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PubMed2003

Volume scattering of distributed microbubbles and its influence on blood flow estimation.

In recent years, microbubble contrast agents have become a potential adjunct in Doppler ultrasound diagnosis. In this paper, we show that volume scattering makes the effective band in Doppler spectrum shift downward after injection of microbubbles. Because the insonified volume comprises a collection of distributed microbubbles, the statistical properties such as the autocorrelation function and ensemble average power spectrum of the echoes from a collection of distributed microbubbles were derived first. It can be observed that, beyond a critical frequency, the theoretical volume backscattering cross section derived from the ensemble average power spectrum of microbubbles decreases with frequency. On the contrary, the volume backscattering cross section of red cells increases with frequency. Using two-dimensional (2-D) Fourier transform, the variation in Doppler spectrum caused by different volume backscattering cross section can be demonstrated, and the consequential downward shifts of the estimated Doppler parameters (e.g., the mean and maximum Doppler shifts, and the variance of Doppler power spectrum) after microbubble injection are shown. In addition, it can be observed that the variation gets larger as the transmitted bandwidth increases. And, the variations in Doppler parameters estimated with experimental data are presented to verify the theoretical deviations.

Blood Flow Velocity↗

PubMed2002

Frailty models with missing covariates.

We present a method for estimating the parameters in random effects models for survival data when covariates are subject to missingness. Our method is more general than the usual frailty model as it accommodates a wide range of distributions for the random effects, which are included as an offset in the linear predictor in a manner analogous to that used in generalized linear mixed models. We propose using a Monte Carlo EM algorithm along with the Gibbs sampler to obtain parameter estimates. This method is useful in reducing the bias that may be incurred using complete-case methods in this setting. The methodology is applied to data from Eastern Cooperative Oncology Group melanoma clinical trials in which observations were believed to be clustered and several tumor characteristics were not always observed.

Clinical Trials, Phase III as Topic↗

PubMed2003

Maximum likelihood methods for nonignorable missing responses and covariates in random effects models.

This article analyzes quality of life (QOL) data from an Eastern Cooperative Oncology Group (ECOG) melanoma trial that compared treatment with ganglioside vaccination to treatment with high-dose interferon. The analysis of this data set is challenging due to several difficulties, namely, nonignorable missing longitudinal responses and baseline covariates. Hence, we propose a selection model for estimating parameters in the normal random effects model with nonignorable missing responses and covariates. Parameters are estimated via maximum likelihood using the Gibbs sampler and a Monte Carlo expectation maximization (EM) algorithm. Standard errors are calculated using the bootstrap. The method allows for nonmonotone patterns of missing data in both the response variable and the covariates. We model the missing data mechanism and the missing covariate distribution via a sequence of one-dimensional conditional distributions, allowing the missing covariates to be either categorical or continuous, as well as time-varying. We apply the proposed approach to the ECOG quality-of-life data and conduct a small simulation study evaluating the performance of the maximum likelihood estimates. Our results indicate that a patient treated with the vaccine has a higher QOL score on average at a given time point than a patient treated with high-dose interferon.

Analysis of Variance↗

PubMed1989

Comparison of Sawchuk-Zaske and Bayesian forecasting for aminoglycosides in seriously ill patients.

1. Individual pharmacokinetic parameters and predicted steady-state serum concentrations of aminoglycosides were calculated by Sawchuck-Zaske (SZ) and Bayesian methods. 2. Predicted concentrations were compared with observed steady-state concentrations for 36 seriously ill patients with systemic infections. Four aminoglycoside concentrations were used for the SZ method. Differing numbers of serum aminoglycoside samples were used in the Bayesian parameter estimation: one sample Bayesian used one post-infusion concentration, two sample Bayesian used a trough plus one post-infusion concentrations and four sample Bayesian used a trough plus three post-infusion concentrations. 3. 79% of the SZ predictions were with +/- 2 mg l-1 of the observed peak concentrations, and 72% of the two sample Bayesian predictions were within the same range. 82% of SZ and the two sample Bayesian predictions were within +/- 1 mg l-1 of the observed trough concentrations. 4. A confidence interval comparison of estimated pharmacokinetic parameters and precision for the predicted concentrations showed no important differences between the SZ and the two sample Bayesian. The four sample Bayesian was the most precise method. 5. We conclude that the Bayesian forecasting method utilizing a trough plus one post-infusion concentrations is as useful as the SZ method which requires three to four serum concentrations in individualizing aminoglycoside therapy for seriously ill patients.

