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PubMed1991

Comparison of different maximum likelihood estimators in a small sample logistic regression with two independent binary variables.

In order to examine the bias of the estimate of the log odds ratio in a 2 x 2 contingency table, Walter computed the entire distribution of the estimated log odds ratio using various small sample sizes. This is equivalent to computing the distribution of the estimated parameter b1 in a logistic regression with one independent binary variable. In this paper, the distributions of the estimated parameters b1 and b2 for two independent binary variables are computed for some small sample logistic regressions using six different estimation methods based on maximum likelihood. These estimates are then compared to the true parameter values. The best estimation method depends on the frequency of the outcome of interest and on whether the bias or mean square error is considered more important.

Bias↗

PubMed1992

Application of theoretically optimal sampling schedule designs for fiber digestion estimation in sacco.

Three different geometrically spaced sampling schedule designs, a theoretically optimal design, and a design that included all sampling times were evaluated by comparing parameter estimates, half-life, R2, and an indicator of variance-covariance space. Alfalfa and oat hays were tested using nylon bags placed in the rumen of a fistulated, non-lactating cow, and the amount of NDF remaining was measured at specified times. Parameters were estimated from f(t, phi) = Ae-K(t-lag) + U, where f (t, phi) = NDF at time t (h), A = degradable NDF, U = undegradable NDF, lag = time before digestion, and K = rate constant (h). A, U, and f(t, phi) are expressed as a fraction of DM at time 0. Estimates A and U did not fluctuate, whereas K and lag varied across designs. All R2 were over .96 and did not vary across designs. Comparison of designs that had the same number of observations showed that the indicator of the variance-covariance space was statistically similar across designs, although the optimal design was ranked best. Parameter estimates were similar when using different sampling schedule designs, but some estimates differed by 29%. The optimal design sampling schedule provided sufficient information to estimate parameters without loss of accuracy when compared with other designs.

Animal Feed↗

PubMed2002

The determination of biperiden in plasma using gas chromatography mass spectrometry: pharmacokinetics after intramuscular administration to guinea pigs.

A gas chromatographic-mass spectrometric (GC-MS) method has been developed for the analysis of the biperiden from plasma. The method utilizes 290 microl of plasma and a simple hexane extraction/clean-up procedure. Standard curves were linear over the range of 1.9-250 ng/mL. The range of correlation coefficients for the individual standard curves was 0.9984-0.9999; the largest coefficient of variation expressed as a percentage (% CV) was 11.5%. Precision and accuracy were examined by assessing between-day and within-day variability. For between-day precision, the % CVs ranged from 2.86 to 5.17%. Accuracy as expressed by percentage error ranging from -2.16 to 5.83%. The study for within-day precision demonstrated % CVs from 0.95 to 5.55% with accuracy from -3.37 to 2.45%. Applicability of the method was demonstrated by examining the pharmacokinetics of intramuscular (i.m.) biperiden as an anticonvulsant treatment in a guinea pig model for organophosphate (OP)-induced seizure activity. Mean pharmacokinetic parameter estimates were similar to literature values; selected mean pharmacokinetic parameter estimates were: apparent volume of distribution, 13.9 L/kg; half-life of elimination, 93 min; time to maximal plasma concentration, 27.4 min; and maximal plasma concentration, 32.22 eta g/mL. The time to maximal plasma concentration was found to be similar to the onset time for terminating OP-induced seizure activity in guinea pigs receiving biperiden as an anticonvulsant treatment. The studies indicate that the method affords the required precision, accuracy and sensitivity to assay biperiden at the doses utilized for these pharmacokinetic studies after i.m. administration to guinea pigs.

Animals↗

PubMed1983

Pharmacokinetic model for diazepam and its major metabolite desmethyldiazepam following diazepam administration.

A five-compartment open model was used to simulate the blood concentration profiles of diazepam and its metabolite, desmethyldiazepam, following single- and multiple-dose administrations of diazepam. The parameter estimates for diazepam were previously reported literature values. The parameters estimates for the metabolite were calculated from literature values of blood concentrations of desmethyldiazepam following the administration of clorazepate. The five-compartment open model suggests that approximately 50% of the administered diazepam is biotransformed to desmethyldiazepam, and that the elimination profile of the metabolite is not altered by the presence of the drug. The model may also be readily adapted to predict the concentrations of diazepam and desmethyldiazepam in cerebrospinal fluid following the administration of diazepam by simply correcting the blood or plasma concentrations of the drug and metabolite for the degree of plasma protein binding.

