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PubMed1999

Mixed-effects modeling of the pharmacodynamic response to the calcimimetic agent R-568.

OBJECTIVE: The parathyroid cell calcium receptor is a novel drug target for affecting parathyroid hormone (PTH) secretion and for treating hyperparathyroidism. R-568 is a calcium receptor agonist that inhibits PTH secretion and increases calcitonin release in preclinical studies. The objective of this study was to evaluate the effect of R-568 on PTH plasma concentrations in humans. METHODS: Eighteen healthy postmenopausal women were included in the study. Single ascending oral doses of 10 to 400 mg were administered in a randomized, placebo-controlled double-blind trial. PTH plasma concentrations were measured for up to 120 hours after each dose. RESULTS: R-568 caused a dose-dependent decrease in plasma PTH, with peak effect observed within 1/2 to 2 hours after dosing. The maximum effect did not increase beyond doses from 80 to 160 mg, but duration of response increased at higher doses. An indirect-response model was developed to estimate the rates of input and output of the active moiety(ies), the inhibitory effect on PTH secretion, and the circadian variability in PTH. Population parameter estimates were 3.02 hour-1 and 0.49 hour-1 for rates of input and output of the active moiety(ies), respectively, IA50 (the unscaled amount of R-568 associated with 50% of Emax) was 16.3 mg, Emax (the maximum effect caused by R-568 expressed as a fraction of the rate of PTH secretion in the absence of any drug effect) was 89%, CPTH(baseline) (the baseline PTH plasma concentration in the absence of any drug effect) was 34.6 pg/mL, KePTH (the elimination rate constant for PTH) was 1.73 hour-1, amplitude of the circadian variability in PTH secretion was 5.8%, and the time of peak PTH secretion occurred at about 6 PM. Intersubject variability in parameter estimates ranged from 7% to 121%, and residual variability was 22%. CONCLUSION: The model correctly described the onset, extent, and duration of effect on PTH after a wide range of doses of R-568.

Administration, Oral↗

PubMed1983

Rapid cell cycle analysis. II. Phase durations and dispersions from computer analysis of RC curves.

In this paper, we present a procedure for the rapid, quantitative estimation of the G1, S, and G2 + M phase durations and dispersions and the growth fraction for asynchronously growing cell populations. In this procedure, the cell population is pulse-labelled with a radioactive DNA precursor at the beginning of the analysis and then sampled periodically. The samples are dispersed, stained with a DNA specific dye, and processed through a cell sorter where cells from mid-S phase and G1 phase are sorted. The radioactivity per cell (RC) is determined for each sorted sample. In addition, the variation in the rate of incorporation of the radioactive DNA precursor across S phase is determined and the fractions of cells in the G1, S, and G2 + M phase are estimated from DNA distributions measured during sorting. We also describe an automatic computer analysis procedure for estimation of the G1, S, and G2 + M phase durations and dispersions and growth fraction by simultaneous analysis of the variations with time in the radioactivity per cell in G1 (RCG1) and radioactivity per cell in mid-S phase (RCS) curves, the G1, S, and G2 + M phase fractions and the variation in the rate of incorporation of radioactive DNA precursor uptake across S phase. The experimental and analytical aspects of the RC procedure are applied in the cell cycle analysis of Chinese hamster M3-1 cells grown in vitro. The parameters estimated by RC analysis agree well with similar parameters estimated by fraction-of-labelled-mitoses analysis.

Animals↗

PubMed1987

OMNE: a new robust membership-set estimator for the parameters of nonlinear models.

A new method for estimating parameters and their uncertainty is presented. Data are assumed to be corrupted by a noise whose statistical properties are unknown but for which bounds are available at each sampling time. The method estimates the set of all parameter vectors consistent with this hypothesis. Its results are compared with those of the weighted least squares, extended least squares, and biweight robust regression approaches on two data sets, one of which includes 33% outliers. On the basis of these preliminary results, the new method appears to have attractive properties of reliability and robustness.

Kinetics↗

PubMed1982

Fitting biological equations to data using non-parametric methods.

