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Estimation of quantitative genetic parameters.

This paper gives a short review of the development of genetic parameter estimation over the last 40 years. This shows the development of more statistically and computationally efficient methods that allow the fitting of more biologically appropriate models. Methods have evolved from direct methods based on covariances between relatives to methods based on individual animal models. Maximum-likelihood methods have a natural interpretation in terms of best linear unbiased predictors. Improvements in iterative schemes to give estimates are discussed. As an example, a recent estimation of genetic parameters for a British population of dairy cattle is discussed. The development makes a connection to relevant work by Bill Hill.

Analysis of Variance↗

Regression analysis of longitudinal binary data with time-dependent environmental covariates: bias and efficiency.

Generalized estimating equations (Liang and Zeger, 1986) is a widely used, moment-based procedure to estimate marginal regression parameters. However, a subtle and often overlooked point is that valid inference requires the mean for the response at time t to be expressed properly as a function of the complete past, present, and future values of any time-varying covariate. For example, with environmental exposures it may be necessary to express the response as a function of multiple lagged values of the covariate series. Despite the fact that multiple lagged covariates may be predictive of outcomes, researchers often focus interest on parameters in a 'cross-sectional' model, where the response is expressed as a function of a single lag in the covariate series. Cross-sectional models yield parameters with simple interpretations and avoid issues of collinearity associated with multiple lagged values of a covariate. Pepe and Anderson (1994), showed that parameter estimates for time-varying covariates may be biased unless the mean, given all past, present, and future covariate values, is equal to the cross-sectional mean or unless independence estimating equations are used. Although working independence avoids potential bias, many authors have shown that a poor choice for the response correlation model can lead to highly inefficient parameter estimates. The purpose of this paper is to study the bias-efficiency trade-off associated with working correlation choices for application with binary response data. We investigate data characteristics or design features (e.g. cluster size, overall response association, functional form of the response association, covariate distribution, and others) that influence the small and large sample characteristics of parameter estimates obtained from several different weighting schemes or equivalently 'working' covariance models. We find that the impact of covariance model choice depends highly on the specific structure of the data features, and that key aspects should be examined before choosing a weighting scheme.

Air Pollutants↗

A note on population pharmacokinetic studies with a single sampling design.

The choice of sampling time point in a population pharmacokinetic study with severe limitation on the number of samples per study subject (single sampling design) is critical in obtaining reliable parameter estimates. The authors have investigated the relationship between the timing as well as the degree of distribution of a sampling point among study subjects and the reliability of the estimates of pharmacokinetic parameters in a population pharmacokinetic study. This was achieved through a simulation, assuming an intravenously administered drug whose pharmacokinetic profile follows a 1-compartment model. The convergence rate of the NLMIXED procedure as well as the values of bias and MSE for the estimated parameters showed great variability depending on the sampling schedules. The results indicate that, in the case of a single sampling design, the sampling points should be distributed as widely as possible over a time range along the concentration-time profile to obtain reliable parameter estimates.

Blood Specimen Collection↗

Sensitivity analysis for an improved estimation of respiratory mechanics parameters.

In this paper a respiratory mechanics model is considered, which is characterized by a biquadratic input impedance, and a sensitivity analysis has been carried out to determine the influence of experimental conditions on parameter estimation. This analysis was effected with data obtained experimentally, in three different patients under intermittent positive pressure ventilation. In all three cases, the model's input impedance demonstrated a maximum sensitivity in relation to the various parameters included in the field of frequencies from 0 to 10 Hz. This seems to suggest therefore, that the use of a low-pass filter with a cut-off frequency equal to 10 Hz could improve the signal/noise ratio and, consequently, the accuracy of the estimation of the parameters. Furthermore, the use of a system input with a bandwidth of 0-10 Hz provides the experimental conditions, under which good estimates of the parameters can be obtained. This conclusion has also been confirmed by simulation studies which have been conducted with different types of input signals.

Biomechanical Phenomena↗

Review of guidelines for good practice in decision-analytic modelling in health technology assessment.