Adolescent↗

PubMed2006

Detecting pulsatile hormone secretions using nonlinear mixed effects partial spline models.

Neuroendocrine ensembles communicate with their remote and proximal target cells via an intermittent pattern of chemical signaling. The identification of episodic releases of hormonal pulse signals constitutes a major emphasis of endocrine investigation. Estimating the number, temporal locations, secretion rate, and elimination rate from hormone concentration measurements is of critical importance in endocrinology. In this article, we propose a new flexible statistical method for pulse detection based on nonlinear mixed effects partial spline models. We model pulsatile secretions using biophysical models and investigate biological variation between pulses using random effects. Pooling information from different pulses provides more efficient and stable estimation for parameters of interest. We combine all nuisance parameters including a nonconstant basal secretion rate and biological variations into a baseline function that is modeled nonparametrically using smoothing splines. We develop model selection and parameter estimation methods for the general nonlinear mixed effects partial spline models and an R package for pulse detection and estimation. We evaluate performance and the benefit of shrinkage by simulations and apply our methods to data from a medical experiment.

Animals↗

PubMed2005

Fractional order viscoelasticity of the aortic valve cusp: an alternative to quasilinear viscoelasticity.

BACKGROUND: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. METHOD OF APPROACH: A one-dimensional (I-D) FOV reduced relaxation function was developed, replacing the QLV "box-spectrum" function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. RESULTS: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant (tau2). The mean (n = 5) fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. RESULTS SUMMARY: mean QLV parameters were C = 0.079, tau1 = 0.004, tau2 = 76, and mean FOV parameters were beta = 0.29, tau = 0.076, and rho = 1.84. CONCLUSIONS: FOV can provide valuable new insights into tissue viscoelastic behavior Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison.

Animals↗

PubMed2001

A constrained formulation for the receiver operating characteristic (ROC) curve based on probability summation.

We propose a principled formulation of the ROC curve that is constrained in a realistic way by the mechanism of probability summation. The constrained and conventional ROC formulations were fitted to 150 separate sets of rating data taken from previous observer studies of 250 or 529 chest radiographs. A total of 20 different readers had used either discrete or continuous rating scales to evaluate those chest cases for likelihood of separate specified abnormalities: interstitial disease, pulmonary nodule, pneumothorax, alveolar infiltrate, or rib fracture. Both ROC formulations were fitted separately to every set of rating data using maximum-likelihood statistical procedures that specified each ROC curve by normally distributed latent variables with two scaling parameters, and estimated the area below the ROC curve (Az) with its standard error. The conventional and constrained binormal formulations usually fitted ROC curves that were nearly indistinguishable in form and in Az. But when fitted to asymmetric rating data that contained few false-positive cases, the conventional ROC curves often rose steeply, then flattened and extrapolated into an unrealistic upward "hook" at the higher false-positive rates. For those sets of rating data, the constrained ROC curves (without hooks) estimated larger values for Az with smaller standard errors. The constrained ROC formulation describes observers' ratings of cases at least as well as the conventional ROC, and always guarantees a realistic fitted curve for observer performance. Its estimated parameters are easy to interpret, and may also be used to predict observer accuracy in localizing the image abnormalities.

Databases as Topic↗

PubMed1988

Pharmacokinetics of teicoplanin in pediatric patients.

