentrations. Prediction bias and precision showed the greatest improvement when non-steady-state gentamicin concentrations were used to determine individualised pharmacokinetic parameters.

Adult↗

PubMed2005

Quantifying and addressing parameter indeterminacy in the classical twin design.

The classical twin design (CTD) is the most common method used to infer genetic and environmental causes of phenotypic variation. As has long been acknowledged, different combinations of the common environment/assortative mating, and additive, dominant, and epistatic genetic effects can lead to the same observed covariation between twin pairs, meaning that there is an inherent indeterminacy in parameter estimates arising from the CTD. The CTD circumvents this indeterminacy by assuming that higher-order epistasis is negligible and that the effects of either dominant genetic variation or the common environment are nonexistent. These assumptions, however, lead to consistent biases in parameter estimation. The current paper quantifies these biases and discusses alternative strategies for dealing with parameter indeterminacy in twin designs. One strategy is to model the similarity among other relatives in addition to twins (extended twin-family designs), which reduces but does not eliminate indeterminacy in parameter estimates. A more general strategy, applicable to all twin designs, is to present the parameter indeterminacy explicitly, as in a graph. Presenting the space of mathematically equally likely parameter values is important, not only because it aids the proper interpretation of twin design findings, but also because it keeps behavioral geneticists themselves mindful of methodological assumptions that can easily go unexamined.

Humans↗

PubMed2006

Evaluation of objective functions for estimation of kinetic parameters.

There is growing interest in quantitatively analyzing in vivo image data, as this facilitates objective comparisons and measurement of effect. In this regard, people increasingly turn to pharmacokinetic models and estimation of parameters of such models. In this work several parameter estimation methodologies were compared within the context of the most common pharmacokinetic model used in positron emission tomography imaging to describe glucose metabolism and receptor-ligand interactions at tracer concentrations. Simulated data were generated with 1000 realizations at each of 5 different noise levels. Estimates of the kinetic parameters were made for each realization using seven iterative, nonlinear estimation methodologies: ordinary least squares (OLS), weighted least squares (WLS), penalized weighted least squares (PWLS), iteratively reweighted least squares (IRLS), and variations of extended least squares (ELS0, ELS1, ELS3). Additionally, generalized linear least squares (GLLS) was also used. With relatively noise-free data, the iterative nonlinear estimation methods generally produced low-bias, high-precision parameter estimates, whereas with GLLS the bias was more prominent. Greater distinction between the estimation methods was seen at the higher, more realistic noise levels, with ELS and IRLS methods generally achieving better precision than the other methods. At the high noise levels WLS, GLLS, and PWLS yielded parameter estimates with large bias (>200%) for some kinetic parameters. In general, there are more favorable estimator methodologies than the frequently employed WLS. Methods that determine values of weights based on model output--IRLS, ELS0, ELS1 and ELS3--generally perform better than methods that determine values of weights based directly on the experimental data.

Analysis of Variance↗

PubMed1989

A prospective evaluation of optimal sampling theory in the determination of the steady-state pharmacokinetics of piperacillin in febrile neutropenic cancer patients.

We examined the use of optimal sampling theory in the determination of the pharmacokinetics of piperacillin in febrile, neutropenic cancer patients. Patients were studied prospectively as part of a randomized, double-blind clinical trial of piperacillin and amikacin versus imipenem and placebo. The results from the analysis of 5 optimal samples were compared with those derived from 15 concentration determinations (10 samples, with the 5 optimal samples assayed in duplicate). The use of a standard least-squares estimator as opposed to a bayesian estimator, with normal prior distributions placed on beta and serum clearance, was also examined. Finally, the use of duplicate determinations in improving the precision of parameter estimation was studied. Plasma concentrations obtained at time points determined by optimal sampling theory, when analyzed with a bayesian estimator, produced estimates of pharmacokinetic parameter values that were in good agreement with those derived from the 15-determination set. Duplicate assay did not improve the precision of parameter estimation. Estimation of plasma clearance was quite robust, irrespective of the estimator used, probably because this evaluation was performed at steady state. Optimal sampling theory is a promising technique that can be employed to determine patient-specific estimates of pharmacokinetic parameter values in target populations.

