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At least 91 records · Page 5Linked to original sources
PubMed2005

Covariate detection in population pharmacokinetics using partially linear mixed effects models.

PURPOSE: To introduce partially linear mixed effects models (PLMEMs), to illustrate their use, and to compare the power and Type I error rate in detecting a covariate effect with nonlinear mixed effects modeling using NONMEM. METHODS: Sparse concentration-time data from males and females (1:1) were simulated under a 1-compartment oral model where clearance was sex-dependent. All possible combinations of number of subjects (50, 75, 100, 150, 250), samples per subject (2, 4, 6), and clearance multipliers (1 to 1.25) were generated. Data were analyzed with and without sex as a covariate using PLMEM (maximum likelihood estimation) and NONMEM (first-order conditional estimation). Four covariate screening methods were examined: NONMEM using the likelihood ratio test (LRT), PLMEM using the LRT, PLMEM using Wald's test, and analysis of variance (ANOVA) of the empirical Bayes estimates (EBEs) for CL treating sex as a categorical variable. The percent of simulations rejecting the null hypothesis of no covariate effect at the 0.05 level was determined. 300 simulations were done to calculate power curves and 1000 simulations were done (with no covariate effect) to calculate Type I error rate. Actual implementation of PLMEMs is illustrated using previously published teicoplanin data. RESULTS: Type I error rates were similar between PLMEM and NONMEM using the LRT, but were inflated (as high as 36%) based on PLMEM using Wald's test. Type I error rate tended to increase as the number of observations per subject increased for the LRT methods. Power curves were similar between the PLMEM and NONMEM LRT methods and were slightly more than the power curve using ANOVA on the EBEs of CL. 80% power was achieved with 4 samples per subject and 50 subjects total when the effect size was approximately 1.07, 1.07, 1.08, and 1.05 for LRT using PLMEMs, LRT using NONMEM, ANOVA on the EBEs, and Wald's test using PLMEMs, respectively. CONCLUSIONS: PLMEM and NONMEM covariate screening using the LRT had similar Type I error rates and power under the data generating model. PLMEMs offers a viable alternative to NONMEM-based covariate screening.

Computer Simulation↗
PubMed2004

A sample size computation method for non-linear mixed effects models with applications to pharmacokinetics models.

We propose a simple method to compute sample size for an arbitrary test hypothesis in population pharmacokinetics (PK) studies analysed with non-linear mixed effects models. Sample size procedures exist for linear mixed effects model, and have been recently extended by Rochon using the generalized estimating equation of Liang and Zeger. Thus, full model based inference in sample size computation has been possible. The method we propose extends the approach using a first-order linearization of the non-linear mixed effects model and use of the Wald chi(2) test statistic. The proposed method is general. It allows an arbitrary non-linear model as well as arbitrary distribution of random effects characterizing both inter- and intra-individual variability of the mixed effects model. To illustrate possible uses of the method we present tables of minimum sample sizes, in particular, with an illustration of the effect of sampling design on sample size. We demonstrate how (D-)optimal or frequent sampling requires fewer subjects in comparison to a sparse sampling design. We also present results from Monte Carlo simulations showing that the computed sample size can produce the desired power. The proposed method greatly reduces computing times compared with simulation-based methods of estimating sample sizes for population PK studies.

Black People↗
PubMed2003

Measuring explained variation in linear mixed effects models.

We generalize the well-known R(2) measure for linear regression to linear mixed effects models. Our work was motivated by a cluster-randomized study conducted by the Eastern Cooperative Oncology Group, to compare two different versions of informed consent document. We quantify the variation in the response that is explained by the covariates under the linear mixed model, and study three types of measures to estimate such quantities. The first type of measures make direct use of the estimated variances; the second type of measures use residual sums of squares in analogy to the linear regression; the third type of measures are based on the Kullback-Leibler information gain. All the measures can be easily obtained from software programs that fit linear mixed models. We study the performance of the measures through Monte Carlo simulations, and illustrate the usefulness of the measures on data sets.