The pharmacokinetics of teicoplanin have been studied in 13 pediatric male patients from 2 to 12 years of age. Patients were given a single 3-mg/kg intravenous dose of teicoplanin for prophylaxis. Blood and urine samples were collected for 8 days after administration, and teicoplanin levels were determined by microbiological assay. Pharmacokinetic parameters were estimated from a three-compartment open pharmacokinetic model and from a noncompartmental analysis. Levels in plasma 1 h after the administration averaged 14.8 mg/liter. The half-lives of the two distribution phases were 1.3 and 9.7 h. The half-life of the terminal phase averaged 57.9 h, with similar estimates obtained from the noncompartmental analysis and from data from urine. The volume of distribution of the central compartment was 0.15 liter/kg, whereas the volume of distribution at steady state and during the elimination phase were 0.80 and 1.25 liters/kg. The total teicoplanin clearance averaged 14.8 ml/h per kg, with renal clearance accounting for about 60% of the total. The average cumulative recovery of teicoplanin in urine over 8 days was 59% of the dose, similar to the value obtained in adult volunteers. There was no significant linear correlation between elimination half-life and age. Preliminary data after repeated administration support the reliability of the model used and the validity of the mean estimated parameters. There were no local or systemic adverse reactions to teicoplanin.

Analysis of Variance↗

PubMed2006

Comparison of censored regression and standard regression analyses for modeling relationships between antimicrobial susceptibility and patient- and institution-specific variables.

In order to identify patients likely to be infected with resistant bacterial pathogens, analytic methods such as standard regression (SR) may be applied to surveillance data to determine patient- and institution-specific factors predictive of an increased MIC. However, the censored nature of MIC data (e.g., MIC < or = 0.5 mg/liter or MIC > 8 mg/liter) imposes certain limitations on the use of SR. In order to investigate the nature of these limitations, simulations were performed to compare a regression tailored for censored data (censored regression [CR]) and one tailored for an SR. By using a model relating piperacillin-tazobactam MICs against Enterobacter spp. to patient age and hospital bed capacity, 200 simulations of 500 isolates were performed. Various MIC censoring patterns were imposed by using 26 left- or right-censored (L,R) pairs (i.e., MICs < or = 2 mg/liter(L) [2L] or MICs > 2 mg/liter(R) [2R], respectively). Data were fit by CR and SR for which censored MICs were either (i) excluded, (ii) replaced by 2L or 2R, or (iii) replaced by 2(L - 1) or 2(R + 1). Total censoring for the 26 pairs ranged from 7 to 86%. By CR, deviations of average parameter estimates from the true parameter values were <0.10 log2 (mg/liter) for all parameters for each of the 26 pairs. By SR, these deviations were >0.10 log2 (mg/liter) for at least 18 of the 26 pairs for all but one parameter. Two-standard-error confidence intervals for individual parameters contained as little as 0% of cases for all SR approaches but > or = 91.5% of cases for the CR approach. When censored MIC data are modeled, CR may reduce or eliminate biased parameter estimates obtained by SR.

Anti-Bacterial Agents↗

PubMed2001

Recruitment times, proliferation, and apoptosis rates during the CD8(+) T-cell response to lymphocytic choriomeningitis virus.

The specific CD8(+) T-cell response during acute lymphocytic choriomeningitis virus (LCMV) infection of mice is characterized by a rapid proliferation phase, followed by a rapid death phase and long-term memory. In BALB/c mice the immunodominant and subdominant CD8(+) responses are directed against the NP118 and GP283 epitopes. These responses differ mainly in the magnitude of the epitope-specific CD8(+) T-cell expansion. Using mathematical models together with a nonlinear parameter estimation procedure, we estimate the parameters describing the rates of change during the three phases and thereby establish the differences between the responses to the two epitopes. We find that CD8(+) cell proliferation begins 1 to 2 days after infection and occurs at an average rate of 3 day(-1), reaching the maximum population size between days 5 and 6 after immunization. The 10-fold difference in expansion to the NP118 and GP283 epitopes can be accounted for in our model by a 3.5-fold difference in the antigen concentration of these epitopes at which T-cell stimulation is half-maximal. As a consequence of this 3.5-fold difference in the epitope concentration needed for T-cell stimulation, the rates of activation and proliferation of T cells specific for the two epitopes differ during the response and in combination can account for the large difference in the magnitude of the response. After the peak, during the death phase, the population declines at a rate of 0.5 day(-1), i.e., cells have an average life time of 2 days. The model accounts for a memory cell population of 5% of the peak population size by a reversal to memory of 1 to 2% of the activated cells per day during the death phase.

