Nonlinear Mixed-effects Framework Research Articles

Comparative analysis of within-host dynamics of acute infection and viral rebound dynamics in postnatally SHIV-infected ART-treated infant rhesus macaques.

Viral dynamics of acute HIV infection and HIV rebound following suspension of antiretroviral therapy may be qualitatively similar but must differ given, for one, development of adaptive immune responses. Understanding the differences of acute HIV infection and viral rebound dynamics in pediatric populations may provide insights into the mechanisms of viral control with potential implications for vaccine design and the development of effective targeted therapeutics for infants and children. Mathematical models have been a crucial tool to elucidate the complex processes driving viral infections within the host. Traditionally, acute HIV infection has been modeled with a standard model of viral dynamics initially developed to explore viral decay during treatment, while viral rebound has necessitated extensions of that standard model to incorporate explicit immune responses. Previous efforts to fit these models to viral load data have underscored differences between the two infection stages, such as increased viral clearance rate and increased death rate of infected cells during rebound. However, these findings have been predicated on viral load measurements from disparate adult individuals. In this study, we aim to bridge this gap, in infants, by comparing the dynamics of acute infection and viral rebound within the same individuals by leveraging an infant nonhuman primate Simian/Human Immunodeficiency Virus (SHIV) infection model. Ten infant Rhesus macaques (RMs) orally challenged with SHIV.C.CH505 375H dCT and given ART at 8 weeks post-infection. These infants were then monitored for up to 60 months post-infection with serial viral load and immune measurements. We use the HIV standard viral dynamics model fitted to viral load measurements in a nonlinear mixed effects framework. We find that the primary difference between acute infection and rebound is the increased death rate of infected cells during rebound. We use these findings to generate hypotheses on the effects of adaptive immune responses. We leverage these findings to formulate hypotheses to elucidate the observed results and provide arguments to support the notion that delayed viral rebound is characterized by a stronger CD8+ T cell response.

Evaluation of the effect of erenumab on migraine-specific questionnaire in patients with chronic and episodic migraine.

Erenumab is a fully human anti-canonical calcitonin gene-related peptide receptor monoclonal antibody approved for migraine prevention. The Migraine-Specific Quality-of-Life Questionnaire (MSQ) is a 14-item patient-reported outcome instrument that measures the impact of migraine on health-related quality of life. Erenumab data from four phase II/III clinical trials were used to develop an item response theory (IRT) model within a nonlinear mixed effects framework, (i) evaluate the MSQ item information with respect to patient disability, (ii) characterize the longitudinal progression of the MSQ, and (iii) quantify the effect of erenumab on the MSQ in patients with migraine. The majority (80%) of information was found to be contained in 9 out of 14 items, extending the current knowledge on the reliability of the MSQ as a psychometric tool. Simulations across three MSQ domains show significant improvement from baseline, exceeding minimally important differences. Overall, the IRT model platform developed herein allows for systematic quantification of the effect of erenumab on the MSQ in patients with migraine.

Mathematical model to calculate the total number of decays in Peptide Receptor Radionuclide Therapy using nonlinear mixed effect modelling

The calculation of an individual total number of decays or time-integrated activities (TIAs) of a radiopharmaceutical for kidneys is desirable for dosimetry in molecular radiotherapy. The accuracy of the TIAs calculation relies heavily on the chosen fit model. Therefore, this study aimed to determine the best mathematical model of 177Lu-DOTATATE in peptide receptor radionuclide therapy (PRRT) using the nonlinear mixed effect (NLME) and model selection method. Pharmacokinetics data of 177Lu-DOTATATE in the kidneys of ten PRRT patients were obtained from the literature (PMID: 33443063). Eleven sums of exponential (SOE) functions were fitted to the pharmacokinetics data in the NLME framework. The model selection was performed based on the goodness of fit test and the corrected Akaike Information Criterion (AICc). The goodness of fit was evaluated based on the fitted graphs visualization, coefficient of variations (CV<50%), and the off-diagonal elements of the correlation matrix (-0,8≤CM≤0,8). In general, all SOE functions were successfully fitted to the pharmacokinetic data of 177Lu-DOTATATE in kidneys. The function was selected as the best mathematical model with an AICc weight of 77.58 %.

