Nonlinear models for repeated measurement data: An overview and update

Latent process model of the 6-minute walk test in Duchenne muscular dystrophy : A Bayesian approach to quantifying rare disease progression

Duchenne muscular dystrophy (DMD) is a rare X-linked genetic pediatric disease characterized by a lack of functional dystrophin production in the body, resulting in muscle deterioration. Lower body muscle weakness progresses to non-ambulation typically by early teenage years, followed by upper body muscle deterioration and ultimately death by the late twenties. The objective of this study was to enhance the quantitative understanding of DMD disease progression through nonlinear mixed effects modeling of the population mean and variability of the 6-min walk test (6MWT) clinical endpoint. An indirect response model with a latent process was fit to digitized literature data using full Bayesian estimation. The modeling data set consisted of 22 healthy controls and 218 DMD patients from one interventional and four observational trials. The model reasonably described the central tendency and population variability of the 6MWT in healthy subjects and DMD patients. An exploratory categorical covariate analysis indicated that there was no apparent effect of corticosteroid administration on DMD disease progression. The population predicted 6MWT began to rise at 1.32 years of age, plateauing at 654 meters (m) at 17.2 years of age for the healthy population. The DMD trajectory reached a maximum of 411 m at 8.90 years before declining and falling below 1 m at age 18.0. The model has potential to be used as a Bayesian estimation and posterior simulation tool to make informed model-based drug development decisions that incorporate prior knowledge with new data.

Evaluation of non-linear-mixed-effect modeling to reduce the sample sizes of pediatric trials in type 2 diabetes mellitus

Recruitment for pediatric trials in Type II Diabetes Mellitus (T2DM) is very challenging, necessitating the exploration of new approaches for reducing the sample sizes of pediatric trials. This work aimed at assessing if a longitudinal Non-Linear-Mixed-Effect (NLME) analysis of T2DM trial could be more powerful and thus require fewer patients than two standard statistical analyses commonly used as primary or sensitivity efficacy analysis: Last-Observation-Carried-Forward (LOCF) followed by (co)variance (AN(C)OVA) analysis at the evaluation time-point, and Mixed-effects Model Repeated Measures (MMRM) analysis. Standard T2DM efficacy studies were simulated, with glycated hemoglobin (HbA1c) as the main endpoint, 24 weeks' study duration, 2 arms, assuming a placebo and a treatment effect, exploring three different scenarios for the evolution of HbA1c, and accounting for a dropout phenomenon. 1000 trials were simulated, then analyzed using the 3 analyses, whose powers were compared. As expected, the longitudinal modeling MMRM analysis was found to be more powerful than the LOCF + ANOVA analysis at week 24. The NLME analysis gave slightly more accurate drug-effect estimations than the two other methods, however it tended to slightly overestimate the magnitude of the drug effect, and it was more powerful than the MMRM analysis only in some scenarios of slow HbA1c decrease. The gain in power afforded by NLME was more apparent when two additional assessments enriched the design; however, the gain was not systematic for all scenarios. Finally, this work showed that NLME analyses may help to reduce significantly the required sample sizes in T2DM pediatric studies, but only for enriched designs and slow HbA1c decrease.

A nonlinear mixed-effects modeling approach for ecological data: Using temporal dynamics of vegetation moisture as an example

Increasingly, often ecologist collects data with nonlinear trends, heterogeneous variances, temporal correlation, and hierarchical structure. Nonlinear mixed-effects models offer a flexible approach to such data, but the estimation and interpretation of these models present challenges, partly associated with the lack of worked examples in the ecological literature.We illustrate the nonlinear mixed-effects modeling approach using temporal dynamics of vegetation moisture with field data from northwestern Patagonia. This is a Mediterranean-type climate region where modeling temporal changes in live fuel moisture content are conceptually relevant (ecological theory) and have practical implications (fire management). We used this approach to answer whether moisture dynamics varies among functional groups and aridity conditions, and compared it with other simpler statistical models. The modeling process is set out "step-by-step": We start translating the ideas about the system dynamics to a statistical model, which is made increasingly complex in order to include different sources of variability and correlation structures. We provide guidelines and R scripts (including a new self-starting function) that make data analyses reproducible. We also explain how to extract the parameter estimates from the R output.Our modeling approach suggests moisture dynamic to vary between grasses and shrubs, and between grasses facing different aridity conditions. Compared to more classical models, the nonlinear mixed-effects model showed greater goodness of fit and met statistical assumptions. While the mixed-effects approach accounts for spatial nesting, temporal dependence, and variance heterogeneity; the nonlinear function allowed to model the seasonal pattern.Parameters of the nonlinear mixed-effects model reflected relevant ecological processes. From an applied perspective, the model could forecast the time when fuel moisture becomes critical to fire occurrence. Due to the lack of worked examples for nonlinear mixed-effects models in the literature, our modeling approach could be useful to diverse ecologists dealing with complex data.