Simulated experimental data were generated for these equations: a straight line, the integrated Michaelis--Menten equation, plus a linear term, the Hill equation, a two-exponential function and a double Michaelis--Menten equation. The equations were fitted to the data using (i) least-squares and (ii) non-parametric methods. The precision and accuracy of the parameter estimates obtained by each method were compared and the methods assessed. For several of the equations, non-parametric methods provided robust techniques for parameter estimation. For the remainder, the results were poor. The reasons for this are discussed.

Computers↗

PubMed2001

Population pharmacokinetics and pharmacodynamics of sotalol in pediatric patients with supraventricular or ventricular tachyarrhythmia.

AIMS: To derive useful pharmacokinetic (PK) and pharmacodynamic (PD) information for guiding the clinical use of sotalol in pediatric patients with supraventricular (SVT) or ventricular tachyarrhythmia (VT). METHODS: Two studies were conducted in-patients with SVT or VT in the age range between birth and 12 years old. Both studies used an extemporaneously compounded formulation prepared from sotalol HCl tablets. In the PK study, following a single dose of 30 mg/m2 sotalol, extensive blood samples (n = 10) were taken. The PK-PD study used a dose escalation design with doses of 10, 30, and 70 mg/m2, each administered three times at 8-hr intervals without a washout. Six ECG recordings for determination of QT and RR were obtained prior to the initial dose of sotalol. Four blood samples were collected six ECG's were determined during the third interval at each dose level. Plasma concentrations of sotalol (C) were assayed by LC/MS/MS. The data analysis used NONMEM to obtain the population PK and PD parameter estimates. The individual PK and PD parameters were estimated with empirical Bayes methodology. RESULTS: A total of 611 C from 58 patients, 477 QTc and 499 RR measurements from 23 and 22 patients, respectively, were available for analysis. The PK of sotalol was best described by a linear two-compartment model. Oral clearance (CL/F) and volume of central compartment (Vc/F) were linearly correlated with body surface area (BSA), body weight or age. CL/F was also linearly correlated with creatinine clearance. The best predictor for both CL/F and Vc/F was BSA. The remaining intersubject coefficients of variation (CV's) in CL/F, and Vc/F were 21.6% and 20.3%, respectively. The relationship of QTc to C was adequately described by a linear model. The intersubject CV's in slope (SL) and intercept (E0) were 56.2 and 4.7%, respectively. The relationship of RR to C was also adequately described by a linear model in which the baseline RR and SL were related to age or BSA. The intersubject CV's for SL and E0 were 86.7 and 14.4%, respectively. CONCLUSIONS: BSA is the best predictor for the PK of sotalol. Both QTc and RR effects are linearly related to C. No covariates are found for the QTc-C relation, while the RR-C relation shows age or BSA dependency.

Anti-Arrhythmia Agents↗

PubMed2004

Comparison of two design optimality criteria applied to a nonlinear model.

In chemical kinetic or pharmacokinetic studies, many mathematical models are nonlinear with respect to the model parameters. This may cause serious problems for parameter estimation. A D-optimum design, which is very popular and effective for linear models, is not so good for nonlinear models with strong parameter curvature. In this article, we compare two optimality criteria applied to a nonlinear model. Both of them minimize the volume of the confidence ellipsoid of the parameters: D-optimality uses a linear approximation of the volume, and Q-optimality uses a quadratic approximation. We compute the relative design efficiencies and use a parameter-effect curvature measure to compute the number of observations that reduces the "curvature effect" to a specified level and improves the parameter estimation. The calculated designs differ significantly, and the Q-optimum design shows increasingly better statistical properties as the curvature increases. We present our results both graphically and as tables of numerical values.

Algorithms↗

PubMed1985

The affected sib method. IV. Sib trios.

The classical sib pair method uses the expected and observed HLA (human leukocyte antigen) haplotype sharing distribution in sib pairs, who are affected with an HLA associated disease, to make inferences about the inheritance of the disease. In this paper we present the expected HLA haplotype sharing distributions in affected sib trios, and sib pairs, from families with three or more affected sibs. The underlying model for both distributions, as for the classical sib pair method, is that disease predisposition is determined by a single allele at an HLA-linked locus. The sib trio tests of hypotheses (additive and recessive), and disease parameter estimates (additive, recessive and intermediate), can be compared with those obtained from the classical sib pair analysis. In addition, the sib trio data allow parameter estimation for a general disease model to be made, if the data fall within the bounds of the expectation. This study forms the basis of later investigations which show that haplotype sharing of affected sib trios for two susceptibility alleles (negative complementation) model, which appears appropriate for insulin dependent diabetes mellitus (IDDM), moves outside the bound of the single susceptibility expectations outlined here, whereas haplotype sharing values for sib pairs are bound by the single susceptibility allele expectations. Available Caucasian IDDM data have been analysed. The results support genetic heterogeneity of IDDM.