Model-based prediction of progression-free survival for combination therapies in oncology.

Progression-free survival (PFS) is an important clinical metric for comparing and evaluating similar treatments for the same disease within oncology. After the completion of a clinical trial, a descriptive analysis of the patients' PFS is often performed post hoc using the Kaplan-Meier estimator. However, to perform predictions, more sophisticated quantitative methods are needed. Tumor growth inhibition models are commonly used to describe and predict the dynamics of preclinical and clinical tumor size data. Moreover, frameworks also exist for describing the probability of different types of events, such as tumor metastasis or patient dropout. Combining these two types of models into a so-called joint model enables model-based prediction of PFS. In this paper, we have constructed a joint model from clinical data comparing the efficacy of FOLFOX against FOLFOX + panitumumab in patients with metastatic colorectal cancer. The nonlinear mixed effects framework was used to quantify interindividual variability (IIV). The model describes tumor size and PFS data well, and showed good predictive capabilities using truncated as well as external data. A machine-learning guided analysis was performed to reduce unexplained IIV by incorporating patient covariates. The model-based approach illustrated in this paper could be useful to help design clinical trials or to determine new promising drug candidates for combination therapy trials.

Implementation of non-linear mixed effects models defined by fractional differential equations.

Fractional differential equations (FDEs), i.e. differential equations with derivatives of non-integer order, can describe certain experimental datasets more accurately than classic models and have found application in pharmacokinetics (PKs), but wider applicability has been hindered by the lack of appropriate software. In the present work an extension of NONMEM software is introduced, as a FORTRAN subroutine, that allows the definition of nonlinear mixed effects (NLME) models with FDEs. The new subroutine can handle arbitrary user defined linear and nonlinear models with multiple equations, and multiple doses and can be integrated in NONMEM workflows seamlessly, working well with third party packages. The performance of the subroutine in parameter estimation exercises, with simple linear and nonlinear (Michaelis-Menten) fractional PK models has been evaluated by simulations and an application to a real clinical dataset of diazepam is presented. In the simulation study, model parameters were estimated for each of 100 simulated datasets for the two models. The relative mean bias (RMB) and relative root mean square error (RRMSE) were calculated in order to assess the bias and precision of the methodology. In all cases both RMB and RRMSE were below 20% showing high accuracy and precision for the estimates. For the diazepam application the fractional model that best described the drug kinetics was a one-compartment linear model which had similar performance, according to diagnostic plots and Visual Predictive Check, to a three-compartment classic model, but including four less parameters than the latter. To the best of our knowledge, it is the first attempt to use FDE systems in an NLME framework, so the approach could be of interest to other disciplines apart from PKs.

Single-time-point dosimetry using model selection and nonlinear mixed-effects modelling: a proof of concept