Maximum likelihood estimation of nonlinear mixed-effects models with crossed random effects by combining first-order conditional linearization and sequential quadratic programming

Nonlinear mixed-effects (NLME) models have become popular in various disciplines over the past several decades. However, the existing methods for parameter estimation implemented in standard statistical packages such as SAS and R/S-Plus are generally limited to single- or multi-level NLME models that only allow nested random effects and are unable to cope with crossed random effects within the framework of NLME modeling. In this study, we propose a general formulation of NLME models that can accommodate both nested and crossed random effects, and then develop a computational algorithm for parameter estimation based on normal assumptions. The maximum likelihood estimation is carried out using the first-order conditional expansion (FOCE) for NLME model linearization and sequential quadratic programming (SQP) for computational optimization while ensuring positive-definiteness of the estimated variance-covariance matrices of both random effects and error terms. The FOCE-SQP algorithm is evaluated using the height and diameter data measured on trees from Korean larch (L. olgensis var. Changpaiensis) experimental plots as well as simulation studies. We show that the FOCE-SQP method converges fast with high accuracy. Applications of the general formulation of NLME models are illustrated with an analysis of the Korean larch data.

Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject.

Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L 2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

Development of a Mixed-Effects Individual-Tree Basal Area Increment Model for Oaks (Quercus spp.) Considering Forest Structural Diversity

In the context of uneven-aged mixed-species forest management, an individual-tree basal area increment model considering forest structural diversity was developed for oaks (Quercus spp.) using data collected from 11,860 observations in 845 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, south-central China. Since the data was longitudinal and had a nested structure, we used a linear mixed-effects approach to construct the model. We also used the variance function and an autocorrelation structure to describe within-plot heteroscedasticity and autocorrelation. Finally, the optimal mixed-effects model was determined based on the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik) and the likelihood ratio test (LRT). The results indicate that the reciprocal transformation of initial diameter at breast height (1/DBH), relative density index (RD), number of trees per hectare (NT), elevation (EL) and Gini coefficient (GC) had a significant impact on the individual-tree basal area increment. In comparison to the basic model developed using least absolute shrinkage and selection operator (LASSO) regression, the mixed-effects model performance was greatly improved. In addition, we observed that the heteroscedasticity was successfully removed by the exponent function and autocorrelation was significantly corrected by AR(1). Our final model also indicated that forest structural diversity significantly affected tree growth and hence should not be neglected. We hope that our final model will contribute to the scientific management of oak-dominated forests.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.

A Simple and Flexible Computational Framework for Inferring Sources of Heterogeneity from Single-Cell Dynamics

Single-cell time-lapse data provide the means for disentangling sources of cell-to-cell and intra-cellular variability, a key step for understanding heterogeneity in cell populations. However, single-cell analysis with dynamic models is a challenging open problem: current inference methods address only single-gene expression or neglect parameter correlations. We report on a simple, flexible, and scalable method for estimating cell-specific and population-average parameters of non-linear mixed-effects models of cellular networks, demonstrating its accuracy with a published model and dataset. We also propose sensitivity analysis for identifying which biological sub-processes quantitatively and dynamically contribute to cell-to-cell variability. Our application to endocytosis in yeast demonstrates that dynamic models of realistic size can be developed for the analysis of single-cell data and that shifting the focus from single reactions or parameters to nuanced and time-dependent contributions of sub-processes helps biological interpretation. Generality and simplicity of the approach will facilitate customized extensions for analyzing single-cell dynamics.

Deconvolving the input to random abstract parabolic systems: a population model-based approach to estimating blood/breath alcohol concentration from transdermal alcohol biosensor data

The distribution of random parameters in, and the input signal to, a distributed parameter model with unbounded input and output operators for the transdermal transport of ethanol are estimated. The model takes the form of a diffusion equation with the input, which is on the boundary of the domain, being the blood or breath alcohol concentration (BAC/BrAC), and the output, also on the boundary, being the transdermal alcohol concentration (TAC). Our approach is based on the reformulation of the underlying dynamical system in such a way that the random parameters are treated as additional spatial variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating a functional diffusivity in a multi-dimensional diffusion equation. The resulting system is referred to as a population model, and well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods can be used to fit it to population data and to analyze the resulting fit. Once the forward population model has been identified or trained based on a sample from the population, the resulting distribution can then be used to deconvolve the BAC/BrAC input signal from the biosensor observed TAC output signal formulated as either a quadratic programming or linear quadratic tracking problem. In addition, our approach allows for the direct computation of corresponding credible bands without simulation. We use our technique to estimate bivariate normal distributions and deconvolve BAC/BrAC from TAC based on data from a population that consists of multiple drinking episodes from a single subject and a population consisting of single drinking episodes from multiple subjects.