Adolescent↗

PubMed2002

Reproducibility of quantitative dynamic MRI of normal human tissues.

The aim of the study was to establish the normal range and to evaluate the reproducibility of dynamic contrast enhanced MRI (DCE-MRI) parameter estimates in normal human pelvic tissues. Nineteen patients with prostate cancer, undergoing androgen deprivation treatment, had paired DCE-MRI examinations of the pelvis using spoiled gradient-echo sequences. Quantitative enhancement parameters were calculated for each examination: transfer constant (K(trans)), leakage space (v(e)) and maximum contrast medium accumulation (MCMA) of pelvic muscles, bone marrow and fat. Descriptive and reproducibility statistics were calculated: within-patient standard deviation (wSD), repeatability and within-patient coefficient of variation (wCV). The femoral head and ischiorectal fat showed large numbers of non-enhancing pixels (81 and 88%, respectively). The ischial bone marrow had the highest values of kinetic parameter estimates (K(trans) 0.554 min(-1), v(e) 18.5% and MCMA 0.164 mmol/kg). Muscle parameters values were lower (K(trans) 0.126-0.137 min(-1), v(e) 10.6-11.5% and MCMA 0.077-0.086 mmol/kg). The mean difference between paired examinations was not significantly different from zero for any parameter. v(e) and MCMA had the lowest wCV (between 19 and 29%). For individuals, a log(10) K(trans) change of approximately 0.90 in muscles and 0.52 in the ischium would be statistically significant. The corresponding absolute changes for v(e) are 6.7% in muscle and 13.6% in the ischium. For a group of 19 patients, small changes are statistically significant (muscle log(10) K(trans) 0.208 and v(e) 1.5% and ischium log(10) K(trans) 0.123 and v(e) 3.1%). Fat and the femoral head are unreliable tissues from which to obtain kinetic parameter estimates due to poor enhancement. v(e) and MCMA have smaller coefficient of variation than K(trans) in muscles and ischium. Reproducibility studies of normal and pathological tissues should be incorporated into clinical research protocols that measure treatment effects by DCE-MRI techniques.

Adipose Tissue↗

PubMed1996

Mefloquine effect on disposition of halofantrine in the isolated perfused rat liver.

Halofantrine and mefloquine are antimalarial drugs used in the treatment of malaria, including that caused by chloroquine-resistant Plasmodium falciparum. Reports of drug-associated adverse reactions, including sudden death in one patient, have prompted concerns over the safety of halofantrine and the potential for drug-drug interactions. We used the isolated perfused rat liver (IPRL) model to investigate a possible hepatic metabolic or pharmacokinetic drug-drug interaction between halofantrine and mefloquine. Pharmacokinetic parameter estimates for halofantrine in the IPRL reflected the pattern seen in in-vivo studies with doses comparable with clinical doses. Halofantrine parameter estimates (mean +/- s.d.) were: volume of distribution (Vd), 7.53 +/- 1.45 mL (g liver)-1; clearance (CL), 0.11 +/- 0.07 mL min-1 (g liver)-1; initial distribution half-life (initial t1/2), 14.62 +/- 2.38 min; terminal half-life (terminal t1/2), 138.7 +/- 178.8 min; AUC 606 +/- 194 mg mL-1 min-1 (g liver)-1; elimination rate constant (Ke), 0.0135 +/- 0.012 min-1. Prior dosing with mefloquine did not affect halofantrine perfusate pharmacokinetic parameter estimates of Vd, Ke, initial and terminal t1/2 (P > 0.05). A single dose, short term (4-6 h) interaction showed significant changes in the perfusate clearance of halofantrine in mefloquine-pretreated livers using higher doses of halofantrine. Substantial changes were seen in bile production (P < 0.05) and biliary clearance (P < 0.05) of halofantrine in mefloquine-pretreated livers. These findings may have clinical implications in models utilizing multiple drug dosages or in patients with severe malaria who have disease-related cholestasis.

Animals↗

PubMed1994

Estimating respiratory mechanical parameters of ventilated patients: a critical study in the routine intensive-care unit.