PurposeThis project aims to develop and evaluate a method for accurately determining time-integrated activities (TIAs) in single-time-point (STP) dosimetry for molecular radiotherapy. It performs a model selection (MS) within the framework of the nonlinear mixed-effects (NLME) model (MS–NLME).MethodsBiokinetic data of [111In]In-DOTATATE activity in kidneys at T1 = (2.9 ± 0.6) h, T2 = (4.6 ± 0.4) h, T3 = (22.8 ± 1.6) h, T4 = (46.7 ± 1.7) h, and T5 = (70.9 ± 1.0) h post injection were obtained from eight patients using planar imaging. Eleven functions were derived from various parameterisations of mono-, bi-, and tri-exponential functions. The functions’ fixed and random effects parameters were fitted simultaneously (in the NLME framework) to the biokinetic data of all patients. The Akaike weights were used to select the fit function most supported by the data. The relative deviations (RD) and the root-mean-square error (RMSE) of the calculated TIAs for the STP dosimetry at T3 = (22.8 ± 1.6) h and T4 = (46.7 ± 1.7) h p.i. were determined for all functions passing the goodness-of-fit test.ResultsThe function f_{4d} left( t right) = A_{1} /left{ {left( {frac{1 - alpha }{{lambda_{1} + lambda_{{{text{phys}}}} }}} right) - left( {frac{alpha }{{lambda_{2} + lambda_{{{text{phys}}}} }}} right) - left( {frac{1 - 2alpha }{{lambda_{bc} + lambda_{{{text{phys}}}} }}} right)} right} cdot e^{{ - lambda_{{{text{phys}}}} t}} cdot left{ {left( {1 - alpha } right) cdot e^{{ - lambda_{1} t}} - alpha cdot e^{{ - lambda_{2} t}} - left( {1 - 2alpha } right) cdot e^{{ - lambda_{bc} t}} } right} with four adjustable parameters and lambda_{bc} = frac{{{text{ln}}left( 2 right)}}{{1;{text{ min}}}} was selected as the function most supported by the data with an Akaike weight of (45 ± 6) %. RD and RMSE values show that the MS–NLME method performs better than functions with three or five adjustable parameters. The RMSEs of TIANLME–PBMS and TIA3-parameters were 7.8% and 10.9% (for STP at T3), and 4.9% and 10.7% (for STP at T4), respectively.ConclusionAn MS–NLME method was developed to determine the best fit function for calculating TIAs in STP dosimetry for a given radiopharmaceutical, organ, and patient population. The proof of concept was demonstrated for biokinetic 111In-DOTATATE data, showing that four-parameter functions perform better than three- and five-parameter functions.

Insights in the maturational processes influencing hydrocortisone pharmacokinetics in congenital adrenal hyperplasia patients using a middle-out approach.

Introduction: Hydrocortisone is the standard of care in cortisol replacement therapy for congenital adrenal hyperplasia patients. Challenges in mimicking cortisol circadian rhythm and dosing individualization can be overcome by the support of mathematical modelling. Previously, a non-linear mixed-effects (NLME) model was developed based on clinical hydrocortisone pharmacokinetic (PK) pediatric and adult data. Additionally, a physiologically-based pharmacokinetic (PBPK) model was developed for adults and a pediatric model was obtained using maturation functions for relevant processes. In this work, a middle-out approach was applied. The aim was to investigate whether PBPK-derived maturation functions could provide a better description of hydrocortisone PK inter-individual variability when implemented in the NLME framework, with the goal of providing better individual predictions towards precision dosing at the patient level. Methods: Hydrocortisone PK data from 24 adrenal insufficiency pediatric patients and 30 adult healthy volunteers were used for NLME model development, while the PBPK model and maturation functions of clearance and cortisol binding globulin (CBG) were developed based on previous studies published in the literature. Results: Clearance (CL) estimates from both approaches were similar for children older than 1 year (CL/F increasing from around 150 L/h to 500 L/h), while CBG concentrations differed across the whole age range (CBGNLME stable around 0.5 μM vs. steady increase from 0.35 to 0.8 μM for CBG PBPK). PBPK-derived maturation functions were subsequently included in the NLME model. After inclusion of the maturation functions, none, a part of, or all parameters were re-estimated. However, the inclusion of CL and/or CBG maturation functions in the NLME model did not result in improved model performance for the CL maturation function (ΔOFV > -15.36) and the re-estimation of parameters using the CBG maturation function most often led to unstable models or individual CL prediction bias. Discussion: Three explanations for the observed discrepancies could be postulated, i) non-considered maturation of processes such as absorption or first-pass effect, ii) lack of patients between 1 and 12 months, iii) lack of correction of PBPK CL maturation functions derived from urinary concentration ratio data for the renal function relative to adults. These should be investigated in the future to determine how NLME and PBPK methods can work towards deriving insights into pediatric hydrocortisone PK.