OBJECTIVES: To identify existing guidelines and develop a synthesised guideline plus accompanying checklist. In addition to provide guidance on key theoretical, methodological and practical issues and consider the implications of this research for what might be expected of future decision-analytic models. DATA SOURCES: Electronic databases. REVIEW METHODS: A systematic review of existing good practice guidelines was undertaken to identify and summarise guidelines currently available for assessing the quality of decision-analytic models that have been undertaken for health technology assessment. A synthesised good practice guidance and accompanying checklist was developed. Two specific methods areas in decision modelling were considered. The first method's topic is the identification of parameter estimates from published literature. Parameter searches were developed and piloted using a case-study model. The second topic relates to bias in parameter estimates; that is, how to adjust estimates of treatment effect from observational studies where there are risks of selection bias. A systematic literature review was conducted to identify those studies looking at quantification of bias in parameter estimates and the implication of this bias. RESULTS: Fifteen studies met the inclusion criteria and were reviewed and consolidated into a single set of brief statements of good practice. From this, a checklist was developed and applied to three independent decision-analytic models. Although the checklist provided excellent guidance on some key issues for model evaluation, it was too general to pick up on the specific nuances of each model. The searches that were developed helped to identify important data for inclusion in the model. However, the quality of life searches proved to be problematic: the published search filters did not focus on those measures specific to cost-effectiveness analysis and although the strategies developed as part of this project were more successful few data were found. Of the 11 studies meeting the criteria on the effect of selection bias, five concluded that a non-randomised trial design is associated with bias and six studies found 'similar' estimates of treatment effects from observational studies or non-randomised clinical trials and randomised controlled trials (RCTs). One purpose of developing the synthesised guideline and checklist was to provide a framework for critical appraisal by the various parties involved in the health technology assessment process. First, the guideline and checklist can be used by groups that are reviewing other analysts' models and, secondly, the guideline and checklist could be used by the various analysts as they develop their models (to use it as a check on how they are developing and reporting their analyses). The Expert Advisory Group (EAG) that was convened to discuss the potential role of the guidance and checklist felt that, in general, the guidance and checklist would be a useful tool, although the checklist is not meant to be used exclusively to determine a model's quality, and so should not be used as a substitute for critical appraisal. CONCLUSIONS: The review of current guidelines showed that although authors may provide a consistent message regarding some aspects of modelling, in other areas conflicting attributes are presented in different guidelines. In general, the checklist appears to perform well, in terms of identifying those aspects of the model that should be of particular concern to the reader. The checklist cannot, however, provide answers to the appropriateness of the model structure and structural assumptions, as these may be seen as a general problem with generic checklists and do not reflect any shortcoming with the synthesised guidance and checklist developed here. The assessment of the checklist, as well as feedback from the EAG, indicated the importance of its use in conjunction with a more general checklist or guidelines on economic evaluation. Further methods research into the following areas would be valuable: the quantification of selection bias in non-controlled studies and in controlled observational studies; the level of bias in the different non-RCT study designs; a comparison of results from RCTs with those from other non-randomised studies; assessment of the strengths and weaknesses of alternative ways to adjust for bias in a decision model; and how to prioritise searching for parameter estimates.

Benchmarking↗

Estimating genetic parameters of survival distributions: a multifactorial model.

For a number of genetically influenced illnesses, age of onset is correlated between relatives. In some cases, age of onset also serves as an index of an individual's inherited liability to an illness. Typically, survival models for age of onset distributions do not allow for these effects. We have used the gamma distribution as the basis of a model which specifies genetic variability in age of onset. Specifically, we allow the hazard frequency parameter of the gamma distribution to be a monotonic function of an individual's inherited liability to an illness. Simulations under various gamma models indicate that age of onset correlations may be strikingly different from correlations in liability. Maximum likelihood estimation procedures were used to obtain parameter estimates from simulated data sets and to determine whether it is possible to discriminate between gamma processes of different order. The results of 1,000 pairs of twins (500 monozygotic and 500 dizygotic) gave parameter estimates that were fairly accurate but that decreased in precision as the order of the gamma process increased. We discuss the effect this may have on inferences made about age of onset.

Age Factors↗

Validation of population pharmacokinetic parameters of phenytoin using the parallel Michaelis-Menten and first-order elimination model.

This study was conducted to assess whether the parallel Michaelis-Menten and first-order elimination (MM+FO) model fitted the data better than the Michaelis-Menten (MM) model, and to validate the MM+FO model and its parameter estimates. The models were fitted to 853 steady state dose: serum concentration pairs obtained in 332 adults with epilepsy using nonlinear mixed-effects modeling (NONMEM). The MM+FO model fitted the data better than the MM model. The validity of the pharmacokinetic models and the estimated population parameter values was tested using the naive prediction method. The estimation and validation of the pharmacokinetic parameters were undertaken in two separate patient groups (cross-validation) obtained by splitting the data set. Patients were randomly allocated to two equally matched groups (groups 1 and 2). The predictive performance was assessed using 770 paired predicted versus actual dose or measured serum concentrations. The population pharmacokinetic parameters estimated by NONMEM in group 1 were validated in group 2 and vice versa. When predicting steady state serum concentration, the MM+FO model was clearly superior to the MM model (mean bias of 0.91 and 8.13 mg/L, respectively).