Diabetes Mellitus, Type 1↗

PubMed1993

The critical power concept. A review.

The basis of the critical power concept is that there is a hyperbolic relationship between power output and the time that the power output can be sustained. The relationship can be described based on the results of a series of 3 to 7 or more timed all-out predicting trials. Theoretically, the power asymptote of the relationship, CP (critical power), can be sustained without fatigue; in fact, exhaustion occurs after about 30 to 60 minutes of exercise at CP. Nevertheless, CP is related to the fatigue threshold, the ventilatory and lactate thresholds, and maximum oxygen uptake (VO2max), and it provides a measure of aerobic fitness. The second parameter of the relationship, AWC (anaerobic work capacity), is related to work performed in a 30-second Wingate test, work in intermittent high-intensity exercise, and oxygen deficit, and it provides a measure of anaerobic capacity. The accuracy of the parameter estimates may be enhanced by careful selection of the power outputs for the predicting trials and by performing a greater number of trials. These parameters provide fitness measures which are mode-specific, combine energy production and mechanical efficiency in 1 variable, and do not require the use of expensive equipment or invasive procedures. However, the attractiveness of the critical power concept diminishes if too many predicting trials are required for generation of parameter estimates with a reasonable degree of accuracy.

Anaerobic Threshold↗

PubMed1987

Analyzing fertility histories: do restrictions bias results?

The straightforward tests we have conducted lead to two major conclusions. First, parameter estimates, such as the proportions that practice contraception or that breastfeed, can be biased in data restricted to the last closed and open interval. This is particularly true the further back in time one goes. However, the second conclusion is that these restrictions do not bias estimates of the structure of the relationships predicting fertility. This may seem surprising, and perhaps even magical. The reason is that multivariate life table techniques allow one to reach the same conclusion even if the proportions in various categories are altered by a criterion such as limiting the analysis to intervals begun by the last and next-to-last live births. Limiting the analysis in this way means that there are fewer short intervals and thus fewer cases of intervals with characteristics associated with short intervals (e.g., no contraceptive use, no breastfeeding, or infant mortality). As long as the model specified in the multivariate life table is an appropriate one, that is, it is not misspecified, and as long as the skew produced by the WFS restriction is not too extreme, then the multivariate life table procedures can produce unbiased estimates of the structure of the relationships predicting birth interval dynamics. Thus even though the WFS data are in fact inappropriate for some simple parameter estimation procedures, they appear to be adequate for the more complex multivariate procedures of the sort used here. Several caveats must be added to the foregoing results. First, we have performed this test in only one country, Korea; it is possible that the same results might not be obtained in other countries. We expect, however, that they would. Second, our procedure only looks at the first 40 months of experience in the birth interval. A procedure that incorporates the long tails of the birth interval distribution may obtain different results. In fact, we caution against analyzing the tail of the distributions using data from the normal WFS sample, since these would be most affected by the restriction to last closed and open intervals. Third, the extent to which these results are generalizable to other types of substantive problems is unknown at present. We suspect, however, that examining the determinants of lengths of breastfeeding will produce similar results. Finally, even with multivariate procedures, it would be highly misleading to impose the WFS restrictions and then examine trends in the length of birth intervals.(ABSTRACT TRUNCATED AT 400 WORDS)

Birth Intervals↗

PubMed2002

Generalized linear least squares algorithms for modeling glucose metabolism in the human brain with corrections for vascular effects.

