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  • 1
    Electronic Resource
    Electronic Resource
    Pharmacokinetic parameter estimates from several least squares procedures: Superiority of extended least squares (1985)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 13 (1985), S. 185-201 
    Details
    ISSN: 1573-8744
    Keywords: least squares ; extended least squares ; maximum likelihood ; weighting ; precision ; parameter estimation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The precision of pharmacokinetic parameter estimates from several least squares parameter estimation methods are compared. The methods can be thought of as differing with respect to the way they weight data. Three standard methods, Ordinary Least Squares (OLS-equal weighting), Weighted Least Squares with reciprocal squared observation weighting [WLS(y−2)], and log transform OLS (OLS(ln))-the log of the pharmacokinetic model is fit to the log of the observations-are compared along with two newer methods, Iteratively Reweighted Least Squares with reciprocal squared prediction weighting (IRLS,(f−2)), and Extended Least Squares with power function “weighting” (ELS(f−ξ)-here ξ is regarded as an unknown parameter). Tne values of the weights are more influenced by the data with the ELS(f−ξ) method than they are with the other methods. The methods are compared using simulated data from several pharmacokinetic models (monoexponential, Bateman, Michaelis-Menten) and several models for the observation error magnitude. For all methods, the true structural model form is assumed known. Each of the standard methods performs best when the actual observation error magnitude conforms to the assumption of the method, but OLS is generally least perturbed by wrong error models. In contrast, WLS(y−2) is the worst of all methods for all error models violating its assumption (and even for the one that does not, it is out performed by OLS(ln). Regarding the newer methods, IRLS(f−2) improves on OLS(ln), but is still often inferior to OLS. ELS(f−ξ), however, is nearly as good as OLS (OLS is only 1–2% better) when the OLS assumption obtains, and in all other cases ELS(f−ξ) does better than OLS. Thus, ELS(f−ξ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01059398
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  • 2
    Electronic Resource
    Electronic Resource
    Computation of the explicit solution to the Michaelis-Menten equation (1987)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 15 (1987), S. 99-99 
    Details
    ISSN: 1573-8744
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01062942
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Three new residual error models for population PK/PD analyses (1995)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 23 (1995), S. 651-672 
    Details
    ISSN: 1573-8744
    Keywords: population PK/PD ; residual error ; intraindividual variability ; autocorrelation ; replicates ; NONMEM
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Residual error models, traditionally used in population pharmacokinetic analyses, have been developed as if all sources of error have properties similar to those of assay error. Since assay error often is only a minor part of the difference between predicted and observed concentrations, other sources, with potentially other properties, should be considered. We have simulated three complex error structures. The first model acknowledges two separate sources of residual error, replication error plus pure residual (assay) error. Simulation results for this case suggest that ignoring these separate sources of error does not adversely affect parameter estimates. The second model allows serially correlated errors, as may occur with structural model misspecification. Ignoring this error structure leads to biased random-effect parameter estimates. A simple autocorrelation model, where the correlation between two errors is assumed to decrease exponentially with the time between them, provides more accurate estimates of the variability parameters in this case. The third model allows time-dependent error magnitude. This may be caused, for example, by inaccurate sample timing. A time-constant error model fit to time-varying error data can lead to bias in all population parameter estimates. A simple two-step time-dependent error model is sufficient to improve parameter estimates, even when the true time dependence is more complex. Using a real data set, we also illustrate the use of the different error models to facilitate the model building process, to provide information about error sources, and to provide more accurate parameter estimates.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02353466
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  • 4
    Electronic Resource
    Electronic Resource
    Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis (1994)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 22 (1994), S. 165-177 
    Details
    ISSN: 1573-8744
    Keywords: population pharmacokinetics ; structural model ; covariate model ; NONMEM ; model selection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The influence of the choice of pharmacokinetic model on subsequent determination of covariate relationships in population pharmacokinetic analysis was studied using both simulated and real data sets. Simulations and data analysis were both performed with the program NONMEM. Data were simulated using a two-compartment model, but at late sample times, so that preferential selection of the two-compartment model should have been impossible. A simple categorical covariate acting on clearance was included. Initially, on the basis of a difference in the objective function values, the two-compartment model was selected over the one-compartment model. Only when the complexity of the one-compartment model was increased in terms of the covariate and statistical models was the difference in objective function values of the two structural models negligible. For two real data sets, with which the two-compartment model was not selected preferentially, more complex covariate relationships were supported with the one-compartment model than with the two-compartment model. Thus, the choice of structural model can be affected as much by the covariate model as can the choice of covariate model be affected by the structural model; the two choices are interestingly intertwined. A suggestion on how to proceed when building population pharmacokinetic models is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02353542
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  • 5
    Electronic Resource
    Electronic Resource
    Comparison of the Akaike Information Criterion, the Schwarz criterion and the F test as guides to model selection (1994)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 22 (1994), S. 431-445 
    Details
    ISSN: 1573-8744
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In pharmacokinetic data analysis, it is frequently necessary to select the number of exponential terms in a polyexponential expression used to describe the concentration-time relationship. The performance characteristics of several selection criteria, the Akaike Information Criterion (AIC), and the Schwarz Criterion (SC), and theF test (α=0.05), were examined using Monte Carlo simulations. In particular, the ability of these criteria to select the correct model, to select a model allowing estimation of pharmacokinetic parameters with small bias and good precision, and to select a model allowing precise predictions of concentration was evaluated. To some extent interrelationships among these procedures is explainable. Results indicate that theF test tends to choose the simpler model more often than does either the AIC or SC, even when the more complex model is correct. Also, theF test is more sensitive to deficient sampling designs. Clearance estimates are generally very robust to the choice of the wrong model. Other pharmacokinetic parameters are more sensitive to model choice, particularly the apparent elimination rate constant. Prediction of concentrations is generally more precise when the correct model is chosen. The tendency for theF test (α=0.05) to choose the simpler model must be considered relative to the objectives of the study.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02353864