Adolescent↗

Evaluation of the estimation of midazolam concentrations and pharmacokinetic parameters in intensive care patients using a bayesian pharmacokinetic software (PKS) according to sparse sampling approach.

The aim of the study was to assess the performance of a bayesian program (PKS System, Abbott) for predicting midazolam concentrations and pharmacokinetic parameters in intensive care patients by comparing the pharmacokinetic parameters estimated by PKS to those calculated according to rich data. The study involved 42 patients receiving midazolam infusion for two hours or for several days. The program was used to predict plasma midazolam concentrations after feedback of 1, 2 or 3 concentrations. High correlation between observed and estimated concentrations was shown (r(2) > 0.992). Mean prediction error, mean absolute prediction error and root mean squared error were low for the patients of the reference and validation groups. From two or three feedback concentrations, midazolam pharmacokinetic parameters estimated by PKS were statistically comparable with those obtained using a rich pharmacokinetic analysis (P > 0.05 paired Wilcoxon test). Thus, PKS is useful for predicting midazolam concentrations and pharmacokinetic parameters when at least two feedback concentrations are known. This software seems to be appropriate for providing significant help to the clinician for midazolam dosage adjustment, according to midazolam concentrations and clinical sedation.

Area Under Curve↗

[Simple kinetic analysis of 99mTc-GSA by direct integral linear least square regression method: calculation of hepatic blood flow and receptor index based on three-compartment model].

To obtain both hepatic blood flow and an index of asialoglycoprotein receptor amount by simple calculation in the asialoglycoprotein receptor imaging with 99mTc-DTPA-Galactosyl Human Serum Albumin (99mTc-GSA), we have tested the applicability of the direct integral linear least square regression (DILS) method based on a linear 3-compartment model (Bronqvist, 1984) to the kinetic analysis of 99mTc-GSA scintigraphy. DILS method can provide hepatic blood flow (k1) and the product of receptor amount and forward binding rate constant (k1k3/k2) as a receptor index, without requiring iterative calculation and initial estimates of the parameters. To compare DILS method with nonlinear least square regression (NLS) method as a standard, data from 35 patients with liver dysfunction were analyzed by both methods. The effect of the data noise to parameter estimate were simulated, and both DILS and NLS method could provide reliable parameter estimate which is relatively insensitive to the data noise. In estimated model parameters, both hepatic blood flow (k1) and the receptor index (k1k3/k2) showed significant correlation between 2 methods (r2 = 0.96, p < 0.0001; r2 = 0.99, p < 0.0001, respectively). We concluded that DILS method was comparable to NLS method in determination of the model parameters and could be useful in the asialoglycoprotein receptor imaging.

Adult↗

Predictability of vancomycin trough concentrations using seven approaches for estimating pharmacokinetic parameters.

PURPOSE: Seven methods for estimating vancomycin pharmacokinetic parameters were studied to determine which method best predicted measured concentrations for patients at a community teaching hospital. METHODS: Data from adult patients who were given vancomycin and had at least one steady-state trough concentration measured were retrospectively reviewed. Data analyzed included laboratory test values, concomitant medications, weight, height, sex, age, laboratory cultures, medical procedures performed, vancomycin dose and interval, measured vancomycin concentrations, and time of measurement. Relevant data were used in seven predictor methods that estimate volume of distribution, vancomycin clearance, and elimination rate constant to determine which yielded the best predictions of actual measured concentrations in the patient population. RESULTS: Data from 189 patients were included in the analyses. The coefficients of determination for the methods ranged from 0.114 to 0.234. Bias ranged from -5.90 to 0.69 mg/L, and precision ranged from 6.05 to 8.08. The Matzke method had the best combination of the least bias and best precision. Predictions were within 2.5 and 5 mg/L of measured concentrations 18.0-43.9% and 43.4-66.1% of the time, respectively. The percentage of predictions within 25% and 50% of measured concentrations ranged from 7.9% to 31.2% and from 18.0% to 48.1%, respectively. Ten (5.3%) patients had trough concentrations exceeding 20 mg/L, and 11 (5.8%) had trough concentrations of < or = 3 mg/L. CONCLUSION: The seven methods studied for estimating vancomycin pharmacokinetic parameters varied widely in predicting vancomycin trough concentrations compared with measured serum concentrations and were not sufficiently reliable to replace therapeutic monitoring of vancomycin serum concentrations.

