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PubMed1997

Fieller's theorem, Scheffé simultaneous confidence intervals, and ratios of parameters of linear and nonlinear mixed-effects models.

The issue of joint confidence region and simultaneous confidence interval estimation for ratios of the parameters of a nonlinear mixed-effects model is addressed using a Fieller's theorem approach. The method presented is similarly applicable to linear mixed-effects models. In addition, previous work on linear fixed-effects models is demonstrated to be a special case of the present method. The methodology is applied to the ratios of slopes in a study of gestational maturation of placental glucose transfer capacity in sheep.

Animals↗
PubMed2026

Scale reliant mixed effects models enhance microbiome data analysis.

Linear models, including those used for differential abundance analyses, are frequently used in microbiome research to assess how experimental conditions (e.g., disease state or age) affect microbial abundance. Linear mixed-effects models (MEMs) extend linear models to accommodate complex designs, such as longitudinal sampling or hierarchical study structures. However, when applied to microbiome data, existing MEM approaches suffer from high false positive and false negative rates because sequence counts are compositional - they reflect relative rather than absolute abundances. Current methods attempt to overcome this limitation through normalization, but these approaches rely on strong, often unrealistic assumptions about the unmeasured biological scale (e.g., total microbial load). Here we introduce scale-reliant mixed-effects models (SR-MEM), which extend our earlier scale-reliant inference framework by explicitly modeling uncertainty in the unmeasured scale via user-defined probability distributions. By treating scale as a latent variable rather than fixing it through normalization, SR-MEM enables robust inference for complex experimental designs. SR-MEM can incorporate external scale measurements (e.g., flow cytometry, qPCR) or leverage scale information from independent studies to further improve inference. Across simulations and multiple real-world case studies, SR-MEM consistently controls the false discovery rate while maintaining comparable or higher power than standard approaches relying on normalization or bias correction. In reanalyses of published datasets, SR-MEM yields results that are more reproducible across studies and more consistent with known biological and pharmacological effects. SR-MEM provides a principled and practical framework for mixed-effects modeling of microbiome sequence count data in the presence of unmeasured biological scale. By avoiding normalization-based assumptions and instead propagating scale uncertainty through inference, SR-MEM improves error control and reproducibility in longitudinal and hierarchical studies. An accessible implementation is provided in the ALDEx3 R package.

Microbiota↗
PubMed2005

Dosing strategy for enoxaparin in patients with renal impairment presenting with acute coronary syndromes.

BACKGROUND: Phase III clinical studies have confirmed that enoxaparin is superior to standard heparin in reducing the rate of recurrent ischaemic events in patients with non-ST elevation acute coronary syndromes. Patients with moderate to severe renal impairment were, however, excluded from these studies. Due to the hydrophilic disposition of enoxaparin, accumulation is likely in patients with renal dysfunction, thereby increasing the risk of haemorrhagic complications if standard weight adjusted treatment doses are used. Arbitrary dose reduction has been reported to increase the risk of ischaemic events, presumably due to inadequate enoxaparin concentrations. AIM: The aims of this study were to investigate the influence of glomerular filtration rate (GFR) on the pharmacokinetics of subcutaneously administered enoxaparin, and to develop a practical dosing algorithm in renal impairment that can easily be used at the bedside. METHODS: Thirty-eight patients, median age 78 years (range 44-87), mean GFR 32 ml min(-1) (range 16-117) and mean weight 69 kg (range 32-95), presenting with acute coronary syndrome were recruited into the study. Approximately 10 anti-Xa concentrations were taken per patient over their period of therapy. A population pharmacokinetic model was developed using non linear mixed effects modelling techniques, utilizing the software NONMEM. Stochastic simulations were performed to identify the most suitable dosing regimen. RESULTS: Three hundred and thirteen anti-Xa concentrations were collected. A two compartment, first order input model was identified as the best baseline model. Covariates found to improve model fitting were GFR as a linear function on clearance (CL) and weight as a linear function on the central volume compartment (Vc). The fraction of drug excreted unchanged (Fu) was estimated at 71%. CL and Vc from the final covariate model were estimated as; CL (l h(-1)) = 0.681 per 4.8 l hr(-1) (GFR) + 0.229 Vc (l) = 5.22 per 80 kg (total body weight) CONCLUSIONS: Clearance of enoxaparin was predictably related to GFR estimated using the Cockroft and Gault equation, with ideal body weight used as the size descriptor. According to our model no dosage adjustment from the standard 1.0 mg kg(-1) 12 hourly is required for the first 48 h of treatment. Maintenance doses thereafter can be calculated using standard proportional adjustments based on Fu equal to 0.71.

