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PubMed1990

Modelling human tibia structural vibrations.

Mode shapes and natural frequencies of human long bones play an important role in the interpretation, prediction and control of their dynamic response to external mechanical loads. This paper describes an experimental and theoretical study of free vibrations in an excised human tibia. Experimentally, seven tibial natural frequencies in the range 0-3 kHz were identified through measured structural transfer functions. Theoretically, a beam type Finite Element model of a human tibia is suggested. Unknown parameters in this model are determined by a Bayesian parameter estimation approach, by which very fine model/observation-accordance was achieved with realistic parameter estimates. A sensitivity analysis of the model confirms that the human tibia in a vibrational sense is more uniform than its complicated geometry would immediately suggest. Accordingly, two simple tibia models are identified, based on uniform beam theory with inclusion of shear deformations.

Biomechanical Phenomena↗

PubMed1997

Cardiac muscarinic receptors. Relationship between the G protein and multiple states of affinity.

An expanded version of the mobile receptor model has been assessed in studies on the binding of N-[3H]methylscopolamine and [35S]GTPgammaS to cardiac muscarinic receptors and their attendant G proteins in ventricular membranes from hamster. The model comprises two pools of receptor, one of which lacks G proteins, and a heterogeneous population of G proteins that compete for the receptor within the G protein-containing pool. To guide the formulation of the model itself and to define the various parameters, data were combined from assays performed under various conditions with native membranes and following irreversible blockade of about 80% of the receptors with propylbenzilylcholine mustard. Multiple G proteins are indicated primarily by multiple states of affinity evident in the dose-dependent effect of guanyl nucleotides on the binding of carbachol; G protein-free receptors are indicated by sites of low affinity for carbachol that survive treatment with the mustard. The expanded model generally succeeds where more frugal schemes have been inadequate, but it nevertheless fails to yield a mechanistically consistent description of the data. Guanyl nucleotides and partial alkylation do not affect the inhibitory potency of carbachol in a manner consistent with their supposed effect on the equilibrium between uncoupled and G protein-coupled receptors. As inferred from the model, G proteins are lost upon alkylation of the receptor, and their numbers are regulated by guanyl nucleotides. Parameters estimated via N-[3H]methylscopolamine are wholly inconsistent with the same parameters estimated via [35S]GTPgammaS. The failure of the model suggests that multiple states of affinity may not arise from a ligand-regulated equilibrium between free receptors and G proteins on the one hand and one or more RG complexes on the other.

Animals↗

PubMed1982

[Mathematical methods in flow cytometry: the problem of evaluating DNA histograms of partially synchronous cell populations].

There is presented a procedure for determining the phase fractions in a cell population (i.e. the fractions of the G1-, S- and G2 + M-cells) from the corresponding DNA histogram obtained by flow cytometry. The evaluation procedure can regard arbitrary apriori information about the model parameters. It is based on a mathematical model of the DNA distribution for a growing cell population which contains the phase fractions and some further values as parameters. The parameter estimations rest on the Maximum-Likelihood-Principle by which the parameters of the theoretical model must be determined in such a way that the measured histogram corresponds to a maximum probability. As a consequence of the model flexibility especially the S-phase fraction which can be determined independently by labeling techniques, can be regarded as a fixed predetermined value. Such apriori information enhances the preciseness of the parameter estimation. The applications have shown that the determination of the S-phase fraction by means of flow cytometry can be very unprecise especially under partial synchronization. For the application of the evaluation programs (programming language ALGOL) the histograms must be free of cell detritus and clumping.

Animals↗

PubMed1978

Estimation of ferrokinetic parameters by a mathematical model in patients with primary acquired sideroblastic anaemia.

Ferrokinetic parameters were estimated in eight patients with primary acquired sideroblastic anaemia (PASA) by means of a mathematical model of iron kinetics. Both plasma 59Fe clearance and red cell utilization curves were used to identify the model parameters. The close agreement between experimental and theoretical data proved that the model can describe iron kinetics in sideroblastic anaemia. Ineffective erythropoiesis was found to be major factor in the production of the anaemia. Various degrees and patterns of peripheral haemolysis were observed. The storage iron was always markedly increased and a large non-erythroid iron turnover was calculated in the most severely affected patients. The results are compared with present knowledge of erythropoiesis in PASA.