Robust Mixed-Effect Estimation of Tumor Growth and Age Based on Gompertz Model

This letter considers the problem of estimating tumor growth and tumor age using the Gompertz model within the nonlinear mixed-effect framework. In particular, the choice for the prior for the population model parameters is the Normal-Laplace distribution. The Maximum A Posteriori (MAP) method provides a robust estimation scheme that leverages the fat-tail properties of such a distribution. Due to the non-differentiability of the distribution, the resulting estimator shows an inaction region in which, for small residues, the best estimate remains the population prior. In addition, a change of variable in the usual Gompertz model sets the tumor age as an extra parameter, which is straightforwardly estimated. This information might provide helpful insights into clinical cancer treatment. Numerical experiments suggest that the proposed estimation scheme renders significantly more accurate estimates in such a vital problem.

Optimized scaling of translational factors in oncology: from xenografts to RECIST

PurposeTumor growth inhibition (TGI) models are regularly used to quantify the PK–PD relationship between drug concentration and in vivo efficacy in oncology. These models are typically calibrated with data from xenograft mice and before being used for clinical predictions, translational methods have to be applied. Currently, such methods are commonly based on replacing model components or scaling of model parameters. However, difficulties remain in how to accurately account for inter-species differences. Therefore, more research must be done before xenograft data can fully be utilized to predict clinical response.MethodTo contribute to this research, we have calibrated TGI models to xenograft data for three drug combinations using the nonlinear mixed effects framework. The models were translated by replacing mice exposure with human exposure and used to make predictions of clinical response. Furthermore, in search of a better way of translating these models, we estimated an optimal way of scaling model parameters given the available clinical data.ResultsThe predictions were compared with clinical data and we found that clinical efficacy was overestimated. The estimated optimal scaling factors were similar to a standard allometric scaling exponent of − 0.25.ConclusionsWe believe that given more data, our methodology could contribute to increasing the translational capabilities of TGI models. More specifically, an appropriate translational method could be developed for drugs with the same mechanism of action, which would allow for all preclinical data to be leveraged for new drugs of the same class. This would ensure that fewer clinically inefficacious drugs are tested in clinical trials.

Comparison of classical tumour growth models for patient derived and cell-line derived xenografts using the nonlinear mixed-effects framework

In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted

An approach to quantify climate-productivity relationships: an example from a widespread Nothofagus forest.

Unique combinations of geographic and environmental conditions make quantifying the importance of factors that influence forest productivity difficult. I aimed to model the height growth of dominant Nothofagus alpina trees in temperate forests of Chile, as a proxy for forest productivity, by building a dynamic model that accounts for topography, habitat type, and climate conditions. Using stem analysis data of 169 dominant trees sampled throughout south-central Chile (35°50' and 41°30' S), I estimated growth model parameters using a nonlinear mixed-effects framework that takes into account the hierarchical structure of the data. Based on the proposed model, I used a system-dynamics approach to analyze growth rates as a function of topographic, habitat type, and climatic variability. I found that the interaction between aspect, slope, and elevation, as well as the effect of habitat type, play an essential role in determining tree height growth rates of N. alpina. Furthermore, the precipitation in the warmest quarter, precipitation seasonality, and annual mean temperature are critical climatic drivers of forest productivity. Given a forecasted climate condition for the region by 2100, where precipitation seasonality and mean annual temperature increase by 10% and 1°C, respectively, and precipitation in the warmest quarter decreases by 10mm, I predict a reduction of 1.4m in height growth of 100-yr-old dominant trees. This study shows that the sensitivity of N. alpina-dominated forests to precipitation and temperature patterns could lead to a reduction of tree height growth rates as a result of climate change, suggesting a decrease in carbon sequestration too. By implementing a system dynamics approach, I provide a new perspective on climate-productivity relationships, bettering the quantitative understanding of forest ecosystem dynamics under climate change. The results highlight that while temperature rising might favor forest growth, the decreasing in both amount and distribution within a year of precipitation can be even more critical to reduce forest productivity.