Administration, Cutaneous↗
PubMed2006

Mixture modeling for the detection of subpopulations in a pharmacokinetic/pharmacodynamic analysis.

To be able to estimate accurately parameters entering a non-linear mixed effects model taking into account that one or more subpopulations of patients can exist rather than assuming that the entire population is best described by unimodal distributions for the random effects, we proposed a methodology based on the likelihood approximation using the Gauss-Hermite quadrature. The idea is to combine the estimation of the model parameters and the detection of homogeneous subgroups of patients in a given population using a Gaussian mixture for the distribution of the random effects. As the accuracy of the likelihood approximation is likely to govern the quality of the estimation of the different parameters entering the non-linear mixed effects model, we based this approximation on the use of an adjustable Gauss-Hermite quadrature. Moreover, to complete this methodology, we propose a strategy allowing the detection and explanation of heterogeneity based on the Kullback-Leibler test, which was used to estimate the number of components in the Gaussian mixture. In order to evaluate the capability of the method to take into account heterogeneity, this strategy was performed in a PK/PD analysis using the database and the structural model selected in a previous analysis. In this analysis, non-responders were found out using NONMEM [Beal and Sheiner. NONMEM Users Guides. NONMEM Project Group, University of California, San Francisio, 1992] in a population of diabetic patients treated with a once-a-day new formulation of an antidiabetic drug. The authors looked for a subpopulation of patients for whom the therapeutic effect would vanish. In this paper, we looked for subpopulations of patients exhibiting specificities with respect to different parameters entering the description of the effect. The results obtained with our approach are compared in terms of parameter estimation and heterogeneity detection to those obtained in the previous analysis.

Blood Glucose↗
PubMed2005

Prediction discrepancies for the evaluation of nonlinear mixed-effects models.

Reliable estimation methods for non-linear mixed-effects models are now available and, although these models are increasingly used, only a limited number of statistical developments for their evaluation have been reported. We develop a criterion and a test to evaluate nonlinear mixed-effects models based on the whole predictive distribution. For each observation, we define the prediction discrepancy (pd) as the percentile of the observation in the whole marginal predictive distribution under H(0). We propose to compute prediction discrepancies using Monte Carlo integration which does not require model approximation. If the model is valid, these pd should be uniformly distributed over (0, 1) which can be tested by a Kolmogorov-Smirnov test. In a simulation study based on a standard population pharmacokinetic model, we compare and show the interest of this criterion with respect to the one most frequently used to evaluate nonlinear mixed-effects models: standardized prediction errors (spe) which are evaluated using a first order approximation of the model. Trends in pd can also be evaluated via several plots to check for specific departures from the model.

Algorithms↗
PubMed1999

A new approach to modelling the relationship between in vitro and in vivo drug dissolution/absorption.

A major goal of the pharmaceutical scientist is finding a relationship between an in vitro characteristic of an oral dosage form and its in vivo performance. One such relationship between drug dissolution (or absorption) in vivo and that in vitro is known as an 'in vitro-in vivo correlation' (IVIVC) whose importance stems from the fact that it may be used to minimize the number of human studies required during product development, assist in setting meaningful in vitro dissolution specifications and justify biowaivers for scale-up and post approval changes. A number of ways of describing an IVIVC have been reported with 'level A' being the most informative and therefore most desirable. In the majority of cases reported to date, both the model and the statistical methods employed for level A IVIVC are very simplistic. The model assumes that the rate and extent of dissolution in vivo are the same as those in vitro. The statistical methods ignore the repeated measures nature of the data and use a response variable as an independent variable without accounting for measurement error. This paper describes some new models which include the simple model as a special case. The modelling approach is based on considering the time at which a drug molecule enters solution (in vitro or in vivo) to be a random variable. The in vitro and in vivo distributions are then related to one another using a proportional odds, proportional hazards or proportional reversed hazards model. The models can be extended by adding a linear time component which describes a time varying relationship. Following the addition of random effects to these structural models in order to account for the repeated measures nature of the data collected, the models may be described as generalized linear mixed effects models. The models were fitted to some data sets using a maximum likelihood based method and the results indicate that these models have potential for describing an in vitro-in vivo relationship which cannot be described using the currently available models.