Animals↗

PubMed2006

Anticoagulant and anti-platelet effects are maintained following coadministration of otamixaban, a direct factor Xa inhibitor, and acetylsalicylic acid.

The pharmacokinetics, pharmacodynamics and safety of the direct factor Xa inhibitor, otamixaban, with and without concomitant acetylsalicylic acid (ASA) were investigated in healthy volunteers. The study was a double-blind, placebo-controlled 3-way crossover study. Sixty-eight male volunteers in total were randomised to otamixaban, ASA, or otamixaban with ASA. ASA (300 mg once a day) was started 2 days before and continued on the day of the otamixaban 6-hour IV infusion (0.3 and 0.5 mg/kg). Pharmacokinetic and pharmacodynamic parameters (coagulation markers, platelet function tests and skin bleeding time) were determined. Drug interaction was assessed by the ratios of geometric means and 90% confidence intervals (90% CI)of the parameter estimates. Pharmacokinetic parameters of otamixaban remained unchanged with ASA. Ratios of geometric means (90% CI) were for Ceoi 96.54 (91.21-102.19) and 95.04 (90.10-100.24) and for AUC 98.0 (93.92-102.25) and 95.90 (92.61-99.31), for 0.3 and 0.5 mg/kg, respectively. No drug interaction was observed between otamixaban and ASA on the coagulation and platelet function parameters. Neither otamixaban nor ASA had an effect on skin bleeding time; their co-administration led to a slight prolongation of skin bleeding time above the normal range without any clinically relevant bleeding. This study demonstrated that the desired effects of otamixaban and ASA, namely anticoagulation and platelet inhibition, respectively, are maintained during co-administration of both drugs.

Adolescent↗

PubMed2006

Modeling sensorimotor learning with linear dynamical systems.

Recent studies have employed simple linear dynamical systems to model trial-by-trial dynamics in various sensorimotor learning tasks. Here we explore the theoretical and practical considerations that arise when employing the general class of linear dynamical systems (LDS) as a model for sensorimotor learning. In this framework, the state of the system is a set of parameters that define the current sensorimotor transformation-the function that maps sensory inputs to motor outputs. The class of LDS models provides a first-order approximation for any Markovian (state-dependent) learning rule that specifies the changes in the sensorimotor transformation that result from sensory feedback on each movement. We show that modeling the trial-by-trial dynamics of learning provides a substantially enhanced picture of the process of adaptation compared to measurements of the steady state of adaptation derived from more traditional blocked-exposure experiments. Specifically, these models can be used to quantify sensory and performance biases, the extent to which learned changes in the sensorimotor transformation decay over time, and the portion of motor variability due to either learning or performance variability. We show that previous attempts to fit such models with linear regression have not generally yielded consistent parameter estimates. Instead, we present an expectation-maximization algorithm for fitting LDS models to experimental data and describe the difficulties inherent in estimating the parameters associated with feedback-driven learning. Finally, we demonstrate the application of these methods in a simple sensorimotor learning experiment: adaptation to shifted visual feedback during reaching.

Algorithms↗

PubMed2000

Evaluating agreement between two analytical methods in clinical chemistry.