A quick and accurate method for the estimation of covariate effects based on empirical Bayes estimates in mixed-effects modeling: Correction of bias due to shrinkage

Nonlinear mixed-effects modeling is a popular approach to describe the temporal trajectory of repeated measurements of clinical endpoints collected over time in clinical trials, to distinguish the within-subject and the between-subject variabilities, and to investigate clinically important risk factors (covariates) that may partly explain the between-subject variability. Due to the complex computing algorithms involved in nonlinear mixed-effects modeling, estimation of covariate effects is often time-consuming and error-prone owing to local convergence. We develop a fast and accurate estimation method based on empirical Bayes estimates from the base mixed-effects model without covariates, and simple regressions outside of the nonlinear mixed-effect modeling framework. Application of the method is illustrated using a pharmacokinetic dataset from an anticoagulation drug for the prevention of major cardiovascular events in patients with acute coronary syndrome. Both the application and extensive simulations demonstrated that the performance of this high-throughput method is comparable to the commonly used maximum likelihood estimation in nonlinear mixed-effects modeling.

Novel Modelling Approaches to Characterize and Quantify Carryover Effects on Sensory Acceptability

Sensory biases caused by the residual sensations of previously served samples are known as carryover effects (COE). Contrast and convergence effects are the two possible outcomes of carryover. COE can lead to misinterpretations of acceptability, due to the presence of intrinsic psychological/physiological biases. COE on sensory acceptability (hedonic liking) were characterized and quantified using mixed and nonlinear models. N = 540 subjects evaluated grape juice samples of different acceptability qualities (A = good, B = medium, C = poor) for the liking of color (C), taste (T), and overall (OL). Three models were used to quantify COE: (1) COE as an interaction effect; (2) COE as a residual effect; (3) COE proportional to the treatment effect. For (1), COE was stronger for C than T and OL, although COE was minimal. For (2), C showed higher estimates (−0.15 to +0.10) of COE than did T and OL (−0.09 to +0.07). COE mainly took the form of convergence. For (3), the absolute proportionality parameter estimate (λ) was higher for C than for T and OL (−0.155 vs. −0.004 to −0.039), which represented −15.46% of its direct treatment effect. Model (3) showed a significant COE for C. COE cannot be ignored as they may lead to the misinterpretation of sensory acceptability results.

A Novel Method to Estimate Long-Term Chronological Changes From Fragmented Observations in Disease Progression

Clinical observations of patients with chronic diseases are often restricted in terms of duration. Therefore, obtaining a quantitative and comprehensive understanding of the chronology of chronic diseases is challenging, because of the inability to precisely estimate the patient's disease stage at the time point of observation. We developed a novel method to reconstitute long-term disease progression from temporally fragmented data by extending the nonlinear mixed-effects model to incorporate the estimation of "disease time" of each subject. Application of this method to sporadic Alzheimer's disease successfully depicted disease progression over 20 years. The covariate analysis revealed earlier onset of amyloid-β accumulation in male and female apolipoprotein E ε4 homozygotes, whereas disease progression was remarkably slower in female ε3 homozygotes compared with female ε4 carriers and males. Simulation of a clinical trial suggests patient recruitment using the information of precise disease time of each patient will decrease the sample size required for clinical trials.

Model selection for clustering of pharmacokinetic responses

BACKGROUND AND OBJECTIVE

Pharmacokinetics comprises the study of drug absorption, distribution, metabolism and excretion over time. Clinical pharmacokinetics, focusing on therapeutic management, offers important insights towards personalised medicine through the study of efficacy and toxicity of drug therapies. This study is hampered by subject's high variability in drug blood concentration, when starting a therapy with the same drug dosage. Clustering of pharmacokinetics responses has been addressed recently as a way to stratify subjects and provide different drug doses for each stratum. This clustering method, however, is not able to automatically determine the correct number of clusters, using an user-defined parameter for collapsing clusters that are closer than a given heuristic threshold. We aim to use information-theoretical approaches to address parameter-free model selection.

METHODS

We propose two model selection criteria for clustering pharmacokinetics responses, founded on the Minimum Description Length and on the Normalised Maximum Likelihood.

RESULTS

Experimental results show the ability of model selection schemes to unveil the correct number of clusters underlying the mixture of pharmacokinetics responses.