Adult↗

PubMed2001

Acetaminophen analgesia in children: placebo effect and pain resolution after tonsillectomy.

BACKGROUND: Pharmacodynamic models of acetaminophen analgesia in children have not explored the efficacy of single oral doses greater than 40 mg/kg. METHODS: Children aged 9.0 +/- 3.0 years (+/- SD) and weight 37.9+/- 16.6 kg undergoing outpatient tonsillectomy were randomised to receive acetaminophen elixir 40 mg/kg (n = 12). high dose acetaminophen elixir 100 mg/kg (n =20) or placebo (n=30) 0.5 -1 h preoperatively. No other analgesics were given. Individual acetaminophen serum concentrations and pain scores [visual analogue scale (VAS) 0-10] were measured over a 4-8 h postoperative period. These data were pooled with data from a previous study investigating acetaminophen pharmacodynamics (n = 120) and analysed using a non-linear mixed effect model. Placebo effects and drug effects were modelled using effect-site concentration models. RESULTS: A one-compartment model with first-order input, lag time and first-order elimination was used to describe the population pharmacokinetics of acetaminophen. Pharmacokinetic parameter estimates were similar to those previously described. Pharmacodynamic population parameter estimates [population variability coefficient of variation (CV)] for a maximum analgesic effect (Emax) model, in which the greatest possible pain relief (VAS 0-10) equates to an Emax of 10, were Emax 5.17 (64%) and 50% effective concentration 9.98 mg/l (107%). The equilibration half-life (t(eq)) of the analgesic effect compartment was 53 min (217%). A placebo drug model for the effects of placebo response had a t(eq) of 1.96 h (40%), an elimination half-life of 2.06 h (50%) and a potency of 1.54 pain relief units (24%). CONCLUSIONS: High dose acetaminophen (100 mg/kg) was no more effective than 40 mg/kg and was associated with increased nausea and vomiting. A target effect compartment concentration of 10 mg/l is expected to produce a pain reduction of 2.6 units. The placebo model accounted for a maximum pain reduction of 5.6 units at 3 h. The combination of placebo effect and preoperative acetaminophen 40 mg/kg results in pain scores below 4 units for 5 h postoperatively.

Acetaminophen↗

PubMed1982

A Pascal program for weighted least squares regression on a microcomputer.

Weighted least-squares regression has been programmed in Pascal for a microcomputer. A double precision Pascal compiler and the Motorola 6809 assembler produce a fast machine-code program occupying 22,000 bytes of memory when appended to the Pascal run-time module. Large data sets fit in the remaining memory. A regression with 72 observations and 24 parameters runs in 7 min, excluding optional print out of large matrices. The maximum dimensions of the design matrix, X, can be altered by modifying two Pascal constants. Minor changes to the Pascal source program will make it compatible with other Pascal compilers. The program optionally orthogonalises the X matrix to detect linearly-dependent columns in X, and/or generate orthogonal parameter estimates. After orthogonalizing X and fitting the model, the parameter estimates for the original X can be retrieved by the program. Regressions on a repeatedly reduced model are performed through elimination of columns in X until the minimum adequate model is obtained.

Computers↗

PubMed2006

An automated procedure for the extraction of metabolic network information from time series data.

Novel high-throughput measurement techniques in vivo are beginning to produce dense high-quality time series which can be used to investigate the structure and regulation of biochemical networks. We propose an automated information extraction procedure which takes advantage of the unique S-system structure and supports model building from time traces, curve fitting, model selection, and structure identification based on parameter estimation. The procedure comprises of three modules: model Generation, parameter estimation or model Fitting, and model Selection (GFS algorithm). The GFS algorithm has been implemented in MATLAB and returns a list of candidate S-systems which adequately explain the data and guides the search to the most plausible model for the time series under study. By combining two strategies (namely decoupling and limiting connectivity) with methods of data smoothing, the proposed algorithm is scalable up to realistic situations of moderate size. We illustrate the proposed methodology with a didactic example.

Algorithms↗

PubMed2001

The process of knowledge discovery from large pharmacokinetic data sets.