Aged↗

PubMed2002

Modeling coagulation kinetics incorporating fractal theories: comparison with observed data.

There are currently four possible approaches in modeling coagulation kinetics: the traditional Euclidean rectilinear; the Euclidean curvilinear; the fractal rectilinear; and the fractal curvilinear. The fractal model includes the Euclidean case as a subset. The primary purpose of this research is to investigate which of the rectilinear models among these best predicts the evolution of experimental observed particle size distribution (PSD). Using a fractal rectilinear model previously developed by the authors, model predictions were compared with a series of observed PSD data obtained from estuarine sediment particles in a 2m settling column, where the average velocity gradient (G) was 20 or 40s(-1). Nonlinear parameter estimation was performed to estimate two free parameters for the fractal model (the fractal dimension, DF, and the collision efficiency factor, a), and one free parameter (the collision efficiency factor, alpha) for the Euclidean model. Compared with the observed PSD, the simulation showed that the fractal rectilinear model was best, and that this model fit better for the larger size particles. The estimated DF was between 2.6 and 3.0. The research demonstrated that the alpha's have multiple values for the same observed data, depending on the coagulation model used. This finding is significant because a is currently used as a single value based on the conventional Euclidean rectilinear model.

Geologic Sediments↗

PubMed1983

The analysis of rates using Poisson regression models.

Models are considered in which the underlying rate at which events occur can be represented by a regression function that describes the relation between the predictor variables and the unknown parameters. Estimates of the parameters can be obtained by means of iteratively reweighted least squares (IRLS). When the events of interest follow the Poisson distribution, the IRLS algorithm is equivalent to using the method of scoring to obtain maximum likelihood (ML) estimates. The general Poisson regression models include log-linear, quasilinear and intrinsically nonlinear models. The approach considered enables one to concentrate on describing the relation between the dependent variable and the predictor variables through the regression model. Standard statistical packages that support IRLS can then be used to obtain ML estimates, their asymptotic covariance matrix, and diagnostic measures that can be used to aid the analyst in detecting outlying responses and extreme points in the model space. Applications of these methods to epidemiologic follow-up studies with the data organized into a life-table type of format are discussed. The method is illustrated by using a nonlinear model, derived from the multistage theory of carcinogenesis, to analyze lung cancer death rates among British physicians who were regular cigarette smokers.

Models, Theoretical↗

PubMed2002

Kinetic analysis of 2-[11C]thymidine PET imaging studies of malignant brain tumors: compartmental model investigation and mathematical analysis.

UNLABELLED: 2-[11C]Thymidine (TdR), a PET tracer for cellular proliferation, may be advantageous for monitoring brain tumor progression and response to therapy. We previously described and validated a five-compartment model for thymidine incorporation into DNA in somatic tissues, but the effect of the blood-brain barrier on the transport of TdR and its metabolites necessitated further validation before it could be applied to brain tumors. METHODS: We investigated the behavior of the model under conditions experienced in the normal brain and brain tumors, performed sensitivity and identifiability analysis to determine the ability of the model to estirmine whether it can distinguish between thymidine transport and retention. RESULTS: Sensitivity and identifiability analysis suggested that the non-CO2 metabolite parameters could be fixed without significantly affecting thymidine parameter estimation. Simulations showed that K1t and KTdR could be estimated accurately (r = .97 and .98 for estimated vs. true parameters) with standard errors < 15%. The model was able to separate increased transport from increased retention associated with tumor proliferation. CONCLUSION: Our model adequately describes normal brain and brain tumor kinetics for thymidine and its metabolites, and it can provide an estimate of the rate of cellular proliferation in brain tumors.

Biological Transport, Active↗

PubMed2001

Failure of traditional trough levels to predict tacrolimus concentrations.