CONCLUSIONS

In this work we were able to devise two model selection criteria to determine the number of clusters in a mixture of pharmacokinetics curves, advancing over previous works. A cost-efficient parallel implementation in Java of the proposed method is publicly available for the community.

Modeling Patient-Specific Dose-Function Response for Enhanced Characterization of Personalized Functional Damage

PURPOSE

Functional-guided radiation therapy (RT) plans have the potential to limit damage to normal tissue and reduce toxicity. Although functional imaging modalities have continued to improve, a limited understanding of the functional response to radiation and its application to personalized therapy has hindered clinical implementation. The purpose of this study was to retrospectively model the longitudinal, patient-specific dose-function response in non-small cell lung cancer patients treated with RT to better characterize the expected functional damage in future, unknown patients.

METHODS AND MATERIALS

Perfusion single-photon emission computed tomography/computed tomography scans were obtained at baseline (n = 81), midtreatment (n = 74), 3 months post-treatment (n = 51), and 1 year post-treatment (n = 26) and retrospectively analyzed. Patients were treated with conventionally fractionated RT or stereotactic body RT. Normalized perfusion single-photon emission computed tomography voxel intensity was used as a surrogate for local lung function. A patient-specific logistic model was applied to each individual patient's dose-function response to characterize functional reduction at each imaging time point. Patient-specific model parameters were averaged to create a population-level logistic dose-response model.

RESULTS

A significant longitudinal decrease in lung function was observed after RT by analyzing the voxelwise change in normalized perfusion intensity. Generated dose-function response models represent the expected voxelwise reduction in function, and the associated uncertainty, for an unknown patient receiving conventionally fractionated RT or stereotactic body RT. Differential treatment responses based on the functional status of the voxel at baseline suggest that initially higher functioning voxels are damaged at a higher rate than lower functioning voxels.

CONCLUSIONS

This study modeled the patient-specific dose-function response in patients with non-small cell lung cancer during and after radiation treatment. The generated population-level dose-function response models were derived from individual patient assessment and have the potential to inform functional-guided treatment plans regarding the expected functional lung damage. This type of patient-specific modeling approach can be applied broadly to other functional response analyses to better capture intrapatient dependencies and characterize personalized functional damage.

Whole Blood Gene Expression Profiling in patients undergoing colon cancer surgery identifies differential expression of genes involved in immune surveillance, inflammation and carcinogenesis

INTRODUCTION

Cancer surgery may represent a potential risk of enhanced growth and metastatic ability of residual cancer cells due to post-operative immune dysfunction. This study identifies changes in transcription of genes involved in immune surveillance, immune suppression and carcinogenesis in the post-operative period of laparoscopic colon-cancer surgery within an ERAS regime.

METHODS

Patients undergoing elective, curatively intended laparoscopic surgery for colon cancer stage I-III UICC were included in the study. Patients followed standard of care in an ERAS setting. Whole blood gene expression profiling (WBGP) was performed on the day prior to surgery and 1, 2, 3 and 10-14 days after surgery. Samples were collected in Paxgene tubes and Labeled cDNA was fragmented and hybridized to Affymetrix GeneChip™ 2.0. Results were corrected for multiple hypothesis testing using the false discovery rate. Pathway analysis was performed through the Molecular Signature Database. Paired fold changes of gene expression were calculated for post-operative compared to pre-operative samples. A mixed effect model was used to test differential gene expression by repeated-measures ANOVA.

RESULTS

WBGP of 33,804 genes at five timepoints in six patients showed 302 significantly differentially expressed genes between samples from the day prior to surgery and the day after surgery. Pathway gene enrichment analysis showed a downregulation of immunologically relevant pathways. There was a significant downregulation of genes involved in T-cell receptor signaling, antigen presentation and NK-cell activity after surgery. Furthermore, there was an upregulation of cytokines related to metastatic ability, growth and angiogenesis.

CONCLUSION

Whole blood gene expression profiling revealed dysregulation of genes involved in immune surveillance, inflammation and carcinogenesis, after laparoscopic colon cancer surgery.

Automated Planning Enables Complex Protocols on Liquid-Handling Robots

Robotic automation in synthetic biology is especially relevant for liquid handling to facilitate complex experiments. However, research tasks that are not highly standardized are still rarely automated in practice. Two main reasons for this are the substantial investments required to translate molecular biological protocols into robot programs, and the fact that the resulting programs are often too specific to be easily reused and shared. Recent developments of standardized protocols and dedicated programming languages for liquid-handling operations addressed some aspects of ease-of-use and portability of protocols. However, either they focus on simplicity, at the expense of enabling complex protocols, or they entail detailed programming, with corresponding skills and efforts required from the users. To reconcile these trade-offs, we developed Roboliq, a software system that uses artificial intelligence (AI) methods to integrate (i) generic formal, yet intuitive, protocol descriptions, (ii) complete, but usually hidden, programming capabilities, and (iii) user-system interactions to automatically generate executable, optimized robot programs. Roboliq also enables high-level specifications of complex tasks with conditional execution. To demonstrate the system's benefits for experiments that are difficult to perform manually because of their complexity, duration, or time-critical nature, we present three proof-of-principle applications for the reproducible, quantitative characterization of GFP variants.