The advent of statistical software with powerful graphical and modeling capabilities has revolutionized the manner in which pharmacokinetic and pharmacodynamic analyses are performed. Knowledge discovery from a large (population) pharmacokinetic data set incorporates all steps taken from data assembly to the development of a population pharmacokinetic model and the communication of the results thereof. The process can be formalized into a number of steps: (1) creation of a data set for pharmacokinetic knowledge discovery, (2) data quality analysis, (3) data structure analysis (exploratory examination of raw data), (4) determination of the basic pharmacokinetic model that best describes the data and generating post hoc empiric individual Bayesian parameter estimates, (5) the search for patterns and relationships between parameters and parameters and covariates by visualization, (6) the use of modern statistical modeling techniques for data structure revelation and covariate selection, (7) consolidation of the discovered knowledge into irreducible form (i.e., developing a population pharmacokinetic model), (8) the determination of model robustness (determination of the reliability of model parameter estimates), and (9) the communication and integration of the discovered pharmacokinetic knowledge. This process is discussed, and a motivating example is presented. The use of modern graphical, modeling, and statistical techniques for knowledge discovery from large pharmacokinetic data sets has given the data analyst the freedom to choose statistical methodology appropriate to the problem at hand with the maximization of information extraction, rather than on the basis of mathematical/statistical tractability.

Adolescent↗

PubMed1989

Phenytoin dosage predictions in paediatric patients.

Phenytoin dosing in paediatric patients is complicated both by alterations in patient requirements due to growth and maturation changes and by the capacity-limited characteristics of phenytoin metabolism. This study examines 2 pharmacokinetic methods to adjust phenytoin dosage based on a single dosing-rate/steady-state serum phenytoin concentration pair. A Bayesian forecaster and a fixed parameter [rate of metabolism (Vmax)] method were examined with previously published sets of a priori parameter estimates. The fixed Vmax method was utilised with the parameter derived from native Japanese (method 1), US Caucasian (method 2) and European (method 3) patients. The Bayesian forecaster used a priori parameter estimates obtained from native Japanese (method 4) and European (method 5) patients. Each method was examined retrospectively in 34 paediatric patients with a total of 48 predictions possible. Measures of absolute predictability, bias (mean error, % dose) and precision (root mean squared error, % dose), were -3.58/12.2, -1.51/12.2, 4.06/9.96, -4.38/13.2, and -3.10/11.5, for methods 1, 2, 3, 4 and 5, respectively. There was no significant difference among the 5 methods. However, the Bayesian algorithm tended to be more robust over a broad range of situations, providing predictions in all cases. The fixed Vmax methods could not provide predictions in every case. Finally, all methods had a significant number of overpredictions of dosage. Poorer results were observed when prediction of steady-state serum concentrations were performed, partly due to the retrospective nature of the study. We conclude that close monitoring of patients, regardless of the method chosen to adjust dosage, is recommended.

Adolescent↗

PubMed2006

Comparison of variance estimation approaches in a two-state Markov model for longitudinal data with misclassification.

We examine the behaviour of the variance-covariance parameter estimates in an alternating binary Markov model with misclassification. Transition probabilities specify the state transitions for a process that is not directly observable. The state of an observable process, which may not correctly classify the state of the unobservable process, is obtained at discrete time points. Misclassification probabilities capture the two types of classification errors. Variance components of the estimated transition parameters are calculated with three estimation procedures: observed information, jackknife, and bootstrap techniques. Simulation studies are used to compare variance estimates and reveal the effect of misclassification on transition parameter estimation. The three approaches generally provide similar variance estimates for large samples and moderate misclassification. In these situations, the resampling methods are reasonable alternatives when programming partial derivatives is not appealing. With smaller chains or higher misclassification probabilities, the bootstrap method appears to be the best choice.

Analysis of Variance↗

PubMed2003

Polymorphism and divergence for island-model species.

Estimates of the scaled selection coefficient, gamma of Sawyer and Hartl, are shown to be remarkably robust to population subdivision. Estimates of mutation parameters and divergence times, in contrast, are very sensitive to subdivision. These results follow from an analysis of natural selection and genetic drift in the island model of subdivision in the limit of a very large number of subpopulations, or demes. In particular, a diffusion process is shown to hold for the average allele frequency among demes in which the level of subdivision sets the timescale of drift and selection and determines the dynamic equilibrium of allele frequencies among demes. This provides a framework for inference about mutation, selection, divergence, and migration when data are available from a number of unlinked nucleotide sites. The effects of subdivision on parameter estimates depend on the distribution of samples among demes. If samples are taken singly from different demes, the only effect of subdivision is in the rescaling of mutation and divergence-time parameters. If multiple samples are taken from one or more demes, high levels of within-deme relatedness lead to low levels of intraspecies polymorphism and increase the number of fixed differences between samples from two species. If subdivision is ignored, mutation parameters are underestimated and the species divergence time is overestimated, sometimes quite drastically. Estimates of the strength of selection are much less strongly affected and always in a conservative direction.