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Some suggestions for measuring predictive performance (1982)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 10 (1982), S. 229-229 
    Details
    ISSN: 1573-8744
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01062337
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  • 7
    Electronic Resource
    Electronic Resource
    A note on confidence intervals with extended least squares parameter estimates (1987)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 15 (1987), S. 93-98 
    Details
    ISSN: 1573-8744
    Keywords: Extended least squares ; ordinary least squares ; confidence intervals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract It has previously been shown that the extended least squares (ELS) method for fitting pharmacokinetic models behaves better than other methods when there is possible heteroscedasticity (unequal error variance) in the data. Confidence intervals for pharmacokinetic parameters, at the target confidence level of 95%, computed in simulations with several pharmacokinetic and error variance models, using a theoretically reasonable approximation to the asymptotic covariance matrix of the ELS parameter estimator, are found to include the true parameter values considerably less than 95% of the time. Intervals with the ordinary least squares method perform better. Two adjustments to the ELS confidence intervals, taken together, result in better performance. These are: (i) apply a bias correction to the ELS estimate of variance, which results in wider confidence intervals, and (ii) use confidence intervals with a target level of 99% to obtain confidence intervals with actual level closer to 95%. Kineticists wishing to use the ELS method may wish to use these adjustments.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01062941
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  • 8
    Electronic Resource
    Electronic Resource
    A Population Pharmacokinetic–Pharmacodynamic Analysis of Repeated Measures Time-to-Event Pharmacodynamic Responses: The Antiemetic Effect of Ondansetron (1999)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 27 (1999), S. 625-644 
    Details
    ISSN: 1573-8744
    Keywords: PK/PD ; ondansetron ; time-to-event ; random effects ; frailty models ; hierarchical models ; emesis ; time-dependent hazard ; repeated-measures ; model diagnostics ; model evaluation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract This paper presents and illustrates methodology for specifying, estimating, and evaluating a predictive model for repeated measures time-to-event responses. The illustrative example specifies a model of the antiemetic effect vs. concentration relationship for the 5-HT 3 antagonist ondansetron in the human ipecac model for emesis. A key part of this model is a time-dependent log hazard function for emesis that is increased by ipecac administration and decreased by ondansetron concentration. The model is fit using an approximate maximum likelihood method. The data consist of the time free of emeses and, for those individuals with emetic episodes, the time(s) of the episode(s). Model evaluation is accomplished using residual plots adapted to time-to-event data and a “posterior predictive check” wherein observed data statistics are compared to those obtained from data simulated from the fitted model. The ondansetron concentration required to obtain a 50% reduction in the hazard of emesis is estimated to be 1.4±0.2 ng/ml, and the rate constant for elimination of ipecac-induced hazard is 1.5±0.2hr −1 .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1020930626404
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  • 9
    Electronic Resource
    Electronic Resource
    Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-menten model: Routine clinical pharmacokinetic data (1980)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 8 (1980), S. 553-571 
    Details
    ISSN: 1573-8744
    Keywords: nonlinear regression ; population pharmacokinetics ; Michaelis-Menten model ; phenytoin ; statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Individual pharmacokinetic parameters quantify the pharmacokinetics of an individual, while population pharmacokinetic parameters quantify population mean kinetics, interindividual variability, and residual intraindividual variability plus measurement error. Individual pharmacokinetics are estimated by fitting individual data to a pharmacokinetic model. Population pharmacokinetic parameters are estimated either by fitting all individual's data together as though there were no individual kinetic differences (the naive pooled data approach), or by fitting each individual's data separately, and then combining the individual parameter estimates (the two-stage approach). A third approach, NONMEM, takes a middle course between these, and avoids shortcomings of each of them. A data set consisting of 124 steady-state phenytoin concentration-dosage pairs from 49 patients, obtained in the routine course of their therapy, was analyzed by each method. The resulting population parameter estimates differ considerably (population mean Km, for example, is estimated as 1.57, 5.36, and 4.44 μg/ml by the naive pooled data, two-stage, and NONMEM approaches, respectively). Simulations of the data were analyzed to investigate these differences. The simulations indicate that the pooled data approach fails to estimate variabilities and produces imprecise estimates of mean kinetics. The two-stage appproach produces good estimates of mean kinetics, but biased and imprecise estimates of interindividual variability. NONMEM produces accurate and precise estimates of all parameters, and also reasonable confidence intervals for them. This performance is exactly what is expected from theoretical considerations and provides empirical support for the use of NONMEM when estimating population pharmacokinetics from routine type patient data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060053
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Some suggestions for measuring predictive performance (1981)
    Springer
    Journal of pharmacokinetics and pharmacodynamics 9 (1981), S. 503-512 
    Details
    ISSN: 1573-8744
    Keywords: predictions ; errors ; measurement ; statistics ; precision ; bias
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The performance of a prediction or measurement method is often evaluated by computing the correlation coefficient and/or the regression of predictions on true (reference) values. These provide, however, only a poor description of predictive performance. The mean squared prediction error (precision) and the mean prediction error (bias) provide better descriptions of predictive performance. These quantities are easily computed, and can be used to compare prediction methods to absolute standards or to one another. The measures, however, are unreliable when the reference method is imprecise. The use of these measures is discussed and illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01060893
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    Paper (German National Licenses)
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