Functional Role of Movement and Performance Variability: Adaptation of Front Crawl Swimmers to Competitive Swimming Constraints

To study the variability in stroking parameters between and within laps and individuals during competitions, we compared and modeled the changes of speed, stroke rate, and stroke length in 32 top-level male and female swimmers over 4 laps (L1-L4) in 200-m freestyle events using video-derived 2-dimensional direct linear transformation. For the whole group, speed was greater in L1, with significant decreases across L2, L3, and L4 (1.80 ± 0.10 vs 1.73 ± 0.08; 1.69 ± 0.09; 1.66 ± 0.09  · s^-1, P < .05). This variability was attributed to a decrease in stroke length (L2: 2.43 ± 0.19 vs L4: 2.20 ± 0.13 m, P < .05) and an increase in stroke rate (L2: 42.8 ± 2.6 vs L4: 45.4 ± 2.3 stroke · min^-1, P < .05). The coefficient of variation and the biological coefficient of variation in speed were greater for male versus female (3.9 ± 0.7 vs 3.1 ± 0.7; 2.9 ± 1.0 vs 2.6 ± 0.7, P < .05) and higher in L1 versus L2 (3.9 ± 1.3 vs 3.1 ± 0.1; 2.9 ± 0.9 vs 2.3 ± 0.7, P < .05). Intra-lap speed values were best represented by a cubic (n = 38), then linear (n = 37) and quadratic model (n = 8). The cubic fit was more frequent for males (43.8%) than females (15.6%), suggesting greater capacity to generate higher acceleration after the turn. The various stroking parameters managements within lap suggest that each swimmer adapts his/her behavior to the race constraints.

Pharmacokinetics of intravenous lithium chloride and assessment of agreement between two methods of lithium concentration measurement in the horse

BACKGROUND

Pharmacokinetics of lithium chloride (LiCl) administered as a bolus, once i.v. have not been determined in horses. There is no point-of-care test to measure lithium (Li⁺ ) concentrations in horses in order to monitor therapeutic levels and avoid toxicity.

OBJECTIVES

To determine the pharmacokinetics of LiCl in healthy adult horses and to compare agreement between two methods of plasma Li⁺ concentration measurement: spectrophotometric enzymatic assay (SEA) and inductively coupled plasma mass spectrometry (ICP-MS).

STUDY DESIGN

Nonrandomised, single exposure with repeated measures over time.

METHODS

Lithium chloride was administered (0.15 mmol/kg bwt) as an i.v. bolus to eight healthy adult horses. Blood samples were collected pre-administration and at multiple times until 48 h post-administration. Samples were analysed by two methods (SEA and ICP-MS) to determine plasma Li⁺ concentrations. Pharmacokinetics were determined based on the reference ICP-MS data.

RESULTS

Adverse side effects were not observed. The SEA showed linearity, R² = 0.9752; intraday coefficient of variation, 2.5%; and recovery, 96.3%. Both noncompartmental and compartmental analyses (traditional two-stage and nonlinear mixed-effects [NLME] modelling) were performed. Geometric mean values of noncompartmental parameters were plasma Li⁺ concentration at time zero, 2.19 mmol/L; terminal elimination half-life, 25.68 h; area under the plasma concentration-time curve from time zero to the limit of quantification, 550 mmol/L min; clearance, 0.273 mL/min/kg; mean residence time, 31.22 h; and volume of distribution at steady state, 511 mL/kg. Results of the traditional two-stage analysis showed good agreement with the NLME modelling approach. Bland-Altman analyses demonstrated poor agreement between the SEA and ICP-MS methods (95% limits of agreement = 0.14 ± 0.13 mmol/L).

MAIN LIMITATIONS

Clinical effects of LiCl have not been investigated.

CONCLUSIONS

The LiCl i.v. bolus displayed pharmacokinetics similar to those reported in other species. The SEA displayed acceptable precision but did not agree well with the reference method (ICP-MS). The Summary is available in Spanish - see Supporting Information.