The objective of this study was to estimate tacrolimus population parameter values and to evaluate the ability of the maximum a posteriori probability (MAP) Bayesian fitting procedure to predict tacrolimus blood levels, using the traditional strategy of monitoring only trough levels, for dosage individualization in liver transplant patients. Forty patients treated with tacrolimus after liver transplantation were studied during the early posttransplant phase (first 2 weeks). This phase was divided into four time periods (1-4 days, 5-7 days, 8-11 days, 12-14 days). Tacrolimus was administered twice daily. Approximately one determination of a tacrolimus trough level on whole blood was performed each day. The NPEM2 program was used to obtain population pharmacokinetic parameter values. With each individual pharmacokinetic parameter estimated by the MAP Bayesian method for a given period, the authors evaluated the prediction of future levels of tacrolimus for that patient for the next period. This evaluation of Bayesian fitting predictive performance was performed using the USC*PACK clinical software. Mean pharmacokinetic parameter values were in the same general range as previously published values obtained with richer data sets. However, during each period, the percentage of blood levels predicted within 20% did not exceed 40%. The traditional strategy of obtaining only trough whole blood levels does not provide enough dynamic information for the MAP Bayesian fitting procedure (the best method currently available) to be used for adaptive control of drug dosage regimens for oral tacrolimus. The authors suggest modifying the blood concentration monitoring scheme to add at least one other concentration measured during the absorptive or distributive phase to obtain more information about the behavior of the drug. D-Optimal design and similar strategies should be considered.

Bayes Theorem↗

PubMed1999

Analytical propagation of errors in dynamic SPECT: estimators, degrading factors, bias and noise.

Dynamic SPECT is a relatively new technique that may potentially benefit many imaging applications. Though similar to dynamic PET, the accuracy and precision of dynamic SPECT parameter estimates are degraded by factors that differ from those encountered in PET. In this work we formulate a methodology for analytically studying the propagation of errors from dynamic projection data to kinetic parameter estimates. This methodology is used to study the relationships between reconstruction estimators, image degrading factors, bias and statistical noise for the application of dynamic cardiac imaging with 99mTc-teboroxime. Dynamic data were simulated for a torso phantom, and the effects of attenuation, detector response and scatter were successively included to produce several data sets. The data were reconstructed to obtain both weighted and unweighted least squares solutions, and the kinetic rate parameters for a two-compartment model were estimated. The expected values and standard deviations describing the statistical distribution of parameters that would be estimated from noisy data were calculated analytically. The results of this analysis present several interesting implications for dynamic SPECT. Statistically weighted estimators performed only marginally better than unweighted ones, implying that more computationally efficient unweighted estimators may be appropriate. This also suggests that it may be beneficial to focus future research efforts upon regularization methods with beneficial bias-variance trade-offs. Other aspects of the study describe the fundamental limits of the bias variance trade-off regarding physical degrading factors and their compensation. The results characterize the effects of attenuation, detector response and scatter, and they are intended to guide future research into dynamic SPECT reconstruction and compensation methods.

Algorithms↗

PubMed2003

Using hierarchical models to analyse clinical indicators: a comparison of the gamma-Poisson and beta-binomial models.

BACKGROUND: Clinical indicators (CIs) are used to assess, compare and determine the potential to improve the care provided by hospitals and physicians. The results for Australian hospitals in 1998-2000 have been reported using a new methodology. The gamma-Poisson hierarchical model was used to correct for the effects of sampling variation by obtaining the empirical Bayesian shrunken estimates for the CI proportions for each hospital. Then, an estimate of the potential system gains that could be achieved if the mean proportion was shifted to the 20th centile is obtained for each of the 185 CIs. The results are sed to prioritize quality improvement activity. OBJECTIVES: To describe the 20th centile method of calculating potential system gains in the health care system; to determine the impact of using the beta-binomial model rather than the gamma-Poisson model to obtain shrunken estimates for the CI proportions; and to compare the computationally simpler Method of Moments (MoM) with the maximum likelihood (ML) method for parameter estimation. METHODS: The formulae for the gamma-Poisson and beta-binomial shrinkage estimators were compared analytically. Each of the shrinkage estimators and the two methods of parameter estimation were applied to the Obstetric and Gynecological CIs, and the results compared. RESULTS The comparison of the formulae for the two shrinkage estimators showed that the gamma-Poisson model results in: greater shrinkage towards the overall mean. This was verified empirically using the clinical indicators. Additionally, the MoM was not a viable alternative to the ML method. CONCLUSIONS: The gamma-Poisson model provided smaller estimates of the potential system gains by up to 6.7% of the numerator for the clinical indicators. The difference in estimation increased with increasing mean proportions and between-hospital variation. We recommend that the beta-binomial model should be used on the basis of both theoretical and empirical grounds.

Australia↗

PubMed1997

Pharmacokinetics of saquinavir, zidovudine, and zalcitabine in combination therapy.