Absorption↗
PubMed2004

Binding of 2,4,6-trinitrotoluene, aniline, and nitrobenzene to dissolved and particulate soil organic matter.

The distribution of TNT* (the sum of TNT and its degradation products), aniline, and nitrobenzene between particulate organic matter (POM), dissolved soil organic matter (DOM), and free compound was studied in controlled kinetic (with and without irradiation) and equilibrium experiments with mixtures of POM and DOM reflecting natural situations in organic rich soils. The binding of TNT* to POM was fast, independent of irradiation, and adsorption isotherms had a great linear contribution (as determined by a mixed model), indicative of a hydrophobic partitioning mechanism. The binding of TNT* to DOM was slower, strongly enhanced under nonirradiated conditions, and adsorption isotherms were highly nonlinear, indicative of a specific interaction between TNT derivatives and functional groups of DOM. Nitrobenzene was associated to both POM and DOM via hydrophobic partitioning, whereas aniline binding was dominated by specific binding to POM and DOM functional groups. On the basis of nitrobenzene and TNT* adsorption parameters determined by a mixed Langmuir + linear model, POM had 2-3 times greater density of hydrophobic moieties as compared to DOM. This difference was reflected by a greater (O + N)/C atomic ratio for DOM. The sum of C-C and C-H moieties, as determined by X-ray photoelectron spectroscopy (XPS), and the sum of aryl-C and alkyl-C, as determined by solid-state cross-polarization magic-angle spinning (CP-MAS) 13C NMR, could only qualitatively account for differences in adsorption parameters. Aliphatic C was found to be more important for the hydrophobic partitioning than aromatic C. On the basis of nonlinear adsorption parameters,the density of functional groups reactive with aniline and TNT derivatives was 1.3-1.4 times greater in DOM than in POM, which was in fair agreement with 13C NMR and XPS data for the sum of carboxyl and carbonyl groups as potential sites for electrostatic and covalent bonding. We conclude that in contaminated soils characterized by continuous leaching of DOM, formation of TNT derivatives (via biotic and abiotic reductive degradation) and their preference for specific functional groups in DOM may contribute to a significant transportation of potentially toxic TNT compounds into surface waters and groundwaters.

Adsorption↗
PubMed2005

Mixed model estimation methods for the Rasch model.

Mixed models take the dependency between observations based on the same person into account by introducing one or more random effects. After introducing the mixed model framework, it is explained, by taking the Rasch model as a generic example, how item response models can be conceptualized as generalized linear and nonlinear mixed models. Common estimation methods for generalized linear and nonlinear models are discussed. In a simulation study, the performance of four estimation methods is assessed for the Rasch model under different conditions regarding the number of items and persons, and the degree of interindividual differences. The estimation methods included in the study are: an approximation of the integral over the random effect by means of Gaussian quadrature; direct maximization with a sixth-order Laplace approximation to the integrand; a linearized approximation of the nonlinear model employing PQL2; and finally a Bayesian MCMC method. It is concluded that the estimation methods perform almost equally well, except for a slightly worse recovery of the variance parameter for PQL2 and MCMC.

Data Interpretation, Statistical↗
PubMed2006

Longitudinal assessment of heart rate variability in very low birth weight infants during their NICU stay.

BACKGROUND: Maturation of the autonomic nervous system has not been studied in high-risk very low birth weight (VLBW) infants in the first few weeks of life. AIM: To characterize developmental changes in autonomic nervous system activity of high-risk VLBW infants from 23 to 38 weeks post-menstrual age by measuring heart rate variability (HRV). STUDY DESIGN AND SUBJECTS: In this prospective cohort study 38 infants admitted to Children's Memorial Hermann Hospital NICU were longitudinally followed weekly or biweekly. Heart period data were recorded while infants were resting in active sleep. OUTCOME MEASURES: Growth of spectral power of HRV in low-frequency (0.05-0.25 Hz) and high-frequency (0.25-1.00 Hz) bands was modeled with linear mixed-effects models. The high-frequency power provides a measure of respiratory sinus arrhythmia (RSA). RESULTS: Low-frequency power increases with post-menstrual age, and intubated infants have lower HRV. The increase in low-frequency power is faster (0.50+/-0.12 dB/week) than the increase in RSA (0.17+/-0.09 dB/week). CONCLUSION: This longitudinal data exhibits developmental maturation of the RSA and of the low-frequency power of HRV in high-risk VLBW infants.

Age Factors↗
PubMed2001

Pharmacodynamic modelling of reversible gastric acid pump inhibition in dog and man.