Fitting Residual Error Structures for Growth Models in SAS PROC MCMC

In behavioral sciences broadly, estimating growth models with Bayesian methods is becoming increasingly common, especially to combat small samples common with longitudinal data. Although Mplus is becoming an increasingly common program for applied research employing Bayesian methods, the limited selection of prior distributions for the elements of covariance structures makes more general software more advantages under certain conditions. However, as a disadvantage of general software's software flexibility, few preprogrammed commands exist for specifying covariance structures. For instance, PROC MIXED has a few dozen such preprogrammed options, but when researchers divert to a Bayesian framework, software offer no such guidance and requires researchers to manually program these different structures, which is no small task. As such the literature has noted that empirical papers tend to simplify their covariance matrices to circumvent this difficulty, which is not desirable because such a simplification will likely lead to biased estimates of variance components and standard errors. To facilitate wider implementation of Bayesian growth models that properly model covariance structures, this article overviews how to generally program a growth model in SAS PROC MCMC and then demonstrates how to program common residual error structures. Full annotated SAS code and an applied example are provided.

Translational learning from clinical studies predicts drug pharmacokinetics across patient populations

Early indication of late-stage failure of novel candidate drugs could be facilitated by continuous integration, assessment, and transfer of knowledge acquired along pharmaceutical development programs. We here present a translational systems pharmacology workflow that combines drug cocktail probing in a specifically designed clinical study, physiologically based pharmacokinetic modeling, and Bayesian statistics to identify and transfer (patho-)physiological and drug-specific knowledge across distinct patient populations. Our work builds on two clinical investigations, one with 103 healthy volunteers and one with 79 diseased patients from which we systematically derived physiological information from pharmacokinetic data for a reference probe drug (midazolam) at the single-patient level. Taking into account the acquired knowledge describing (patho-)physiological alterations in the patient cohort allowed the successful prediction of the population pharmacokinetics of a second, candidate probe drug (torsemide) in the patient population. In addition, we identified significant relations of the acquired physiological processes to patient metadata from liver biopsies. The presented prototypical systems pharmacology approach is a proof of concept for model-based translation across different stages of pharmaceutical development programs. Applied consistently, it has the potential to systematically improve predictivity of pharmacokinetic simulations by incorporating the results of clinical trials and translating them to subsequent studies.

Physiologically based modeling together with Bayesian statistics allows the prediction of drug pharmacokinetics in specific patient populations. An interdisciplinary group of clinicians and computational scientists led by Dr. Lars Kuepfer from Bayer developed a generic workflow consisting of several consecutive learning steps where knowledge about both individual physiology as well as drug physicochemistry can be efficiently derived from plasma concentration profiles. The acquired information is then be used for the prediction of the pharmacokinetic behavior of a new drug candidate in a diseased population. This allows to simulate the variability in drug exposure virtually before starting clinical investigation in real patients in order to evaluate drug safety or efficacy through the simulation of virtual populations. Further development of this workflow could improve the safety of clinical development programs to assess the risk-benefit ratio of novel drug candidates in silico.

Nonlinear mixed-effects model reveals a distinction between learning and performance in intensive reach training post-stroke

BACKGROUND

We recently showed that individuals with chronic stroke who completed two sessions of intensive unassisted arm reach training exhibited improvements in movement times up to one month post-training. Here, we study whether changes in movement times during training can predict long-term changes.

METHODS

Sixteen participants with chronic stroke and ten non-disabled age-matched participants performed two sessions of reach training with 600 movements per session. Movement time data during training were fitted to a nonlinear mixed-effects model consisting of a decreasing exponential term to model improvements of performance due to learning and an increasing linear term to model worsening of performance due to activity-dependent fatigability and/or other factors unrelated to learning.

RESULTS

For non-disabled age-matched participants, movement times gradually decreased overall during training and overall changes in movement times during training predicted long-term changes. In contrast, for participants post-stroke, movement times often worsened near the end of training. As a result, overall changes in movement times during training did not predict long-term changes in movement times in the stroke group. However, improvements in movement times due to training, as estimated by the exponential term of the model, predicted long-term changes in movement times.

CONCLUSION

Participants post-stroke showed a distinction between learning and performance in unassisted intensive arm reach training. Despite worsening of performance in later trials, extended training was beneficial for long-term gains.