Anti-Bacterial Agents↗

Integrating in vitro kinetic data from compounds exhibiting induction, reversible inhibition and mechanism-based inactivation: in vitro study design.

Drug:drug interactions continue to be an obstacle for the pharmaceutical industry in the development of potential drug candidates. Considering the number of compounds that have been withdrawn from the market due to drug:drug interactions (e.g. cisapride, terfenadine and mibefradil), more pressure is placed on the pharmaceutical industry to investigate potential interactions prior to regulatory submission. In particular, induction and inhibition of drug metabolizing enzymes can profoundly alter the pharmacological and toxicological effects observed during monotherapy. However, due to differences in the expression and regulation of both metabolic enzymes and nuclear receptors responsible for induction, in vivo studies with pre-clinical species are not predictive of the human clinical situation. Although in vitro kinetic data also have limitations when extrapolating in vivo, in vitro testing has become more commonplace due to reduced cost and higher throughput. However, in the in vitro setting, complex enzyme kinetics can alter the estimation of kinetic parameters. Time-dependent or non-Michaelis-Menten kinetics can alter parameter estimates if experimental conditions are not optimal, and can therefore confound clinical predictions. Furthermore, mechanism-based inactivation (MBI) will reduce the active enzyme pool, both in vitro and in vivo, and thus complicate any parameter estimates. To further complicate matters, some compounds (e.g., ritonavir) inhibit, induce, as well as cause mechanism-based enzyme inactivation. For compounds such as ritonavir, the accurate estimation of kinetic parameters requires optimal experimental design at a minimum. This review will highlight the challenges in estimating enzyme kinetic parameters when both inhibition and induction are present, and will offer experimental viewpoints for the optimization of the experimental conditions.

Data Interpretation, Statistical↗

A modified two-portion absorption model to describe double-peak absorption profiles of ranitidine.

BACKGROUND: The pharmacokinetics of oral drugs exhibiting double peaks cannot be adequately described by using conventional compartmental models. OBJECTIVE: To propose and evaluate a modified two-portion absorption model based on physiological and biopharmaceutical considerations to describe the double-peak concentration-time curve of ranitidine. MODEL DESIGN: The proposed model assumes that oral ranitidine is absorbed sequentially in two portions due to delayed gastric emptying, and thus includes a gut compartment in addition to the central and peripheral compartments. METHODS: Validation of the model was performed with respect to structural identifiability, parameter estimability and model applicability. Using initial estimates of parameters obtained from previous intravenous data, the model was used to fit oral ranitidine data from six subjects who manifested clear double-peak concentration-time profiles as well as from six subjects who showed irregular but apparent single-peak concentration-time curves. RESULTS: Based on goodness-of-fit criteria, the model fitted well for both double-peak and single-peak concentration-time curves of ranitidine (for the two groups: weighted residual sum of squares, 0.044 +/- 0.027 and 0.054 +/- 0.036; correlation between observed and model predicted concentrations, 0.995 +/- 0.003 and 0.995 +/- 0.005). Simulation studies with concentrations generated with 10% normally distributed random error showed that all model fitted parameters had good accuracy and reasonable precision. The mean percentage bias ranged from -7.0 to 28.6%, and the coefficient of variance was within 30% for the majority of parameters compared with the theoretical values. CONCLUSION: The modified two-portion absorption model may afford a useful approach to characterise the absorption phase and estimate pharmacokinetic parameters for drugs with two absorption peaks.

Adult↗

Estimation of population pharmacokinetic parameters using destructively obtained experimental data: a simulation study of the one-compartment open model.

A simulation study of the one-compartment open pharmacokinetic model has been made. The population pharmacokinetic parameters which characterize the population of drug residues over time are assumed to be stochastic. A general theoretical model framework for parameter estimation via the method of extended least squares is presented. Formulas approximating the required mean and variance time functions are developed and subsequently used in the simulation study. The effects of four different designs in four different animal populations are presented. The simulated data are those of the single observation per animal per time point type. The characterizing population pharmacokinetic parameters have been analyzed for bias and reliability in both a naive and second-order mean model. Recommendations for choosing an appropriate sampling design are included.

Analysis of Variance↗

GOFCOX: a computer program for the goodness-of-fit analysis of the Cox proportional hazards model.