Nonlinear Mixed-Effects Models for PET Data.

The current state-of-the-art for compartment modeling of dynamic PET data can be described as a two-stage approach. In Stage 1, individual estimates of kinetic parameters are obtained by fitting models using standard techniques, such as nonlinear least squares, to each individual's data one subject at a time. Population-level effects, such as the difference between diagnostic groups, are analyzed in Stage 2 using standard statistical methods by treating the individual estimates as if they were observed data. While this approach is generally valid, it is possible to increase efficiency and precision of the analysis, allow more complex models to be fitted, and also to permit parameter-specific investigation by fitting data across subjects simultaneously. We explore the application of nonlinear mixed-effects (NLME) models for estimation and inference in this setting. In the NLME framework, subjects are modeled simultaneously through the inclusion of random effects of subjects for each kinetic parameter; meanwhile, population parameters are estimated directly in a joint model. Simulation results indicate that NLME outperforms the two-stage approach in estimating group-level effects and also has improved power to detect differences across groups. We applied our NLME approach to clinical PET data and found effects not detected by the two-stage approach. The proposed NLME approach is more accurate and correspondingly more powerful than the two-stage approach in compartment modeling of PET data. The NLME method can broaden the methodological scope of PET modeling because of its efficiency and stability.

Sexual-perception processes in acquaintance-targeted sexual aggression.

This study analyzes data from seven published studies to examine whether three performance-based indices of men's misperception of women's sexual interest (MSI), derived from a self-report questionnaire, are associated with sexual-aggression history, rape-supportive attitudes, sociosexuality, problem drinking, and self-reported MSI. Almost 2000 undergraduate men judged the justifiability of a man's increasingly unwanted advances toward a woman on the Heterosocial Perception Survey-Revised. Participants self-reported any sexual-aggression history, and some completed questionnaires assessing rape-supportive attitudes, sociosexuality, problem drinking, and self-reported MSI. A three-parameter logistic function was fitted to participants' justifiability ratings within a non-linear mixed-effects framework, which provided precise participant-specific estimates of three sexual-perception processes (baseline justifiability, bias, and sensitivity). Sexual-aggression history and rape-supportive attitudes predicted: (a) reduced sensitivity to women's affect; (b) more liberal biases, such that the woman's affect had to be more negative before justifiability ratings dropped substantially; and (c) greater baseline justifiability of continued advances after a positive response. Sexual-aggression history and attitudes correlated more strongly with sensitivity than baseline justifiability; remaining variables showed the opposite pattern. This work underscores the role of sexual-perception processes in sexual aggression and illustrates the derivation of performance-based estimates of sexual-perception processes from questionnaire responses.

Dynamical systems modeling of early childhood self-regulation.

Self-regulation can be conceptualized in terms of dynamic tension between highly probable reactions (prepotent responses) and use of strategies that can modulate those reactions (executive processes). This study investigated the value of a dynamical systems approach to the study of early childhood self-regulation. Specifically, ordinary differential equations (ODEs) were used to model the interactive influences of 115 36-month-olds' executive processes (strategy use) and prepotent responses to waiting to open a gift (desire for the gift and frustration about waiting to open it). Using a pair of coupled second-order ODEs in a nonlinear mixed effects framework, the study tested predictions for specific within- and between-child patterns of prepotent response-executive process coupling. Dynamic modeling results articulated the limits of 36-month olds' strategic efforts. They engaged executive processes when their prepotent responding levels were high, which delayed the resurgence of prepotent responses, but ultimately did not damp prepotent responding over the course of the wait. There was, however, preliminary evidence that the effectiveness of 36-month-olds' self-regulation depended upon child characteristics. Externalizing behavior problems were associated with more regulatory interference. Temperamental negative affectivity was marginally associated with more regulatory inefficiency. Compared with conventional methods of studying self-regulation, dynamic modeling yielded complementary and unique findings, suggesting its potential. (PsycINFO Database Record