The generalized linear least squares (GLLS) algorithm has been found useful in image-wide parameter estimation for the generation of parametric images with positron emission tomography (PET) as it is computationally efficient and statistically reliable. However, the original algorithm was designed for parameter estimation with non-uniformly sampled instantaneous measurements. When dynamic PET data are sampled with the optimal image sampling schedule (OISS) to reduce memory and storage space, only a few temporal image frames are recorded. As a result, the direct application of GLLS is no longer appropriate. In this paper, we extend the GLLS algorithm to a five parameter model for the study of human brain metabolism, which accounts for the effect of cerebral blood volume (CBV), using OISS sampled data, with as few as five temporal samples. The formulation for this new GLLS algorithm is developed, and its computational efficiency and statistical reliability are investigated and validated using computer simulations and clinical PET [18F]-2-fluoro-2-deoxy-D-glucose (FDG) data.

Algorithms↗

PubMedDate not supplied

Correlation of proliferating cell nuclear antigen assessment, histologic parameters and age with survival in patients with glioblastoma multiforme.

A series of 27 glioblastomas multiforme were studied to compare the prognostic value of age and histologic parameters known to influence survival with that of proliferating cell nuclear antigen (PCNA). The labelling index (LI) of PCNA has been found in previous studies to correlate well with flow cytometry, tritiated thymidine, bromodeoxyuridine incorporation and Ki 67. The histologic parameters estimated were endothelial proliferation, number of mitoses per high power field, cellularity and a grading of necroses. The correlation coefficients between survival and each of the histologic parameters as well as with age were found to be negative but statistically insignificant. The values of these correlations in descending order were survival/age (r = -0.22), survival/endothelial proliferation (r = -0.20), survival/mitoses (r = -0.16), survival/cellularity (r = -0.07) and survival/necroses (r = -0.04). The correlation coefficient between survival and PCNA LI was also found to be negative, higher than those between survival and other estimated parameters (r = -0.37) but in a wide variation and still statistically insignificant. Despite this variation, our finding that for PCNA LI > 35% no patient survived more than 6 months may be of clinical importance.

Adult↗

PubMed2003

Using lowess to remove systematic trends over time in predictor variables prior to logistic regression with quantile categories.

In case-control studies one may employ logistic regression to model the relationship between binary responses and continuous predictor variables that have been categorized by the empirical quartiles of the controls. Sometimes, however, systematic trends over time (or drifts) contaminate the laboratory measurements of predictor variables. In this paper we consider the use of locally weighted robust regression (lowess) to estimate and remove these systematic trends when the trends for the cases and controls have a common shape. One can then use the lowess adjusted data in the desired logistic regression model. We illustrate these methods with a case-control study that was designed to assess the risk of oesophageal cancer as a function of the quartile categories of sphinganine levels in the blood serum. Upon examination of the data, it was discovered that the sphinganine laboratory measurements were contaminated by a systematic trend, the magnitude of which depended only on the day of analysis. This trend needed to be removed before performing further analyses of the data. In addition, we present simulations to examine the use of lowess methods to estimate and remove various shapes of trends from contaminated predictor data before constructing logistic regression models with quartile categories. We found that using the trend-contaminated data tends to give attenuated parameter estimates and hence lower significance and power levels than using the uncontaminated data. Conversely, using appropriate lowess methods to adjust the data tends to give nearly unbiased parameter estimates, near nominal significance levels, and improved power.

Adult↗

PubMed2001

Bioavailability of Cd to the common carp, Cyprinus carpio, in the presence of humic acid.