Antipsychotic Agents↗
PubMed2005

A note on joint versus gene-specific mixed model analysis of microarray gene expression data.

Currently, linear mixed model analyses of expression microarray experiments are performed either in a gene-specific or global mode. The joint analysis provides more flexibility in terms of how parameters are fitted and estimated and tends to be more powerful than the gene-specific analysis. Here we show how to implement the gene-specific linear mixed model analysis as an exact algorithm for the joint linear mixed model analysis. The gene-specific algorithm is exact, when the mixed model equations can be partitioned into unrelated components: One for all global fixed and random effects and the others for the gene-specific fixed and random effects for each gene separately. This unrelatedness holds under three conditions: (1) any gene must have the same number of replicates or probes on all arrays, but these numbers can differ among genes; (2) the residual variance of the (transformed) expression data must be homogeneous or constant across genes (other variance components need not be homogeneous) and (3) the number of genes in the experiment is large. When these conditions are violated, the gene-specific algorithm is expected to be nearly exact.

Algorithms↗
PubMed2002

Modelling HIV viral rebound using non-linear mixed effects models.

Individuals infected with the human immunodeficiency virus type 1 (HIV-1) who initiate antiretroviral therapy typically experience a marked decline in concentrations of HIV-1 RNA in plasma. Often, however, viral rebound occurs within the first year of treatment and this rebound may be associated with resistance to antiretroviral therapy. For this reason, it is important to study the patterns of virological response of HIV-1 RNA to treatment. In particular, there is interest in the relationship between the lowest level of plasma HIV-1 RNA attained after initiation of therapy (nadir value) and the time until rebound. To investigate this question, we implement a simple and flexible non-linear mixed effects model for the trajectory of the HIV-1 RNA until rebound. This model is also consistent with biological insights into the effects of treatment. We also show how the problem of censoring of HIV-1 RNA values at the lower limit of assay quantification can be addressed using a multiple imputation scheme. The algorithm is simple to implement and is based on accessible software. Our application makes use of data from clinical trial 315 conducted by the AIDS Clinical Trials Group (ACTG 315). We find a strong relationship between HIV-1 RNA nadir and time to rebound, with potentially important consequences for the management of HIV-infected individuals.

Adolescent↗
PubMedDate not supplied

Non-linear mixed effects modeling of sparse concentration data from rats: application to a glycogen phosphorylase inhibitor.

We investigated the use of non-linear mixed effects modeling in two preclinical studies of the glycogen phosphorylase inhibitor 1,4-dideoxy-1,4-imino-D-arabinitol (DAB). In a 28-day repeated-dose toxicity study rats were dosed once daily p.o. with 0, 20, 45, 100, or 470 mg/kg of DAB in aqueous solutions by oral gavage. Three blood samples were obtained from each animal using a staggered sampling scheme. During the cause of model development, data were included from a safety pharmacological cardiovascular study, in which rats were dosed once orally with 0, 4, 40, or 400 mg/kg of DAB thereby enabling an extension of the dose range of the model. DAB was assayed in plasma using a validated LC/MS/MS method. Non-linear mixed effects modeling was performed using the software NONMEM. The covariate analysis comprised dose, sex and time. Exposure results (Cmax, AUC) obtained by mixed effects modeling were compared to results from noncompartmental analysis using naïve pooling of data. The final model was a one-compartment model with first order absorption and a saturation-like dose dependent increase of the (oral) clearance (CL/f) and volume of distribution (V/f). Furthermore, V/f increased (by 55%) from Day 1 to Day 28. The dose dependencies of CL/f and V/f were most likely due to dose dependent decreases of the fraction systemically absorbed (f). The mechanism behind the dose dependencies may be saturation of a (putative) carrier mediated transport or modulation of tight junctions causing a reduced paracellular transport across the intestinal epithelium. Exposure results obtained from the model compared well with results obtained using noncompartmental analysis. An analysis of the data requirements for non-linear mixed effects modeling showed that at least three concentration values per animal were required for model development. We conclude that non-linear mixed effects modeling is feasible even with dose dependent pharmacokinetics in preclinical studies, such as 28-day toxicity studies in rodents. Supplementing data from additional preclinical studies may be required in order to extend the dose range. Non-linear mixed effects models may prove to be valuable tools in early PK and PK-PD modeling during drug development.