A test and a reference analytical method are usually compared for agreement based on paired data obtained from several independent subjects. Bias between two methods can be classified as constant and proportional. Bias is modeled as an average bias between two methods (constant bias) and proportional bias related to individual measurements. A weighted least square approach is followed for estimating the parameters. Estimates of constant and proportional biases are tested individually and their significance can be used to explain the sources of disagreement between two methods and help deciding a remedial strategy. The proposed model can also be used to determine an optimum combination of subjects and runs per subject and facilitate the allocation of the resources.

Clinical Chemistry Tests↗

PubMed2006

Mapping quantitative trait loci for longitudinal traits in line crosses.

Quantitative traits whose phenotypic values change over time are called longitudinal traits. Genetic analyses of longitudinal traits can be conducted using any of the following approaches: (1) treating the phenotypic values at different time points as repeated measurements of the same trait and analyzing the trait under the repeated measurements framework, (2) treating the phenotypes measured from different time points as different traits and analyzing the traits jointly on the basis of the theory of multivariate analysis, and (3) fitting a growth curve to the phenotypic values across time points and analyzing the fitted parameters of the growth trajectory under the theory of multivariate analysis. The third approach has been used in QTL mapping for longitudinal traits by fitting the data to a logistic growth trajectory. This approach applies only to the particular S-shaped growth process. In practice, a longitudinal trait may show a trajectory of any shape. We demonstrate that one can describe a longitudinal trait with orthogonal polynomials, which are sufficiently general for fitting any shaped curve. We develop a mixed-model methodology for QTL mapping of longitudinal traits and a maximum-likelihood method for parameter estimation and statistical tests. The expectation-maximization (EM) algorithm is applied to search for the maximum-likelihood estimates of parameters. The method is verified with simulated data and demonstrated with experimental data from a pseudobackcross family of Populus (poplar) trees.

Chromosome Mapping↗

PubMed1999

Association of growth hormone loci with milk yield traits in Holstein bulls.

A pedigree analysis was used to investigate the association of bovine growth hormone loci with milk production traits of Holstein cattle. Holstein bulls were typed for three bovine growth hormone loci located in exon V, intron C, and the 3' region of the gene. Phenotypic data were daughter yield deviations for milk, fat, and protein yields and for fat and protein percentages. Analysis of linkage across families was applied to the data using one or two bovine growth hormone loci as markers linked to a putative biallelic quantitative trait locus. Estimated parameters were allele frequency, genotypic means, within-genotype standard deviation of a putative quantitative trait locus, and recombination fraction between the markers and the quantitative trait locus. Parameters were estimated by maximum likelihood techniques. The estimated frequency of the quantitative trait locus allele that decreased the value of the phenotype ranged from 0.1 for milk yield to 0.6 for protein yield. The estimated effect of an allele substitution at the quantitative trait locus, given in phenotypic standard deviation units, ranged from 0.75 for fat percentage to 1.6 for milk yield. The standard deviation within genotype ranged from 0.67 for fat yield to 0.87 for milk yield. The estimated recombination fraction was close to zero for protein percentage, indicating physical linkage between a quantitative trait locus affecting the trait and the bovine growth hormone loci.

Alleles↗

PubMed2003

Adaptive control of the nitrate level in an activated sludge process.

In an activated sludge process for nitrogen removal, nitrate may be reduced to nitrogen gas by facultative heterotrophic bacteria in an anoxic environment. In order to guarantee sufficient supplies of readily biodegradable carbon compounds, an external carbon source often needs to be added. In this paper, an automatic control strategy for controlling the nitrate level using an external carbon source is presented. The external carbon source is added in the first anoxic zone to control the nitrate concentration in the last anoxic zone. Key process parameters are estimated on-line for a simplified Activated Sludge Model No 1. The estimated parameters are used for updating a linear quadratic controller. The strategy is illustrated in a simulation study with realistic influent data and is shown to perform very well.

Bioreactors↗

PubMed2005

Parametric imaging of myocardial blood flow with 15O-water and PET using the basis function method.