H 335/25, a 4-amino quinoline, belongs to a new class of reversible gastric acid pump inhibitors. A potential advantage of such drugs over the irreversible proton pump inhibitors (PPIs) is better control over the effect-time profile. Dose escalation studies were performed to characterize the effect on acid secretion in dogs (n=24) and healthy male subjects (n=12). The effect-time profile was delayed compared to the concentration-time profile. A model-based approach, using non-linear mixed effects modelling, was applied to quantify and elucidate the mechanism for the delayed effect. Three different models were investigated: (1) a slow equilibration preceding the formation of drug-enzyme complex, modelled by an effect-compartment, (2) a slow equilibration between free drug, free enzyme and drug-enzyme complex, described by a kinetic binding model, and (3) a delay between enzyme inhibition and the measured response, described by an indirect response model. Model 2 was shown to be superior to models 1 and 3, for both dog and human data. The dissociation rate constant, k(off), was estimated to be 0.85 and 0.88 h and the calculated equilibration constant, K(d), was 160 and 250 nM in dog and man, respectively. Simulations of the predicted time-course of the effect beyond the 4-5-h observation period was similar for the three models.

Administration, Oral↗
PubMed2001

Population pharmacokinetic-pharmacodynamic modelling of S 15535, a 5-HT(1A) receptor agonist, using a behavioural model in rats.

The pharmacokinetic-pharmacodynamic relationship of S 15535 (1-(benzodioxan-5-yl) 4-(indan-2-yl)piperazine) and its active 5-hydroxy metabolite S 32784 (1-(benzodioxan-5-yl) 4-(5-hydroxyindan-2-yl)piperazine), and buspirone as a reference, were studied in male Wistar rats using a behavioural model of anxiety by determining the reduction in the number of fear-induced ultrasonic vocalisations. S 15535 and buspirone were administered p.o. and i.v. S 32784, present in man but not in rat, was administered i.v. The pharmacokinetics and pharmacokinetic-pharmacodynamic relationships were described using non-linear mixed effects modelling. The no-drug effect was constant and all compounds were active in the model, reducing ultrasonic vocalisations immediately after administration. The sigmoid E(max) model was used to describe the pharmacokinetic-pharmacodynamic relationships, with E(max) values of a 90% decrease in baseline ultrasonic vocalisations. Corrected for plasma protein binding, all compounds showed similar potency. The study shows that ultrasonic vocalisations can be considered a suitable endpoint for the anxiolytic effect when used in conjunction with non-linear mixed effects modelling to overcome the limited sampling and effect measurements.

Animals↗
PubMed2001

Two-stage methods for the analysis of pooled data.

Epidemiologic studies of disease often produce inconclusive or contradictory results due to small sample sizes or regional variations in the disease incidence or the exposures. To clarify these issues, researchers occasionally pool and reanalyse original data from several large studies. In this paper we explore the use of a two-stage random-effects model for analysing pooled case-control studies and undertake a thorough examination of bias in the pooled estimator under various conditions. The two-stage model analyses each study using the model appropriate to the design with study-specific confounders, and combines the individual study-specific adjusted log-odds ratios using a linear mixed-effects model; it is computationally simple and can incorporate study-level covariates and random effects. Simulations indicate that when the individual studies are large, two-stage methods produce nearly unbiased exposure estimates and standard errors of the exposure estimates from a generalized linear mixed model. By contrast, joint fixed-effects logistic regression produces attenuated exposure estimates and underestimates the standard error when heterogeneity is present. While bias in the pooled regression coefficient increases with interstudy heterogeneity for both models, it is much smaller using the two-stage model. In pooled analyses, where covariates may not be uniformly defined and coded across studies, and occasionally not measured in all studies, a joint model is often not feasible. The two-stage method is shown to be a simple, valid and practical method for the analysis of pooled binary data. The results are applied to a study of reproductive history and cutaneous melanoma risk in women using data from ten large case-control studies.

Adolescent↗
PubMed1996

Goodness-of-fit in generalized nonlinear mixed-effects models.