Animals↗
PubMed2001

Application of linear mixed effects models to the evaluation of dissolution profiles.

The performance of linear mixed effects models for the comparison of dissolution profiles is examined. This type of model is frequently used by statisticians, but is rather unknown to people that work in dissolution laboratories. Hence, an extensive theoretical part was introduced to make the methodology more accessible. Firstly, repeated measures ANOVA is discussed, followed by the "real" linear mixed effects models. The theory is applied to two types of dissolution data: one corresponding to an immediate and another to a slow release formulation. We tried to use as much as possible the standard settings of the statistical software (S-plus). Suggestions are given to solve problems encountered during model fitting. It was found that the statistical limits are much more discriminative than the similarity factor.

Analysis of Variance↗
PubMed2002

Non-linear mixed effects models for the evaluation of dissolution profiles.

The use of non-linear mixed effects models to describe dissolution data has been evaluated. A theoretical part is included to introduce this approach to scientists who are not familiar with this type of statistics. The standard settings of the statistical software package (S-plus) are used as much as possible. Several mathematical functions like the Weibull, logistic, first-order and Gompertz are employed as basis for the non-linear mixed effects models. Examples are given using dissolution data of immediate and extended release tablets. The results are compared with those obtained using linear mixed effects models.

Linear Models↗
PubMed2001

Weight gain in a controlled study of risperidone in children, adolescents and adults with mental retardation and autism.

As part of an ongoing, prospective, ABA design, double-blind crossover study of risperidone versus placebo for the treatment of aggressive, destructive and self-injurious behavior in persons aged 6-65 years with mental retardation (MR) and autism, we measured the weight of 19 subjects at each study visit. We compared mean weight gain during the 16-week acute phase and 24-week open maintenance phase with that during the initial and middle placebo phases statistically, using a linear mixed model procedure. Results of the linear mixed model analysis showed that relative weight gain observed during the acute and maintenance drug phases was significantly greater than that observed during the initial and middle placebo phases respectively (p = .0001 and p = .0001). Over approximately a year, children aged 8-12 (n = 5) gained a mean of 8.2 kg (range = 2.7-17.7 kg); adolescents (n = 6) aged 13-16 gained a mean of 8.4 kg (range 3.6-15.5 kg); adults aged 21-51 (n = 8) gained a mean of 5.4 kg (range 0-9.5 kg). Weight gain observed in this controlled study of risperidone treatment in children, adolescents, and adults with MR and autism was significant. It may be greater in this population than in others reported and in this study was not limited to an acute effect only. Rate of weight gain diminished rapidly on tapering and stopping the drug. Further studies are urgently needed, including those incorporating diet and exercise programming.

Adolescent↗
PubMed2005

Extended information criterion (EIC) approach for linear mixed effects models under restricted maximum likelihood (REML) estimation.

In clinical data analysis, the restricted maximum likelihood (REML) method has been commonly used for estimating variance components in the linear mixed effects model. Under the REML estimation, however, it is not straightforward to compare several linear mixed effects models with different mean and covariance structures. In particular, few approaches have been proposed for the comparison of linear mixed effects models with different mean structures under the REML estimation. We propose an approach using extended information criterion (EIC), which is a bootstrap-based extension of AIC, for comparing linear mixed effects models with different mean and covariance structures under the REML estimation. We present simulation studies and applications to two actual clinical data sets.

Biometry↗
PubMed2001

Multilevel models for censored and latent responses.