UNLABELLED: Regional myocardial blood flow (MBF) can be measured with 15O-water and PET using the 1-tissue-compartment model with perfusable tissue fraction, which provides an MBF value that is free from the partial-volume effect. Studies with 15O-water have several advantages, such as the ability to repeat a scan. However, because of the short scanning time and the small distribution volume of 15O-water in the myocardium, the image quality of 15O-water is limited, impeding the computation of MBF and perfusable tissue fraction at the voxel level. We implemented the basis function method for generating parametric images of MBF, perfusable tissue fraction, and arterial blood volume (Va) with 15O-water and PET. The basis function method linearizes the solution of the 1-tissue-compartment model, which results in a computationally much faster method than the conventional nonlinear least-squares fitting method in estimating the parameters. METHODS: To validate the basis function method, we performed a series of PET studies on miniature pigs (n = 7). After acquisition of the transmission scan for attenuation correction and the 15O-CO scan for obtaining the blood-pool image, repeated PET scans with 15O-water were obtained with varying doses of adenosine or CGS-21680 (selective adenosine A(2a) receptor agonist). MBF, perfusable tissue fraction, and Va values of the myocardial region for each scan were computed using the basis function method and the nonlinear least-squares method, and the parameters estimated by the 2 methods were compared. RESULTS: MBF images generated by the basis function method demonstrated an increase in blood flow after administration of adenosine or CGS-21680. The MBF values estimated by the basis function method and by the nonlinear least-squares method correlated strongly. CONCLUSION: The basis function method produces parametric images of MBF, perfusable tissue fraction, and Va with 15O-water and PET. These images will be useful in detecting regional myocardial perfusion abnormalities.

Algorithms↗

PubMed2006

[Bioequivalence assessment of pioglitazone hydrochloride oral preparation by limited sampling strategy].

AIM: To develop limited sampling strategy (LSS) for estimation of C(max) and AUC(0-t) and assessing the bioequivalence of two pioglitazone hydrochloride (PGT) preparations. METHODS: Healthy subjects (n = 20), enrolled in a bioequivalence study, were received 30 mg PGT po of reference or test formulation. The plasma concentration of PGT was determined by the validated HPLC method. A multiple linear regression analysis of the Cmax and AUC(0-t) against the PGT concentration for the reference formulation was carried out to develop LSS models to estimate these parameters. The models were internally validated by the Jackknife method and externally validated using simulated sets generated by Monte Carlo method. The best model was employed to assess bioequivalence of the two PGT formulations. RESULTS: The linear relationship between pharmacokinetics parameters and single concentration point was poor. Several models for these parameters estimation met the predefined criteria (r2 > 0.9). The Jackknife validation procedure revealed that LSS models based on two sampling times (C1, C2.5 and C1.5, C2.5 for C(max); C1.5, C9 and C2.5, C9 for AUC(0-t) predict accurately. Mean prediction errors (MPE) were less than 3%, and mean absolute prediction error (MAE) were less than 9%. The prediction error (PE) beyond 20% was less than 5% of total samples. Model external validation by Monte Carlo simulated data indicated that the most informative sampling combinations were C1.5, C2.5 for C(max), and C1.5, C9 for AUC(0-t), respectively. MPE and MAE of the proposed models were less than 5% , and 9% respectively. The PE beyond 20% was less than 5% of the total. Bioequivalence assessment of the two PGT formulations, based on the best LSS models, provided results similar to those obtained using all the observed concentration-time data points, and indicated that the two PGT formulations were bioequivalent. CONCLUSION: The LSS method for bioequivalence assessment of PGT formulations was established and proved to be applicable and accurate. Thus, it could be considered appropriate for PGT bioequivalence study with inexpensive cost of sampling acquisition and analysis. Key words: pioglitazone hydrochloride; limited sampling strategy; Monte Carlo simulation; bioequivalence

Administration, Oral↗