Modeling a Composite Score in Parkinson\u2019s Disease Using Item Response Theory

In the current work, we present the methodology for development of an Item Response Theory model within a non-linear mixed effects framework to characterize the longitudinal changes of the Movement Disorder Society (sponsored revision) of Unified Parkinson’s Disease Rating Scale (MDS–UPDRS) endpoint in Parkinson’s disease (PD). The data were obtained from Parkinson’s Progression Markers Initiative database and included 163,070 observations up to 48 months from 430 subjects belonging to De Novo PD cohort. The probability of obtaining a score, reported for each of the items in the questionnaire, was modeled as a function of the subject’s disability. Initially, a single latent variable model was explored to characterize the disease progression over time. However, based on the understanding of the questionnaire set-up and the results of a residuals-based diagnostic tool, a three latent variable model with a mixture implementation was able to adequately describe longitudinal changes not only at the total score level but also at each individual item level. The linear progression rates obtained for the patient-reported items and the non-sided items were similar, each of which roughly take about 50 months for a typical subject to progress linearly from the baseline by one standard deviation. However for the sided items, it was found that the better side deteriorates quicker than the disabled side. This study presents a framework for analyzing MDS–UPDRS data, which can be adapted to more traditional UPDRS data collected in PD clinical trials and result in more efficient designs and analyses of such studies.

Modeling of free fatty acid dynamics: insulin and nicotinic acid resistance under acute and chronic treatments

Nicotinic acid (NiAc) is a potent inhibitor of adipose tissue lipolysis. Acute administration results in a rapid reduction of plasma free fatty acid (FFA) concentrations. Sustained NiAc exposure is associated with tolerance development (drug resistance) and complete adaptation (FFA returning to pretreatment levels). We conducted a meta-analysis on a rich pre-clinical data set of the NiAc–FFA interaction to establish the acute and chronic exposure-response relations from a macro perspective. The data were analyzed using a nonlinear mixed-effects framework. We also developed a new turnover model that describes the adaptation seen in plasma FFA concentrations in lean Sprague–Dawley and obese Zucker rats following acute and chronic NiAc exposure. The adaptive mechanisms within the system were described using integral control systems and dynamic efficacies in the traditional I_{text{max}} model. Insulin was incorporated in parallel with NiAc as the main endogenous co-variate of FFA dynamics. The model captured profound insulin resistance and complete drug resistance in obese rats. The efficacy of NiAc as an inhibitor of FFA release went from 1 to approximately 0 during sustained exposure in obese rats. The potency of NiAc as an inhibitor of insulin and of FFA release was estimated to be 0.338 and 0.436 {upmu {text{M}}}, respectively, in obese rats. A range of dosing regimens was analyzed and predictions made for optimizing NiAc delivery to minimize FFA exposure. Given the exposure levels of the experiments, the importance of washout periods in-between NiAc infusions was illustrated. The washout periods should be sim2 h longer than the infusions in order to optimize 24 h lowering of FFA in rats. However, the predicted concentration-response relationships suggests that higher AUC reductions might be attained at lower NiAc exposures.