Biological Evolution↗

PubMed1981

The use of hypothetical cohorts in estimating demographic parameters under conditions of changing fertility and mortality.

The indirect methods of demographic estimation available to date are often inadequate to estimate levels in the presence of trends. The use of measures relative to hypothetical cohorts to minimize the effects of trends and estimate period levels is described. Procedures allowing the estimation of inter-survey levels of fertility, child mortality and adult mortality are illustrated using data from Thailand and Peru.

Adolescent↗

PubMed2001

A general algorithm for optimal sampling schedule design in nuclear medicine imaging.

Optimal sampling schedule (OSS) is of great interest in biomedical experiment design, as it can improve the physiological parameter estimation precision and significantly reduce the samples required. A number of well designed algorithms and software packages have been developed, which deal with the instantaneous measurements at discrete times. However, in nuclear medicine tracer kinetic studies, the imaging systems, such as positron emission tomography (PET) and single photon emission computed tomography (SPECT), take measurements (images) based on continuous accumulation over time intervals. In this case, the existing algorithms cannot be used to design OSS so as to reduce the image frame numbers. In this paper, a general OSS design algorithm for the accumulative measurement is proposed. The potential usefulness of the algorithm is demonstrated by its designing OSS in [18F] fluoro-2-deoxy-D-glucose (FDG) studies with PET to estimate the local cerebral metabolic rate of glucose. The robustness of parameter estimation using the OSS with respect to intra-subject and inter-subject parameter variations is also presented.

Algorithms↗

PubMed2003

Estimation of parameters of dose-volume models and their confidence limits.

Predictions of the normal-tissue complication probability (NTCP) for the ranking of treatment plans are based on fits of dose-volume models to clinical and/or experimental data. In the literature several different fit methods are used. In this work frequently used methods and techniques to fit NTCP models to dose response data for establishing dose-volume effects, are discussed. The techniques are tested for their usability with dose-volume data and NTCP models. Different methods to estimate the confidence intervals of the model parameters are part of this study. From a critical-volume (CV) model with biologically realistic parameters a primary dataset was generated, serving as the reference for this study and describable by the NTCP model. The CV model was fitted to this dataset. From the resulting parameters and the CV model, 1000 secondary datasets were generated by Monte Carlo simulation. All secondary datasets were fitted to obtain 1000 parameter sets of the CV model. Thus the 'real' spread in fit results due to statistical spreading in the data is obtained and has been compared with estimates of the confidence intervals obtained by different methods applied to the primary dataset. The confidence limits of the parameters of one dataset were estimated using the methods, employing the covariance matrix, the jackknife method and directly from the likelihood landscape. These results were compared with the spread of the parameters, obtained from the secondary parameter sets. For the estimation of confidence intervals on NTCP predictions, three methods were tested. Firstly, propagation of errors using the covariance matrix was used. Secondly, the meaning of the width of a bundle of curves that resulted from parameters that were within the one standard deviation region in the likelihood space was investigated. Thirdly, many parameter sets and their likelihood were used to create a likelihood-weighted probability distribution of the NTCP. It is concluded that for the type of dose response data used here, only a full likelihood analysis will produce reliable results. The often-used approximations, such as the usage of the covariance matrix, produce inconsistent confidence limits on both the parameter sets and the resulting NTCP values.

Dose-Response Relationship, Radiation↗

PubMed1999

Estimating regression parameters and degree of dependence for multivariate failure time data.

Multivariate failure time data are frequently encountered in longitudinal studies when subjects may experience several events or when there is a grouping of individuals into a cluster. To take into account the dependence of the failure times within the unit (the individual or the cluster) as well as censoring, two multivariate generalizations of the Cox proportional hazards model are commonly used. The marginal hazard model is used when the purpose is to estimate mean regression parameters, while the frailty model is retained when the purpose is to assess the degree of dependence within the unit. We propose a new approach based on the combination of the two aforementioned models to estimate both these quantities. This two-step estimation procedure is quicker and more simple to implement than the EM algorithm used in frailty models estimation. Simulation results are provided to illustrate robustness, consistency, and large-sample properties of estimators. Finally, this method is exemplified on a diabetic retinopathy study in order to assess the effect of photocoagulation in delaying the onset of blindness as well as the dependence between the two eyes blindness times of a patient.

Biometry↗

PubMed2000

Physiological relevance of uniform elastic tube-models to infer descending aortic wave reflection: a problem of identifiability.