We investigated the pharmacokinetics of zidovudine, zalcitabine, and saquinavir in AIDS Clinical Trial Group protocol 229. Patients received either saquinavir, zalcitabine, or a combination of both, together with zidovudine three times a day. Approximately 100 patients were enrolled in each treatment arm, and intensive pharmacokinetic studies were performed on about 25 patients per arm at weeks 1 and 12. We estimated the pharmacokinetic parameters of all three drugs by using parametric and nonparametric methods. The mean values of the pharmacokinetic parameters of zidovudine (clearance [CL]/bioavailability [F], 168 liters/h; volume of distribution [V]/F, 185 liters; half-life, 0.76 h) and zalcitabine (CL/F, 25 liters/h; V/F, 92.2 liters; half-life, 2.7 h) were similar to those reported previously. For saquinavir, the mean pharmacokinetic parameter estimates using parametric methods were as follows: maximum concentration of drug in serum [Cmax], 70.8 ng/ml; time to Cmax, 3.11 h; area under the curve, 809 ng x h/ml; CL/F, 989 liters/h; V/F, 1,503 liters; half-life, 1.38 h. For all three drugs, clearance decreased with age. Weight did not influence the clearance of zidovudine, but the clearance of zalcitabine and saquinavir increased with weight. There were no differences in pharmacokinetic parameters between study weeks and arms, suggesting that there is no change in kinetics with chronic administration and that there are no significant pharmacokinetic interactions among these three drugs.

Adult↗

PubMed1978

Morphometrical analysis on topographical difference in size distribution, number and volume of islets in the human pancreas.

Seven pancreases from nondiabetic autopsy cases were submitted to morphometrical analysis of the islets of Langerhans as a preliminary investigation of the diabetic pancreas. The pancreatic islets were approximately simulated by spheres of different sizes randomly dispersed in the three-dimensional space; thereon the parameters of Weibull function assumed for the distribution of islet radii were estimated stereologically from chord length measurements on histologic sections taken from different portions of the pancreas. By means of the estimated parameters topographical comparison of the number, volume, mean radius and size distribution of islets in a unit volume were performed. This islet distribution appeared to change the pattern gradually according to the position from the pancreatic head to the tail: the head was characterized by abundance of small islets that corresponded to a slightly higher islet population threat, whereas the tail by moderate increase of larger islets that caused a steep increase of islet volume here. To estimate parameters for the whole pancreas a histologic section from a range between the midposition of the pancreas and the one-fourth position from the splenic end was regarded to be a fairly good representative.

Adult↗

PubMed1989

Characterization of normal brain tissue using seven calculated MRI parameters and a statistical analysis system.

A statistical analysis system for classifying normal brain tissue has been applied to the analysis of MRI scans on 45 volunteers. The Bayes Maximum Likelihood method was used to achieve a discrimination accuracy of 84% for 13 tissue types among three age group sets, with classification accuracies for individual regions ranging from 50 to 100%. In order to attain this level of discrimination a set of seven derived relaxation-type parameters was used to categorize the tissue types. Values for these experimentally estimated parameters were derived from the MRI intensities of eight images in the following pulse sequences: (1) a Carr-Purcell-Meiboom-Gill (CPMG) four-echo train, (2) a single-echo inversion recovery, and (3) three single-echo sequences with varying repetition times, TR, and echo delays, TE. The T2 values derived from ratios of single-echo intensities showed better discrimination power than those from the four-echo CPMG train. The general precision of the seven estimated parameters was excellent, with percentage standard deviations ranging from 4 to 18% for the various regions studied. The tissue discrimination achieved by use of just three relaxation parameters, T1, T2, and proton density, calculated from intensities of images from a four-echo sequence, an inversion recovery sequence, and a short TR single-echo sequence, was not as good, being only 55%.

Adult↗

PubMed2006

Establishing bioequivalence in serial sacrifice designs.