Nonlinear mixed-effects models for pharmacokinetic data analysis: assessment of the random-effects distribution

Nonlinear mixed-effects models are frequently used for pharmacokinetic data analysis, and they account for inter-subject variability in pharmacokinetic parameters by incorporating subject-specific random effects into the model. The random effects are often assumed to follow a (multivariate) normal distribution. However, many articles have shown that misspecifying the random-effects distribution can introduce bias in the estimates of parameters and affect inferences about the random effects themselves, such as estimation of the inter-subject variability. Because random effects are unobservable latent variables, it is difficult to assess their distribution. In a recent paper we developed a diagnostic tool based on the so-called gradient function to assess the random-effects distribution in mixed models. There we evaluated the gradient function for generalized liner mixed models and in the presence of a single random effect. However, assessing the random-effects distribution in nonlinear mixed-effects models is more challenging, especially when multiple random effects are present, and therefore the results from linear and generalized linear mixed models may not be valid for such nonlinear models. In this paper, we further investigate the gradient function and evaluate its performance for such nonlinear mixed-effects models which are common in pharmacokinetics and pharmacodynamics. We use simulations as well as real data from an intensive pharmacokinetic study to illustrate the proposed diagnostic tool.

ROC Estimation from Clustered Data with an Application to Liver Cancer Data

In this article, we propose a regression model to compare the performances of different diagnostic methods having clustered ordinal test outcomes. The proposed model treats ordinal test outcomes (an ordinal categorical variable) as grouped-survival time data and uses random effects to explain correlation among outcomes from the same cluster. To compare different diagnostic methods, we introduce a set of covariates indicating diagnostic methods and compare their coefficients. We find that the proposed model defines a Lehmann family and can also introduce a location-scale family of a receiver operating characteristic (ROC) curve. The proposed model can easily be estimated using standard statistical software such as SAS and SPSS. We illustrate its practical usefulness by applying it to testing different magnetic resonance imaging (MRI) methods to detect abnormal lesions in a liver.

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals' predicted trajectories, and vice versa.

Multivariate Longitudinal Analysis with Bivariate Correlation Test

In the context of multivariate multilevel data analysis, this paper focuses on the multivariate linear mixed-effects model, including all the correlations between the random effects when the dimensional residual terms are assumed uncorrelated. Using the EM algorithm, we suggest more general expressions of the model's parameters estimators. These estimators can be used in the framework of the multivariate longitudinal data analysis as well as in the more general context of the analysis of multivariate multilevel data. By using a likelihood ratio test, we test the significance of the correlations between the random effects of two dependent variables of the model, in order to investigate whether or not it is useful to model these dependent variables jointly. Simulation studies are done to assess both the parameter recovery performance of the EM estimators and the power of the test. Using two empirical data sets which are of longitudinal multivariate type and multivariate multilevel type, respectively, the usefulness of the test is illustrated.

Two-component mixtures of generalized linear mixed effects models for cluster correlated data

Finite mixtures of generalized linear mixed effect models are presented to handle situations where within-cluster correlation and heterogeneity (subpopulations) exist simultaneously. For this class of model, we consider maximum likelihood (ML) as our main approach to estimation. Owing to the complexity of the marginal loglikelihood of this model, the EM algorithm is employed to facilitate computation. The major obstacle in this procedure is to integrate over the random effects’ distribution to evaluate the expectation in the E step. When assuming normally distributed random effects, we consider adaptive Gaussian quadrature to perform this integration numerically. We also discuss nonparametric ML estimation under a relaxation of the normality assumption on the random effects. Two real data sets are analysed to compare our proposed model with other existing models and illustrate our estimation methods.

Plasma radiometabolite correction in dynamic PET studies: Insights on the available modeling approaches

Full kinetic modeling of dynamic PET images requires the measurement of radioligand concentrations in the arterial plasma. The unchanged parent radioligand must, however, be separated from its radiometabolites by chromatographic methods. Thus, only few samples can usually be analyzed and the resulting measurements are often noisy. Therefore, the measurements must be fitted with a mathematical model. This work presents a comprehensive analysis of the different models proposed in the literature to describe the plasma parent fraction (PPf) and of the alternative approaches for radiometabolite correction. Finally, we used a dataset of [(11)C]PBR28 brain PET data as a case study to guide the reader through the PPf model selection process.

Bayesian Population Physiologically-Based Pharmacokinetic (PBPK) Approach for a Physiologically Realistic Characterization of Interindividual Variability in Clinically Relevant Populations