A uniform, frictional elastic tube terminating in a pure resistor (model A), was compared with a uniform, frictionless elastic tube, terminating in a first-order low-pass filter load (model B). The aim was to address an identifiability problem in uniqueness of parameter estimates and to evaluate the physiological meaning of tube-length estimates obtained from these models applied to the descending aortic circulation. Measurements of high descending aortic pressure and flow were taken from three anaesthetized, open-chest dogs and used to estimate the model parameters. A simultaneous measurement of terminal aortic pressure was used to estimate the foot-to-foot pulse wave velocity. A flow-fitting procedure yielded a multiplicity of equivalent solutions for the wave transit time across the transmission tubes (tau(ai), for model A and tau(bi) for model B, i=0,1,2,...,N,...) and the related tube-lengths d(ai) and d(bi), respectively. The tube length represents the distance to an effective reflection site (effective length) of the descending aortic circulation. Assuming that this length should be no longer than the dimensions of the body, the lowest estimates (i=0) of wave transit time and tube length (average +/- SE: tau(ao)=85.7+/-10.8 ms and d(ao)=53.4+/-3.7 cm for model A; tau(bo)=46.6+/-6.7 ms and d(bo)= 29.1+/-3.5 cm for model B) were identifiable as unique and acceptable solutions. Model A located the effective reflection site a few centimeters below the terminal aortic region. This location is inconsistent with the use of a pure resistor as a tube's terminal load. Further, relatively high estimates of longitudinal frictional losses violated the assumption of small losses across the transmission path and yielded an unphysiological mean-pressure drop of 7.1+/-2.3 mmHg. The estimates of d(bo) provided by model B located the effective reflection site near the origin of the renal arteries. The model-predicted pressure wave at this location approximated the measured pressure. Thus, model B represents a significant improvement over model A as a tool to infer wave travel and reflection in the descending aortic circulation.

Animals↗

PubMed1994

Application of optimal sampling theory to the determination of metacycline pharmacokinetic parameters: effect of model misspecification.

Use of optimal sampling theory (OST) in pharmacokinetic studies allows the number of sampling times to be greatly reduced without loss in parameter estimation precision. OST has been applied to the determination of the bioavailability parameters (area under the curve (AUC), maximal concentration (Cmax), time to reach maximal concentration (Tmax), elimination half-life (T1/2), of metacycline in 16 healthy volunteers. Five different models were used to fit the data and to define the optimal sampling times: one-compartment first-order, two-compartment first-order, two-compartment zero-order, two-compartment with Michaelis-Menten absorption kinetics, and a stochastic model. The adequacy of these models was first evaluated in a 6-subject pilot study. Only the stochastic model with zero-order absorption kinetics was adequate. Then, bioavailability parameters were estimated in a group of 16 subjects by means of noncompartmental analysis (with 19 samples per subject) using each optimal sampling schedule based procedure (with 6 to 9 samples depending on the model). Bias (PE) and precision (RMSE) of each bioavailability parameter estimation were calculated by reference to noncompartmental analysis, and were satisfactory for the 3 adequate models. The most relevant criteria for discrimination of the best model were the coefficient of determination, the standard deviation, and the mean residual error vs. time plot. Additional criteria were the number of required sampling times and the coefficient of variation of the estimates. In this context, the stochastic model was superior and yielded very good estimates of the bioavailability parameters with only 8 samples per subject.

Adult↗

PubMed1998

The use of biochemical and molecular parameters to estimate dose-response relationships at low levels of exposure.

Biomarkers based on alterations in molecular and biochemical parameters may be useful in chemical risk assessment for establishing the presence of an exposure, ranking relative risks among exposed individuals, and estimating risks at low levels of exposure. Because it is unlikely that the relation between toxic responses and the degree of alteration in the biomarker is equivalent at all doses, quantification of risks at low levels is not necessarily more accurate using these biomarkers for extrapolation. The application of response biomarkers for risk evaluation at low levels of exposure is discussed in relation to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD), a compound that causes induction of cytochromes CYP1A1 and CYP1A2 in liver and other tissues. CYP1A1 induction in liver increases monotonically with TCDD dosage; however, several of the dose-response curves for hepatic effects of TCDD are U-shaped. The U-shaped dose-response curve for hepatic tumor promotion appears to result because the integrated toxicologic response depends on multiple underlying processes--mitosuppression, toxicity, and cell proliferation--each of which has a different dose-response relationship with respect to TCDD. Although dose-response relationships for the biomarkers are not expected to duplicate the complex shapes seen with the integrated responses, measurements and pharmacodynamic modeling of the changes in these molecular and biochemical parameters can still be useful for obtaining an upperbound risk estimate at low levels of exposure.

Animals↗