Airflow and pressure were measured post-operatively in eight mechanically ventilated patients in the routine intensive care unit. Analysis of the input impedance spectra versus frequency suggested that respiratory data cannot be adequately reproduced using the classic two-element R-C model, as the real part of input impedance decreases with frequency. To fit in with this behaviour, we adopted a three-element model with an additional parallel compliance. The three parameters of this model were estimated separately in the frequency and time domains by minimising suitable least-square criterion functions. The results demonstrate a good agreement between the parameter estimates in the frequency and time domains, and show that the three-element model reproduces the input impedance frequency pattern in the range 0.2-8 Hz. Comparison of different linear models in the time domain demonstrated that the precision of parameter estimates and the quality of best fitting sharply increase from the two-element to the three-element model. The addition of a fourth resistive parameter, like in the Mead model, does not lead to appreciable improvement and makes the model almost unidentifiable. The possible contribution of a ventilator-patient circuit of the upper airway shunting and of the peripheral airway obstruction are also discussed.

Airway Resistance↗

PubMed2002

Estimation of pharmacokinetic parameters by orthogonal regression: comparison of four algorithms.

The contribution of non-linear orthogonal regression for estimation of individual pharmacokinetic parameters when drug concentrations and sampling times are subject to error was studied. The first objective was to introduce and compare four numerical approaches that involve different degrees of approximation for parameter estimation by orthogonal regression. The second objective was to compare orthogonal with non-orthogonal regression. These evaluations were based on simulated data sets from 300 'subjects', thereby enabling precision and accuracy of parameter estimates to be determined. The pharmacokinetic model was a one-compartment open model with first-order absorption and elimination rates. The inter-individual coefficients of variation (CV) of the pharmacokinetic parameters were in the range 33-100%. Eight measurement-error models for times and concentrations (homo- or heteroscedastic with constant CV) were considered. Accuracy of the four algorithms was very close in almost all instances (typical bias, 1-4%). Precision showed three expected trends: root mean squared error (RMSE) increased when the residual error was larger or the number of observations was smaller, and it was highest for the absorption rate constant and common error variance. Overall, RMSE ranged from 5 to 40%. It was found that the simplest algorithm for othogonal regression performed as well as the more complicated approaches. Errors in sampling time resulted in an increased bias and imprecision in individual parameter estimates (especially for k(a) in our example) and in common error variance when the estimation method did not take into account these errors. In this situation, use of orthogonal regression resulted in smaller bias and better precision.

Algorithms↗

PubMed1978

A procedure for obtaining initial estimates of parameters appearing in steady-state rate or equilibrium binding equations.

A "peeling" procedure is described for obtaining initial estimates of the parameters in the equation: formula: (see text), where P(x) and Q(x) are polynomials in x. The method is illustrated, in the context of enzyme kinetics, using data which are fitted to the following equation: formula: (see text), where v denotes the initial steady-state velocity at an initial substrate concentration S, and a1, a2, b1, and b2 are non-negative constants. The applicability and limitations of the method for data fitting in fields such as enzyme kinetics and ligand-binding studies are discussed.

Carboxypeptidases↗

PubMed1978

General treatment of competitive binding of small molecules to macromolecules as applied to dynamic dialysis: theoretical analysis.

A mathematical analysis of the dynamic dialysis process is presented, demonstrating how the process can be applied generally to study competitive and noncompetitive binding between small molecules and macromolecules. A law of mass action model for competitive binding with independent sites and classes with equivalent sites (CIE) is considered as a specific case without loss of generality. The escape profiles of two compounds are calculated to illustrate the effect of an increasing degree of binding competition. Noisy data are generated using the CIE model to test the presented method of estimating competitive binding parameters. The parameters estimated by the nonlinear regression technique came close to the true values, considering the degree of noise added to the exact dialysis data. A transformation approach is presented, enabling initial estimates of the binding parameters in the CIE model to be determined by multiple linear regression, thereby eliminating the main problem in the nonlinear estimation. The presented method of analysis is extended to strongly bound compounds, which also bind significantly to the dialysis membrane.

Binding, Competitive↗

PubMed1991

A compartmental model to analyze ruminal digestion.