Nonclinical in vivo animal studies have to be completed before starting clinical studies of the pharmacokinetic behavior of a drug in human subjects. The classic complete data design, where each animal is sampled for analysis once per time point, is usually only applicable for large animals using the traditional two-stage approach. The first stage involves estimation of pharmacokinetic parameters for each animal separately and the second stage uses the individual parameter estimates for statistical inference. In the case of rats and mice, where blood sampling is restricted, the batch design or the serial sacrifice design may be applicable. In batch designs samples are taken more than once from each animal, but not at all time points. In serial sacrifice designs only one sample is taken from each animal. In this paper, three methods are presented to construct confidence intervals for the ratio of two AUCs assessed in a serial sacrifice design, which can be used to assess bioequivalence in this parameter. The presented methods are compared in a simulation study.

Animals↗

PubMed2006

Uncertainty analysis in matched-field geoacoustic inversions.

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach, is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data.

Journal Article↗

PubMed2005

A case-cohort design for assessing covariate effects in longitudinal studies.

The case-cohort design for longitudinal data consists of a subcohort sampled at the beginning of the study that is followed repeatedly over time, and a case sample that is ascertained through the course of the study. Although some members in the subcohort may experience events over the study period, we refer to it as the "control-cohort." The case sample is a random sample of subjects not in the control-cohort, who have experienced at least one event during the study period. Different correlations among repeated observations on the same individual are accommodated by a two-level random-effects model. This design allows consistent estimation of all parameters estimable in a cohort design and is a cost-effective way to study the effects of covariates on repeated observations of relatively rare binary outcomes when exposure assessment is expensive. It is an extension of the case-cohort design (Prentice, 1986, Biometrika73, 1-11) and the bidirectional case-crossover design (Navidi, 1998, Biometrics54, 596-605). A simulation study compares the efficiency of the longitudinal case-cohort design to a full cohort analysis, and we find that in certain situations up to 90% efficiency can be obtained with half the sample size required for a full cohort analysis. A bootstrap method is presented that permits testing for intra-subject homogeneity in the presence of unidentifiable nuisance parameters in the two-level random-effects model. As an illustration we apply the design to data from an ongoing study of childhood asthma.

Animals↗

PubMed2006

Analysing multitrait-multimethod data with structural equation models for ordinal variables applying the WLSMV estimator: what sample size is needed for valid results?

Convergent and discriminant validity of psychological constructs can best be examined in the framework of multitrait-multimethod (MTMM) analysis. To gain information at the level of single items, MTMM models for categorical variables have to be applied. The CTC(M-1) model is presented as an example of an MTMM model for ordinal variables. Based on an empirical application of the CTC(M-1) model, a complex simulation study was conducted to examine the sample size requirements of the robust weighted least squares mean- and variance-adjusted chi(2) test of model fit (WLSMV estimator) implemented in Mplus. In particular, the simulation study analysed the chi(2) approximation, the parameter estimation bias, the standard error bias, and the reliability of the WLSMV estimator depending on the varying number of items per trait-method unit (ranging from 2 to 8) and varying sample sizes (250, 500, 750, and 1000 observations). The results showed that the WLSMV estimator provided a good -- albeit slightly liberal -- chi(2) approximation and stable and reliable parameter estimates for models of reasonable complexity (2-4 items) and small sample sizes (at least 250 observations). When more complex models with 5 or more items were analysed, larger sample sizes of at least 500 observations were needed. The most complex model with 9 trait-method units and 8 items (72 observed variables) requires sample sizes of at least 1000 observations.

Humans↗

PubMed1991

A simulation model of AIDS in San Francisco: II. Simulations, therapy, and sensitivity analysis.

The HIV and AIDS incidences each year for homosexual men in San Francisco are estimated from data. A computer simulation model for HIV transmission dynamics and progression to AIDS is used to reconstruct the HIV epidemic. Using some a priori parameter estimates, simulations are found that give good fits to the incidence data. In the stimulations the populations is divided into risk groups whose sexual activities are found to be strongly connected. There is saturation in the high-risk group, but changes in sexual behavior are more important in obtaining adequate fits. The simulation modeling yields useful parameter estimates, but the remaining uncertainty in parameter values implies that the simulation forecasts are also uncertain. Changes in HIV incidence lead to changes in AIDS incidence about 6-10 years later. Simulation models with and without zidovudine treatment both fit the incidence data; thus the effects of therapy on AIDS incidence are unclear. The fits of the simulation model are most sensitive to the yearly migration rate, the number of stages in the progression to AIDS, and the average number of new sexual partners per month; thus better estimates of these parameters would be desirable.

Acquired Immunodeficiency Syndrome↗