Interindividual variability in anatomical and physiological properties results in significant differences in drug pharmacokinetics. The consideration of such pharmacokinetic variability supports optimal drug efficacy and safety for each single individual, e.g. by identification of individual-specific dosings. One clear objective in clinical drug development is therefore a thorough characterization of the physiological sources of interindividual variability. In this work, we present a Bayesian population physiologically-based pharmacokinetic (PBPK) approach for the mechanistically and physiologically realistic identification of interindividual variability. The consideration of a generic and highly detailed mechanistic PBPK model structure enables the integration of large amounts of prior physiological knowledge, which is then updated with new experimental data in a Bayesian framework. A covariate model integrates known relationships of physiological parameters to age, gender and body height. We further provide a framework for estimation of the a posteriori parameter dependency structure at the population level. The approach is demonstrated considering a cohort of healthy individuals and theophylline as an application example. The variability and co-variability of physiological parameters are specified within the population; respectively. Significant correlations are identified between population parameters and are applied for individual- and population-specific visual predictive checks of the pharmacokinetic behavior, which leads to improved results compared to present population approaches. In the future, the integration of a generic PBPK model into an hierarchical approach allows for extrapolations to other populations or drugs, while the Bayesian paradigm allows for an iterative application of the approach and thereby a continuous updating of physiological knowledge with new data. This will facilitate decision making e.g. from preclinical to clinical development or extrapolation of PK behavior from healthy to clinically significant populations.

Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models

Context

Mathematical models may help the analysis of biological systems by providing estimates of otherwise un-measurable quantities such as concentrations and fluxes. The variability in such systems makes it difficult to translate individual characteristics to group behavior. Mixed effects models offer a tool to simultaneously assess individual and population behavior from experimental data. Lipoproteins and plasma lipids are key mediators for cardiovascular disease in metabolic disorders such as diabetes mellitus type 2. By the use of mathematical models and tracer experiments fluxes and production rates of lipoproteins may be estimated.

Results

We developed a mixed effects model to study lipoprotein kinetics in a data set of 15 healthy individuals and 15 patients with type 2 diabetes. We compare the traditional and the mixed effects approach in terms of group estimates at various sample and data set sizes.

Conclusion

We conclude that the mixed effects approach provided better estimates using the full data set as well as with both sparse and truncated data sets. Sample size estimates showed that to compare lipoprotein secretion the mixed effects approach needed almost half the sample size as the traditional method.

Training for eye contact modulates gaze following in dogs

Following human gaze in dogs and human infants can be considered a socially facilitated orientation response, which in object choice tasks is modulated by human-given ostensive cues. Despite their similarities to human infants, and extensive skills in reading human cues in foraging contexts, no evidence that dogs follow gaze into distant space has been found. We re-examined this question, and additionally whether dogs' propensity to follow gaze was affected by age and/or training to pay attention to humans. We tested a cross-sectional sample of 145 border collies aged 6 months to 14 years with different amounts of training over their lives. The dogs' gaze-following response in test and control conditions before and after training for initiating eye contact with the experimenter was compared with that of a second group of 13 border collies trained to touch a ball with their paw. Our results provide the first evidence that dogs can follow human gaze into distant space. Although we found no age effect on gaze following, the youngest and oldest age groups were more distractible, which resulted in a higher number of looks in the test and control conditions. Extensive lifelong formal training as well as short-term training for eye contact decreased dogs' tendency to follow gaze and increased their duration of gaze to the face. The reduction in gaze following after training for eye contact cannot be explained by fatigue or short-term habituation, as in the second group gaze following increased after a different training of the same length. Training for eye contact created a competing tendency to fixate the face, which prevented the dogs from following the directional cues. We conclude that following human gaze into distant space in dogs is modulated by training, which may explain why dogs perform poorly in comparison to other species in this task.

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We provide the first evidence that dogs can follow human gaze to distant space.

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There were no age effects on gaze following to human gaze cues.

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Gazing patterns of young and elderly dogs were influenced by higher distractibility.

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Training decreased dogs' gaze following and increased gaze to the human face.

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Dogs' tendency to follow human gaze is modulated by training for eye contact.

A case study of modeling and exposure-response prediction for count data

Even with two doses of an experimental drug in Phase III studies, with the commonly used approach for assessing treatment effects of individual doses, it may still be difficult to determine the final commercial dose. In such a scenario, with plasma concentration data collected in the studies, a modeling approach can be applied to predict treatment effects at different plasma concentration levels. Through an established relationship between plasma concentration and dose, the treatment effects of doses not studied in the Phase III studies can then be predicted. The results can further be applied to justify the final dose confirmation or selection. In this article, a Phase III program example with count data as the primary endpoint in the multiple sclerosis area is used to illustrate the application of such a technique for dose confirmation. Several models, such as the overdispersion Poisson model, negative binomial model, and recurrent event models, are considered. The negative binomial model is preferable due to better data fitting and the capability of within-treatment assessment and between-treatment comparison.

Approximate testing in two-stage nonlinear mixed models

We investigate here small sample properties of approximate F-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximate F-test is constructed based on large sample approximation to the distribution of nonlinear least squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large sample Fisher information matrix (See [1]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modified F-test under the null hypothesis, especially accuracy of p-values (See [2]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [3, 4]).