Multilevel models were originally developed to allow linear regression or ANOVA models to be applied to observations that are not mutually independent. This lack of independence commonly arises due to clustering of the units of observations into 'higher level units' such as patients in hospitals. In linear mixed models, the within-cluster correlations are modelled by including random effects in a linear model. In this paper, we discuss generalizations of linear mixed models suitable for responses subject to systematic and random measurement error and interval censoring. The first example uses data from two cross-sectional surveys of schoolchildren to investigate risk factors for early first experimentation with cigarettes. Here the recalled times of the children's first cigarette are likely to be subject to both systematic and random measurement errors as well as being interval censored. We describe multilevel models for interval censored survival times as special cases of generalized linear mixed models and discuss methods of estimating systematic recall bias. The second example is a longitudinal study of mental health problems of patients nested in clinics. Here the outcome is measured by multiple questionnaires allowing the measurement errors to be modelled within a linear latent growth curve model. The resulting model is a multilevel structural equation model. We briefly discuss such models both as extensions of linear mixed models and as extensions of structural equation models. Several different model structures are examined. An important goal of the paper is to place a number of methods that readers may have considered as being distinct within a single overall modelling framework.

Adolescent↗
PubMed2004

Functional data analysis in longitudinal settings using smoothing splines.

Data in many experiments arise as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is termed functional data analysis (FDA). In longitudinal studies, recent developments in FDA have extended classical linear models and linear mixed effects models to functional linear models (also termed varying-coefficient models) and functional mixed effects models. In this paper we focus our review on the functional mixed effects models using smoothing splines, because functional linear models are special cases of this more general framework. Due to the connection between smoothing splines and linear mixed effects models, functional mixed effects models can be fitted using existing software such as SAS Proc Mixed. A case study is presented as an illustration.

Biomedical Research↗
PubMed2006

Statistical models for autocorrelated count data.

A generalized linear mixed model is an increasingly popular choice for the modelling of correlated, non-normal responses in a regression setting. A number of methods are currently available for fitting a generalized linear mixed model including Monte-Carlo Markov-Chain maximum likelihood algorithms, approximate maximum likelihood (PQL), iterative bias correction, and others. Of interest in this paper is to compare the parameter estimation of the various methods in the modelling of a count data set, the incidence of polio in the USA over the period 1970-1983, using a longlinear generalized linear mixed model with an autoregressive correlation structure. Despite the fact that all of these methods are considered valid modelling techniques, we find that parameter estimates and standard errors differ substantially between analyses, particularly in the estimation of the parameters describing the random effects distribution. A small simulation study is helpful in understanding some of these differences. The methods lead to reasonably similar predictions for future observations, with small differences observed in some monthly counts.

Algorithms↗
PubMed1995

Maximizing selection efficiency for categorical traits.

Genetic improvement of categorically recorded traits is hampered because information content of categorical records is low and ordinary linear breeding value estimation methods do not apply theoretically. The ordinary animal or linear mixed model (LMM), which ignored the categorical nature of the trait, is compared to a generalized linear mixed model (GLMMp) that assumes a linear mixed model for an underlying continuous variable. The GLMMp takes full account of the categorical nature of the trait and is a straightforward extension of LMM. In a closed nucleus breeding scheme (e.g., cattle, pigs, or poultry), rates of genetic gain increased by 1 to 2%, when GLMMp was used instead of LMM. Rates of genetic gain increased by 7 to 20%, when the best sires were used on the best herds (i.e., when there was some confounding between sire and herd effects). When considering a binary trait (e.g., disease incidence) initial incidences of 25% could be reduced to 2.8% within 10 generations of selection. Rates of gain can be increased by up to 84% by gathering more information on high-incidence categories (i.e., by dividing these categories into subcategories). Subdividing low-incidence categories (e.g., splitting diseased animals into moderately and severely diseased) hardly increased rates of gain. Direct recording of the underlying variable, which requires uncovering of the physiological background of the categorical trait, yielded 109 to 278% more genetic gain than selection for a binary trait.

Animals↗
PubMed1999

Likelihood-based diagnostics for influential individuals in non-linear mixed effects model selection.