In contrast to digestion models that include a discrete lag phase, a compartmental digestion model was proposed. It assumed the existence of a lag compartment and a digestion compartment. Substrate present in the digestion compartment was subject to first-order kinetics digestion. Flow of substrate from the lag compartment to the digestion compartment was proposed to be a first-order process and likely was affected by hydration of substrate, bacterial attachment, and colonization. The proposed model was compared with models that assumed the existence of a discrete lag phase. Parameter estimates for these models were obtained either through logarithmic transformation of data or nonlinear regression. Statistically, there was no difference between the compartmental model and the nonlinear model with a discrete lag phase. Differences in parameter estimates between these two models were small. Residual mean squares were higher for the logarithmically transformed models. Differences in parameter estimates between these models and the compartmental model depended on the structure of the experimental data. In a number of cases, the nonlinear parameters of the compartmental model converged to the same value, resulting in a different interpretation of the model. Residual mean squares for predicting rate of disappearance were lowest for the compartmental model.

Animals↗

PubMed1976

[Simple dynamic model of the human blood pressure regulatory system as based on the orthostatic load sequence].

The two statistical parameter estimation methods, the recursive least squares and the recursive generalized least squares, are dealt with briefly. An additional noncorrelated disturbance is necessary for unbiased parameter estimation in the closed-loop system. The disturbance is realized by an orthostatic load sequence shaped according to the experimental programme. Men and women were subjected to head-up tilt between 10 degrees and 55 degrees. The disturbance, mean blood pressure and heart rate were measured. These discrete data were used for parameter estimation of transfer functions.

Adolescent↗

PubMed2005

Robust population pharmacokinetic experiment design.

The population approach to estimating mixed effects model parameters of interest in pharmacokinetic (PK) studies has been demonstrated to be an effective method in quantifying relevant population drug properties. The information available for each individual is usually sparse. As such, care should be taken to ensure that the information gained from each population experiment is as efficient as possible by designing the experiment optimally, according to some criterion. The classic approach to this problem is to design "good" sampling schedules, usually addressed by the D-optimality criterion. This method has the drawback of requiring exact advanced knowledge (expected values) of the parameters of interest. Often, this information is not available. Additionally, if such prior knowledge about the parameters is misspecified, this approach yields designs that may not be robust for parameter estimation. In order to incorporate uncertainty in the prior parameter specification, a number of criteria have been suggested. We focus on ED-optimality. This criterion leads to a difficult numerical problem, which is made tractable here by a novel approximation of the expectation integral usually solved by stochastic integration techniques. We present two case studies as evidence of the robustness of ED-optimal designs in the face of misspecified prior information. Estimates from replicate simulated population data show that such misspecified ED-optimal designs recover parameter estimates that are better than similarly misspecified D-optimal designs, and approach estimates gained from D-optimal designs where the parameters are correctly specified.

Algorithms↗

PubMed1998

Alternative models for analyses of liver and mammary transorgan metabolite extraction data.

Alternative models for analyses of liver and mammary transorgan data were formulated and fitted to liver and mammary data sets respectively. The models considered metabolite inputs to and effluxes from an extracellular pool. In general, fits were greatly improved over previous efforts using other models (Miller et al. 1991a; Hanigan et al. 1992; Wray-Cahen et al. 1997). Errors of prediction were generally less than 15% for liver and less than 20% for mammary glands. With the possible exception of glutamine for the udder, all metabolites exhibited linear responses to extracellular concentrations within the observed ranges of inputs. However, prediction biases were evident for beta-hydroxybutyrate, acetate, and propionate by liver and for arginine, histidine, citrulline and glycerol by mammary tissue. These biases were hypothesized to be caused by the existence of additional regulatory complexity. With the exception of histidine, parameter estimates for essential amino acid removal by liver were 2-3-fold lower than for mammary gland. Infusion of an amino acid mixture into the mesenteric vein did not alter parameter estimates for removal of amino acids by the liver. Treatment of cows with bovine somatotropin resulted in changes in mammary parameter estimates for aspartate, glutamate, leucine, phenylalanine, glucose, and glycerol.

Amino Acids↗