GOFCOX is a user-friendly FORTRAN program for assessing the adequacy of the Cox proportional hazards model. The underlying methodology is based on the comparison of the maximum partial likelihood estimator and a weighted parameter estimator. The latter is the root to an estimation equation that assigns varying weights to the individual contributions to the partial likelihood score function. The weighted and unweighted parameter estimators have the same expectation under the Cox model, but tend to differ when the model is inappropriate. The GOFCOX program computes a rich class of weighted parameter estimators and corresponding goodness-of-fit test statistics. The program runs on both mainframe computers and microcomputers. The running time is minimal even for large data sets. A simple example is provided to illustrate the features of the program.

Computers, Mainframe↗

Vancomycin dosing in haemodialysis patients and Bayesian estimate of individual pharmacokinetic parameters.

A dose reduction of vancomycin to 1000 mg once a week usually is recommended for haemodialysis patients. Our modified dosing schedule consists of a loading dose of 1000 mg and a maintenance dose of 500 mg administered 3 times a week after haemodialysis. Different vancomycin regimens were retrospectively evaluated by therapeutic drug monitoring and bayesian parameter estimates in 39 dialysis patients. The mean (+/- SD) trough level in 7 patients receiving only the conventional dosage regimen was significantly lower than in 17 patients strictly treated by the modified schedule (7 +/- 4 versus 17 +/- 8 mg/L; p = 0.001). The corresponding peaks were low in both groups and no different (23 +/- 10 versus 27 +/- 12 mg/L). The one week average vancomycin clearance was significantly lower in the conventional dosage group compared to the modified dosage group (6 +/- 3 versus 10 +/- 3 ml/min; p = 0.001). High-flux dialysers were not used in the conventional dosage group but for 30 percent of the procedures in the modified dosage group, where the vancomycin one week average elimination half-life was 66 hours (+/- 18) and the volume of distribution 50 litres (+/- 5). As compared to the bayesian programme, NONMEM calculated comparable pharmacokinetic parameters but could be applied only in 5 cases with a sufficient number of concentration measurements. Ototoxicity occurred in 1 patient, whereas vancomycin treatment was judged as ineffective against infection in 5 of the 39 patients. Their troughs were below 15 mg/L.(ABSTRACT TRUNCATED AT 250 WORDS)

Acute Kidney Injury↗

Uncertainties of Monod kinetic parameters nonlinearly estimated from batch experiments.

Monod kinetic parameters (Ks, micromax, and Y) that are estimated from batch experimental data can have large uncertainties due to linear correlations between them. The degree of correlation and the resulting uncertainties of the Monod parameters are functions of the initial experimental conditions, the values of the parameters, the type and magnitude of measurement errors, and the sampling number. Careful manipulation of experimental conditions can reduce the correlations between Monod parameters allowing for the estimation of Monod kinetic parameters with the lowest degree of uncertainty. By dimensionless analysis, the correlation and relative standard deviations of Monod parameters were found to be functions of a few dimensionless variables involving the initial substrate (S0) and cell (X0) concentrations. Quantitative relationships were analyzed between the dimensionless variables and the correlation and the uncertainties of the Monod parameters. This analysis allowed for identification of the optimal experimental conditions for estimating Monod parameters under both no growth and growth conditions coupled with two kinds of measurement errors: those with constant absolute standard deviation and those with constant relative standard deviation. Examples involving the microbial reduction of iron(III) as an electron acceptor are used to illustrate the application of the developed technique.

Cell Division↗

Determination of analytical error function for beta-blockers as a possible weighting method for the estimation of the regression parameters.

Three analytical methods have been developed and validated for the quantification of beta-blockers (celiprolol, bisoprolol and oxprenolol) using high performance liquid chromatography (HPLC) with UV detection. The methods were determined to be linear, precise and accurate (RSDs were lower than 5%), which allowed the quantitation of beta-blockers assayed at concentrations in the range 25-0.78 micrograms ml-1. After validation of reversed-phase HPLC methods, their analytical error functions were established by a rapid, simple and economical procedure. The discrimination of the best function for each active principle was performed by an appropriate polynomial statistical analysis, yielding SD (microgram ml-1) = 0.0295 + 0.0124C - 3.88 x 10(-4)C2 for celiprolol, 0.0199 + 0.011C - 1.27 x 10(-5)C3 for bisoprolol; and 0.0183 + 0.0089C - 9.68 x 10(-6)C3 for oxprenolol. These analytical error functions are an alternative to the weighting methods used in parameter estimation of beta-blockers.

Adrenergic beta-Antagonists↗