In recent years, generalized linear and nonlinear mixed-effects models have proved to be powerful tools for the analysis of unbalanced longitudinal data. To date, much of the work has focused on various methods for estimating and comparing the parameters of mixed-effects models. Very little work has been done in the area of model selection and goodness-of-fit, particularly with respect to the assumed variance-covariance structure. In this paper, we present a goodness-of-fit statistic which can be used in a manner similar to the R2 criterion in linear regression for assessing the adequacy of an assumed mean and variance-covariance structure. In addition, we introduce an approximate pseudo-likelihood ratio test for testing the adequacy of the hypothesized convariance structure. These methods are illustrated and compared to the usual normal theory likelihood methods (Akaike's information criterion and the likelihood ratio test) using three examples. Simulation results indicate the pseudo-likelihood ratio test compares favorably with the standard normal theory likelihood ratio test, but both procedures are sensitive to departures from normality.

Adolescent↗
PubMed2005

Non-linearity of Parkinson's disease progression: implications for sample size calculations in clinical trials.

BACKGROUND: Estimation of sample size for long-term studies of neuroprotection in Parkinson's disease requires information on expected clinical decline. Values may be obtained by analyzing existing long-term data sets or by prediction models of clinical decline applied to available data from shorter-term trials. The most commonly used measure to track clinical decline is the Unified Parkinson's Disease Rating Scale (UPDRS) but this measure is also affected by symptomatic therapy. Models can help better understand behavior of the UPDRS after initiation of symptomatic therapy when scores will improve and eventually start deteriorating again. PURPOSE: To understand how UPDRS scores progress after initiation of symptomatic therapy and how this progression impacts sample size calculations. METHODS: We developed a non-linear model of UPDRS after introduction of symptomatic therapy. The model is specified as a non-linear mixed effects model and is applied to three different data sets from clinical trials. The model is then used to produce estimates for the change in UPDRS and its associated variance for a period of up to five years of follow-up. The estimates produced by the model serve as the basis for sample-size calculations for different lengths of follow-up (one through five years) and for different values of clinically meaningful change in UPDRS. RESULTS: Despite differences in the short-term benefit of the dopaminergic drugs, after a period of approximately six months UPDRS scores progress linearly at an estimated rate of approximately three points a year. The sample size that is required for a clinical trial where the baseline coincides with initiation of symptomatic therapy is very large. On the other hand, if baseline is set at six months after initiation of symptomatic therapy then the sample size required decreases with length of follow-up. LIMITATIONS: Model specification and estimation is based on a set of simplifying assumptions regarding the progression of individual level UPDRS scores. CONCLUSIONS: Sample size calculations based on these estimates indicate a substantial reduction in sample size if patients are required to be on symptomatic treatment for a period of time before being randomized to a neuroprotective trial.

Antiparkinson Agents↗
PubMed2004

Mitochondrial DNA polymorphisms and sperm motility in Mytilus edulis (Bivalvia: Mytilidae).

The system of mitochondrial DNA (mtDNA) inheritance in Mytilus and other bivalves, termed doubly uniparental inheritance (DUI), is novel among animals. Males pass on their male transmitted (M-type) mtDNA from fathers to their sons whereas females pass on their female transmitted (F-type) mtDNA from mothers to both sons and daughters. Thus, Mytilus males contain two distinct types of mtDNA. Interestingly, sperm contains only the paternal mtDNA. Phylogenetic analysis has shown that some female types have been able to switch their route of inheritance. These "recently masculinized" mitochondrial genomes behave as a typical M-type in that they are transmitted from generation to generation through sperm. Because the "recently masculinized" and "standard" male mitotypes in M. edulis exhibit approximately 8.7% amino acid sequence divergence, we hypothesized that these differences could affect mitochondrial, and hence sperm, functions. Furthermore, since recently masculinized mitotypes have been shown to replace standard male types periodically over evolutionary timescales, we tested the hypothesis that sperm swimming speeds would be greater for males with recently masculinized M-type genomes. Sperm activity was videotaped, digitized and tracked. A linear mixed effects model found no significant difference in linear velocities or curvilinear speeds between the mitotypes suggesting that swimming speeds are similar for both in the period shortly after spawning.

Animals↗
PubMed2002

Penalized likelihood approach to estimate a smooth mean curve on longitudinal data.

This paper aims to propose a penalized likelihood approach to estimate a smooth mean curve for the evolution with time of a Gaussian variable taking into account the correlation structure of longitudinal data. The model is an extension of the mixed effects linear model including an unspecified function of time f(t). The estimator (circumflex)f(t) is defined as the solution of the maximization of the penalized likelihood and is approximated on a basis of cubic M-spline with a reduced number of knots. We present modifications of four criteria (cross-validation, generalized cross-validation, T of Rice, Akaike's criterion) to estimate the smoothing parameter when data are correlated; these four criteria gave very similar results in the simulation study. The simulation study showed also the superiority of the Bayesian confidence bands of the mean curve over the frequentist ones. We develop empirical Bayes estimates of subject-specific deviations. This approach was applied to study the progression of CD4+ lymphocyte counts in a cohort of HIV patients treated with protease inhibitors.