PURPOSE: Data from single individuals, or a small group of subjects may influence non-linear mixed effects model selection. Diagnostics routinely applied in model building may identify such individuals, but these methods are not specifically designed for that purpose and are, therefore, not optimal. We describe two likelihood-based diagnostics for identifying individuals that can influence the choice between two competing models. METHODS: One method is based on a jackknife of the raw data on the individual level and refitting the model to each new data set. The second method is a calculation which utilises the contribution each individual make to the objective function values under each of the two models. The two methods were applied to model selection during analysis of a real data set. RESULTS: The agreement between the methods was high. Individuals for whom there was a discrepancy between the methods tended to be those for which neither of the contending models described the data appropriately. Both methods identified individuals that influenced the model selection. CONCLUSIONS: Two objective, specific and quantitative methods for identifying influential individuals in nonlinear mixed effects model selection have been presented. One of the methods doesn't require additional model fitting and is therefore particularly attractive.

Age Factors↗
PubMedDate not supplied

Exploring spatio-temporal patterns of mortality using mixed effects models.

A linear mixed effects (LME) model previously used for a spatial analysis of mortality data for a single time period is extended to include time trends and spatio-temporal interactions. This model includes functions of age and time period that can account for increasing and decreasing death rates over time and age, and a change-point of rates at a predetermined age. A geographic hierarchy is included that provides both regional and small area age-specific rate estimates, stabilizing rates based on small numbers of deaths by sharing information within a region. The proposed log-linear analysis of rates allows the use of commercially available software for parameter estimation, and provides an estimator of overdispersion directly as the residual variance. Because of concerns about the accuracy of small area rate estimates when there are many instances of no observed deaths, we consider potential sources of error, focusing particularly on the similarity of likelihood inferences using the LME model for rates as compared to an exact Poisson-normal mixed effects model for counts. The proposed LME model is applied to breast cancer deaths which occurred among white women during 1979-1996. For this example, application of diagnostics for multiparameter likelihood comparisons suggests a restriction of age to a minimum of either 25 or 35, depending on whether small area rate estimates are required. Investigation into a convergence problem led to the discovery that the changes in breast cancer geographic patterns over time are related more to urbanization than to region, as previously thought. Published in 2000 by John Wiley & Sons, Ltd.

Adolescent↗
PubMed2005

PsN-Toolkit--a collection of computer intensive statistical methods for non-linear mixed effect modeling using NONMEM.

PsN-Toolkit is a collection of statistical tools for pharmacometric data analysis using the non-linear mixed effect modeling software NONMEM. The toolkit is object oriented and written in the programming language Perl using the programming library Perl-speaks-NONMEM (PsN). Five methods: the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building are included as separate classes and may be used in user-written Perl scripts or through stand-alone command line applications. The tools are designed with the ability to cooperate and with an emphasis on common structures for workflow and result handling. Parallel execution of independent tool sections is supported on shared memory multiprocessor (SMP) computers, Mosix/openMosix clusters and distributed computing environments following the NorduGrid standard. In conclusion, PsN-Toolkit makes it easier to use the Bootstrap, the Jackknife, Log-likelihood Profiling, Case-deletion Diagnostics and Stepwise Covariate Model building in pharmacometric data analysis.

Cluster Analysis↗
PubMed2003

Combining multiple outcome measures in a meta-analysis: an application.

In meta-analysis of clinical trials published in the medical literature it is customary to restrict oneself to standard univariate fixed or random effects models. If multiple endpoints are present, each endpoint is analysed separately. A few articles have been written in the statistical literature on multivariate methods for multiple outcome measures. However, these methods were not easy to apply in practice, because self-written programs had to be used, and the examples were only two-dimensional. In this paper we consider a meta-analysis on the effect on stroke-free survival of surgery compared to conservative treatment in patients with increased risk of stroke. Three summary measures per trial are available: short-term post-operative morbidity/mortality in the surgical group; long-term event rate in the surgical group, and the event rate in the conservative group. We analyse the three outcomes jointly with a general linear MIXED model, compare the results with the standard univariate approaches and discuss the many advantages of multivariate modelling. It turns out that the general linear MIXED model is a very convenient framework for multivariate meta-analysis. All analyses could be carried out in standard general linear MIXED model software.

Disease-Free Survival↗