The uptake of cadmium by the common carp, Cyprinus carpio, was studied in chemically defined freshwater in the absence and presence of commercial humic acid. This was done to evaluate whether the cadmium uptake by carp in the presence of humic acid was related to the ambient Cd2+ -ion activity or whether the complexed metal also contributed to the uptake. Uptake of Cd during a 3-h period of exposure was used as a measure of the biological availability of the metal. The uptake rate data for Cd in total fish and gills obtained in the absence (control) and presence (treatment) of humic acid were analyzed using a Michaelis-Menten model for mediated transport. The Michaelis-Menten parameters KM and Vmax obtained in the control and the treatment experiment were compared for each of the two investigated carp compartments (total fish and gills). The model parameter estimates for Cd uptake by total carp in the treatment experiment (KM = 0.41 +/- 0.11 micromol l(-1); Vmax = 0.66 +/- 0.13 micromol kg(-1) h(-1)) were not significantly different from the model parameters in the control experiment (KM = 0.34+/-0.06 micromol l(-1); Vmax = 0.58+/-0.07 micromol kg(-1) h(-1)) on the basis of Welch's approximate t-test. Similarly, the Michaelis-Menten model parameter estimates for Cd uptake by carp gills in the treatment experiment (KM = 0.15 +/- 0.06 micromol l(-1); Vmax = 5.14 +/- 1.07 micromol kg(-1) h(-1)) were not significantly different from the model parameters derived from the control experiment (KM =0.27 +/- 0.09 micromol l(-1); Vmax = 7.63+/-1.38 micromol kg(-1) h(-1)). This indicated that the Cd uptake rate by total carp and in carp gills in the presence of commercial humic acid followed the measured variations in Cd2+ -ion activity as predicted by the control experiment.

Animals↗

PubMed1997

Application of composite estimation in studies of animal population production with two-stage repeated sample designs.

This paper reports results from two example data sets of a two-stage sampling design where sampling (in panels) both farms and animals within selected farms increases the efficiency of parameter estimation from measurements recorded over time. With such a design, not only are farms replaced from time-to-time but also animals subsampled within retained farms are subject to replacement. Three general categories of parameters estimated for the population (the set of animals belonging to the universe of farms of interest) were (1) the total at each measurement occasion; (2) the difference between means or totals on successive measurement occasions; (3) the total over a sequence of successive measurement periods. Whereas several responses at the farm level were highly correlated over time (rho 1), the corresponding animal responses were less correlated over time (rho 2)-leading to only moderate gains in relative efficiency. Intraclass correlation values were too low in most cases to counteract the overall negative impact of rho 2. In general, sizeable gains in relative efficiency were observed for estimating change-confirming a previous result which showed this to be true provided that rho 1 was high (irrespective of rho 2).

Animal Husbandry↗

PubMed2001

A fast nonlinear method for parametric imaging of myocardial perfusion by dynamic (13)N-ammonia PET.

UNLABELLED: A parametric image of myocardial perfusion (mL/min/g) is a quantitative image generated by fitting a tracer kinetic model to dynamic (13)N-ammonia PET data on a pixel-by-pixel basis. There are several methods for such parameter estimation problems, including weighted nonlinear regression (WNLR) and a fast linearizing method known as Patlak analysis. Previous work showed that sigmoidal networks can be used for parameter estimation of mono- and biexponential models. The method used in this study is a hybrid of WNLR and sigmoidal networks called nonlinear regression estimation (NRE). The purpose of the study is to compare NRE with WNLR and Patlak analysis for parametric imaging of perfusion in the canine heart by (13)N-ammonia PET. METHODS: A simulation study measured the statistical performance of NRE, WNLR, and Patlak analysis for a probabilistic model of time-activity curves. Four canine subjects were injected with 740 MBq (13)N-ammonia and scanned dynamically. Images were reconstructed with filtered backprojection and resliced into short-axis cuts. Parametric images of a single midventricular plane per subject were generated by NRE, WNLR, and Patlak analysis. Small regions of interest (ROIs) were drawn on each parametric image (8 ROIs per subject for a total of 32). RESULTS: For the simulation study, the median absolute value of the relative error for a perfusion value of 1.0 mL/min/g was 16.6% for NRE, 17.9% for WNLR, 19.5% for Patlak analysis, and 14.5% for an optimal WNLR method (computable by simulation only). All methods are unbiased conditioned on a wide range of perfusion values. For the canine studies, the least squares line fits comparing NRE (y) and Patlak analysis (z) with WNLR (x) for all 32 ROIs were y = 1.02x - 0.028 and z = 0.90x + 0.019, respectively. Both NRE and Patlak analysis generate 128 x 128 parametric images in seconds. CONCLUSION: The statistical performance of NRE is competitive with WNLR and superior to Patlak analysis for parametric imaging of myocardial perfusion. NRE is a fast nonlinear alternative to Patlak analysis and other fast linearizing methods for parametric imaging. NRE should be applicable to many other tracers and tracer kinetic models.

Ammonia↗

PubMed2006

Probe-level measurement error improves accuracy in detecting differential gene expression.