Pharmacokinetics of Tranexamic Acid in Neonates, Infants, and Children Undergoing Cardiac Surgery With Cardiopulmonary Bypass

Background Tranexamic acid (TXA) is one of the most commonly used antifibrinolytic medications in children undergoing repair of congenital heart defects. However, a pharmacokinetics analysis of TXA has never been performed in neonates or young children undergoing complex cardiac surgeries using cardiopulmonary bypass, hypothermia, circulatory arrest, and ultrafiltration. A comprehensive pharmacokinetics study was performed in this patient population. Methods Fifty-five patients ranging from 2 days through 4 yr old were categorized into three groups: children less than 2 months old, infants 2 months to 1 yr old, and children greater than 1 yr old and weighing up to 20 kg. TXA was given as a bolus of 100 mg/kg followed by an infusion of 10 mg · kg · h throughout the surgery. A dose of 100 mg/kg was placed in the cardiopulmonary bypass prime. A total of 16 to 18 samples were obtained from all patients throughout surgery. Plasma TXA concentrations were measured by high-performance liquid chromatography and modeled under a nonlinear mixed-effects framework with a two-compartment structural model. Results Cardiopulmonary bypass had a statistically significant impact on all pharmacokinetic parameters. Age was a better covariate than body weight, affecting both the distribution and the elimination of TXA. However, weight performed well in some cases. Other covariates including body surface area, pump prime volume, ultrafiltrate volume, and body temperature did not improve the model. Conclusions This TXA pharmacokinetic analysis is reported for the first time in neonates and young children undergoing complex cardiac surgeries with cardiopulmonary bypass. Dosing recommendations are provided as guidance for maintaining desired target concentrations.

Pharmacokinetics of tranexamic acid in neonates, infants, and children undergoing cardiac surgery with cardiopulmonary bypass.

Tranexamic acid (TXA) is one of the most commonly used antifibrinolytic medications in children undergoing repair of congenital heart defects. However, a pharmacokinetics analysis of TXA has never been performed in neonates or young children undergoing complex cardiac surgeries using cardiopulmonary bypass, hypothermia, circulatory arrest, and ultrafiltration. A comprehensive pharmacokinetics study was performed in this patient population. Fifty-five patients ranging from 2 days through 4 yr old were categorized into three groups: children less than 2 months old, infants 2 months to 1 yr old, and children greater than 1 yr old and weighing up to 20 kg. TXA was given as a bolus of 100 mg/kg followed by an infusion of 10 mg · kg · h throughout the surgery. A dose of 100 mg/kg was placed in the cardiopulmonary bypass prime. A total of 16 to 18 samples were obtained from all patients throughout surgery. Plasma TXA concentrations were measured by high-performance liquid chromatography and modeled under a nonlinear mixed-effects framework with a two-compartment structural model. Cardiopulmonary bypass had a statistically significant impact on all pharmacokinetic parameters. Age was a better covariate than body weight, affecting both the distribution and the elimination of TXA. However, weight performed well in some cases. Other covariates including body surface area, pump prime volume, ultrafiltrate volume, and body temperature did not improve the model. This TXA pharmacokinetic analysis is reported for the first time in neonates and young children undergoing complex cardiac surgeries with cardiopulmonary bypass. Dosing recommendations are provided as guidance for maintaining desired target concentrations.

Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

We propose a nonlinear mixed-effects framework to jointly model longitudinal and repeated time-to-event data. A parametric nonlinear mixed-effects model is used for the longitudinal observations and a parametric mixed-effects hazard model for repeated event times. We show the importance for parameter estimation of properly calculating the conditional density of the observations (given the individual parameters) in the presence of interval and/or right censoring. Parameters are estimated by maximizing the exact joint likelihood with the stochastic approximation expectation–maximization algorithm. This workflow for joint models is now implemented in the Monolix software, and illustrated here on five simulated and two real datasets.

Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

We propose a nonlinear mixed-effects framework to jointly model longitudinal and repeated time-to-event data. A parametric nonlinear mixed-effects model is used for the longitudinal observations and a parametric mixed-effects hazard model for repeated event times. We show the importance for parameter estimation of properly calculating the conditional density of the observations (given the individual parameters) in the presence of interval and/or right censoring. Parameters are estimated by maximizing the exact joint likelihood with the stochastic approximation expectation–maximization algorithm. This workflow for joint models is now implemented in the Monolix software, and illustrated here on five simulated and two real datasets.