Acquired Immunodeficiency Syndrome↗
PubMed1998

Genetic "clocks" and "soft" events: a twin model for pubertal development and other recalled sequences of developmental milestones, transitions, or ages at onset.

We propose and explore a twin model to examine the basis for synchrony that often characterizes different facets of normal development. In so doing we also present an approach to the analysis of "soft" events; events for which available reports of dates or ages of occurrence are unreliable or inconsistent. Discrepancies among reports are accounted for by a statistical measurement model. This combines current status error reflecting uncertain definition of onset and two mechanisms for the phenomenon of "telescoping," namely, systematic compression of the time scale and heteroscedastic random measurement error. Statistically, the model can be viewed as a mixed generalized linear model with random effects within both mean and variance functions or, alternatively, as involving multiplicative random effects. We apply the model to multiple maternal reports on menarche and onset of breast development in twin daughters. Fitted to data from the Virginia Twin Study Of Adolescent and Behavioral Development by the use of penalized/predictive quasi-likelihood, the model provided much improved estimates of the true age-at-onset distribution as compared to those from a naive analysis. Results suggested that the observed variance was made up almost entirely of genetic variance and measurement error variance due to telescoping and current status errors and that the timing of breast development and menarche are largely under the control of a common set of genes. Results also indicated that maternal recollections of the onset of breast development were both more poorly defined and subject to greater recall errors than maternal recollections of menarche.

Adolescent↗
PubMed2004

Comparative population pharmacokinetics of lorazepam and midazolam during long-term continuous infusion in critically ill patients.

AIMS: It is well established that there is a wide intra- and interindividual variability in dose requirements for lorazepam and midazolam in intensive care patients. The objective of this study was to compare the population pharmacokinetics of lorazepam and midazolam after long-term continuous infusion in mechanically ventilated critically ill patients. METHODS: Forty-nine critically ill patients randomly received either lorazepam (n = 28) or midazolam (n = 21) by continuous infusion for at least 24 h. Multiple blood samples were obtained for determination of the drug and metabolite concentrations by HPLC. Population pharmacokinetic models were developed using the Non-Linear Mixed Effect Modelling (NONMEM) program. The influence of selected covariates was investigated. The prospective performance of the models was evaluated on the basis of results in separate groups of patients for lorazepam (n = 31) and midazolam (n = 33). RESULTS: The pharmacokinetics of lorazepam were best described by a two-compartment model. Alcohol abuse, positive end expiratory pressure (PEEP) and age were identified as significant covariates. Total body clearance for patients without alcohol abuse was 4.13 - (PEEP - 5) x 0.42 l h-1, and 0.74 l h-1 for patients with alcohol abuse. The volume of distribution was 0.74 l, the steady state volume of distribution was 56 - (age - 58) x 2.1 l and the intercompartmental clearance was 10 l h-1. The proportional residual error was 15% and the median absolute prediction error was 13.6% with a bias of 1.5%. The pharmacokinetics of midazolam were best described by a two-compartment model with alcohol abuse, APACHE score and age as significant covariates. Total body clearance for patients without alcohol abuse was 11.3 - (age - 57) x 0.14 l h-1, and 7.27 - (age -57) x 0.14 l h-1 for patients with alcohol abuse. The volume of distribution was 7.15 l, the steady state volume of distribution was 431 l, and the intercompartmental clearance was 40.8 - (APACHE score - 26) x 2.75 l h-1. The proportional residual error was 31% with an additive residual error of 32 ng ml-1. The median absolute prediction error was 12.9% with a bias of 1.2%. The prospective performance in the lorazepam evaluation group was better with the covariate adjusted model, but in the midazolam evaluation group it was not better than with the simple model. In all models a tendency to overestimate the lower plasma concentrations was observed. CONCLUSIONS: The pharmacokinetics of both lorazepam and midazolam were well described by a two-compartment model. Inclusion of alcohol abuse and age as covariates improved both models. PEEP was identified as an additional covariate for lorazepam, and the APACHE score for midazolam. For both drugs there is a large interindividual variability in their pharmacokinetics when used for long-term sedation in critically ill patients. However, the intra-individual variability is much lower for lorazepam.

Adolescent↗