MOTIVATION: Finding differentially expressed genes is a fundamental objective of a microarray experiment. Numerous methods have been proposed to perform this task. Existing methods are based on point estimates of gene expression level obtained from each microarray experiment. This approach discards potentially useful information about measurement error that can be obtained from an appropriate probe-level analysis. Probabilistic probe-level models can be used to measure gene expression and also provide a level of uncertainty in this measurement. This probe-level measurement error provides useful information which can help in the identification of differentially expressed genes. RESULTS: We propose a Bayesian method to include probe-level measurement error into the detection of differentially expressed genes from replicated experiments. A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy. The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions. Using the measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we test PPLR on a spike-in dataset and a mouse time-course dataset. Results show that the inclusion of probe-level measurement error improves accuracy in detecting differential gene expression. AVAILABILITY: The MAP approximation and variational inference described in this paper have been implemented in an R package pplr. The MCMC method is implemented in Matlab. Both software are available from http://umber.sbs.man.ac.uk/resources/puma.

Algorithms↗

PubMed1993

Interpretation of simulation studies for efficient estimation of population pharmacokinetic parameters.

OBJECTIVE: To develop new approaches for evaluating results obtained from simulation studies used to determine sampling strategies for efficient estimation of population pharmacokinetic parameters. METHODS: One-compartment kinetics with intravenous bolus injection was assumed and the simulated data (one observation made on each experimental unit [human subject or animal]), were analyzed using NONMEM. Several approaches were used to judge the efficiency of parameter estimation. These included: (1) individual and joint confidence intervals (CIs) coverage for parameter estimates that were computed in a manner that would reveal the influence of bias and standard error (SE) on interval estimates; (2) percent prediction error (%PE) approach; (3) the incidence of high pair-wise correlations; and (4) a design number approach. The design number (phi) is a new statistic that provides a composite measure of accuracy and precision (using SE). RESULTS: The %PE approach is useful only in examining the efficiency of estimation of a parameter considered independently. The joint CI coverage approach permitted assessment of the accuracy and reliability of all model parameter estimates. The phi approach is an efficient method of achieving an accurate estimate of parameter(s) with good precision. Both the phi for individual parameter estimation and the overall phi for the estimation of model parameters led to optimal experimental design. CONCLUSIONS: Application of these approaches to the analyses of the results of the study was found useful in determining the best sampling design (from a series of two sampling times designs within a study) for efficient estimation of population pharmacokinetic parameters.

Bias↗

PubMed2001

A biomathematical model of particle clearance and retention in the lungs of coal miners.

To understand better the factors influencing the relationships among airborne particle exposure, lung burden, and fibrotic lung disease, we developed a biologically based kinetic model to predict the long-term retention of particles in the lungs of coal miners. This model includes alveolar, interstitial, and hilar lymph node compartments. The 131 miners in this study had worked in the Beckley, West Virginia, area and died during the 1960s. The data used to develop this model include exposure to respirable coal mine dust by intensity and duration within each job, lung and lymph node dust burdens at autopsy, pathological classification of fibrotic lung disease, and smoking history. Initial parameter estimates for this model were based on both human and animal data of particle deposition and clearance and on the biological and physical factors influencing these processes. Parameter estimation and model fit to the data were determined using least squares. Results show that the end-of-life lung dust burdens in these coal miners were substantially higher than expected from first-order clearance kinetics, yet lower than expected from the overloading of alveolar clearance predicted from rodent studies. The best-fitting and most parsimonious model includes processes for first-order alveolar-macrophage-mediated clearance and transfer of particles to the lung interstitium. These results are consistent with the particle retention patterns observed previously in the lungs of primates. The findings indicate that rodent models extrapolated to humans, without adjustment for the kinetic differences in particle clearance and retention, would be inadequate for predicting lung dust burdens in humans. Also, this human lung kinetic model predicts greater retained lung dust burdens from occupational exposure than predicted from current human models based on lower exposure data. This model is useful for risk assessment of particle-induced lung diseases, by estimating equivalent internal doses in rodents and humans and predicting lung burdens in humans with occupational dust exposures.

Air Pollutants, Occupational↗