Stochastic Approximation Expectation Maximization Research Articles

Estimating genetic parameters and trends in growth curve traits of Zandi sheep using the SAEM algorithm.

The objectives of this study were to evaluate the influence of environmental effects on growth curve traits of Zandi lambs and estimate their genetic parameters with the best-fit animal model. For this purpose, live body weight (BW) records (n = 10,607) of 2,519 individuals (which were progeny of 278 rams and 1,485 ewes) were used to estimate genetic effects on growth curve traits from birth to yearling age of Zandi lambs. Using the Stochastic Approximation Expectation Maximization (SAEM) algorithm the growth curve parameters of five different mixed functions (i.e., Brody, Richards, Von Bertalanffy, Gompertz and Logistic) were obtained, then for the most appropriate model the genetic parameters were estimated using a Bayesian approach fitted multivariate animal model and ignoring or including maternal genetic effect. Except Richards model, all other mixed functions used here closely fitted actual BW records (R2 > 0.96). However, the Logistic function provided the best fit in every type. So, studied growth curve traits were estimated asymptotic weight which considered as mature weight (a), rate parameter (b), rate of maturing (k), and age (Ai)/weight (Wi) at the point of inflection. Of the fixed effects studied (i.e., gender, birth type, dam age, season and year of birth), the only non-significant relationship was the effect dam age on b and Ai. Based on the best-fitted model, posterior means of heritability estimates for a, b, k, Wi and Ai were 0.142 ± 0.036, 0.094 ± 0.029, 0.143 ± 0.063, 0.149 ± 0.039 and 0.029 ± 0.013, respectively. Posterior means of genetic correlations between mentioned traits ranged from -0.018 ± 0.069 (b-k) to 0.959 ± 0.029 (a-b), whereas the phenotypic correlation varied from -0.047 ± 0.014 (b-k) to 0.836 ± 0.007 (a-b). It was concluded that the model including only direct additive effect was sufficient to explain the variation in all investigated growth traits of Zandi lambs, selection for these traits results in slow genetic gain (due to the lack of sufficient genetic variation), but it would not be difficult to improve their mature weight and rate of maturing jointly. The results indicate that although the rate of genetic change for mature weight has been small (0.008 ± 0.003 kgyear-1; P < 0.05) but in the favorable direction for this breed.

Population Pharmacokinetics and Limited Sampling Strategy of Mycophenolate Mofetil for Indian Patients With Lupus Nephritis.

Mycophenolic acid is widely used to treat lupus nephritis (LN). However, it exhibits complex pharmacokinetics with large interindividual variability. This study aimed to develop a population pharmacokinetic (popPK) model and a 3-sample limited sampling strategy (LSS) to optimize therapeutic drug monitoring in Indian patients with LN. Five blood samples from each LN patient treated with mycophenolic acid were collected at steady-state predose and 1, 2, 4, and 6 hours postdose. Demographic parameters were tested as covariates to explain interindividual variability. PopPK analysis was performed using Monolix and the stochastic approximation expectation-maximization algorithm. An LSS was derived from 500 simulated pharmacokinetic (PK) profiles using maximum a posteriori Bayesian estimation to estimate individual PK parameters and area under the curve (AUC). The LSS-calculated AUC was compared with the AUC calculated using the trapezoidal rule and all the simulated samples. A total of 51 patients were included in this study. Based on the 245 mycophenolic acid concentrations, a 1-compartmental model with double absorption using gamma distributions best fitted the data. None of the covariates improved the model significantly. The model was internally validated using diagnostic plots, prediction-corrected visual predictive checks, and bootstrapping. The best LSS included samples at 1, 2, and 4 hours postdose and exhibited good performances in an external dataset (root mean squared error, 21.9%; mean bias, -4.20%). The popPK model developed in this study adequately estimated the PK of mycophenolic acid in adult Indian patients with LN. This simple LSS can optimize TDM based on the AUC in routine practice.

RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

Extending the code in the open-source saemix package to fit joint models of longitudinal and time-to-event data

Background and ObjectiveJoint modeling of longitudinal and time-to-event data has gained attention over recent years with extensive developments including nonlinear models for longitudinal outcomes and flexible time-to-event models for survival outcomes, possibly involving competing risks. However, in popular software such as R, the function used to describe the biomarker dynamic is mainly linear in the parameters, and the survival submodel relies on pre-implemented functions (exponential, Weibull, ...). The objective of this work is to extend the code from the saemix package (version 3.1 on CRAN) to fit parametric joint models where longitudinal submodels are not necessary linear in their parameters, with full user control over the model function. MethodsWe used the saemix package, designed to fit nonlinear mixed-effects models (NLMEM) through the Stochastic Approximation Expectation Maximization (SAEM) algorithm, and extended the main functions to joint model estimation. To compute standard errors (SE) of parameter estimates, we implemented a recently developed stochastic algorithm. A simulation study was proposed to assess (i) the performances of parameter estimation, (ii) the SE computation and (iii) the type I error when testing independence between the two submodels. Four joint models were considered in the simulation study, combining a linear or nonlinear mixed-effects model for the longitudinal submodel, with a single terminal event or a competing risk model. ResultsFor all simulation scenarios, parameters were precisely and accurately estimated with low bias and uncertainty. For complex joint models (with NLMEM), increasing the number of chains of the algorithm was necessary to reduce bias, but earlier censoring in the competing risk scenario still challenged the estimation. The empirical SE of parameters obtained over all simulations were very close to those computed with the stochastic algorithm. For more complex joint models (involving NLMEM), some estimates of random effects variances had higher uncertainty and their SE were moderately under-estimated. Finally, type I error was controlled for each joint model. Conclusionssaemix is a flexible open-source package and we adapted it to fit complex parametric joint models that may not be estimated using standard tools. Code and examples to help users get started are freely available on Github.

Pharmacokinetic/LDL-C and exposure-response analysis of tafolecimab in Chinese hypercholesterolemia patients: Results from phase I, II, and III studies.

Tafolecimab, a novel fully human monoclonal antibody targeting PCSK9, has been assessed in Chinese healthy volunteers and patients with hypercholesterolemia. This analysis is to develop and qualify a population pharmacokinetics (PopPKs)/LDL-C model to characterize tafolecimab PK and LDL-C profiles, evaluate the impact of potential covariates on tafolecimab, estimate individual predicted exposure, and LDL-C decreasing, furthermore, explore exposure-response relationship to support clinical use. Data from six clinical trials in China were used to develop the PopPK/LDL-C model. A Michaelis-Menten approximation of the target-mediated drug disposition (TMDD) model was used to describe PK data and indirect response (IDR) model was developed to estimate the LDL-C profile. A stochastic approximation expectation maximization algorithm was applied to estimate PopPK/LDL-C parameters. The PK/LDL-C time course data for tafolecimab were well described by TMDD/IDR model. Baseline covariates resulting in statistically significant changes in PK/LDL-C parameters included: body weight and sex on absorption rate constant; body weight, sex, and unbound PCSK9 on central volume; body weight and sex on clearance; baseline LDL-C on first-order rate constants for the removal of an effect); and disease and sex on maximum effect. However, the magnitudes of changes associated with these covariates do not necessitate dose adjustment. Exposure-efficacy relationship indicated that the nadir of LDL-C reduction achieved with the steady-state trough plasma concentration (Ctrough ) of tafolecimab at 5 μg/mL, and no further LDL-C decreasing with the increasing Ctrough . There was no exposure dependency observed in exposure-safety exploration. The PopPK/LDL-C model was successfully developed, validated, and predicted tafolecimab/LDL-C concentrations and individual exposures.

Nlive: an R package to facilitate the application of the sigmoidal and random changepoint mixed models

BackgroundThe use of mixed effect models with a specific functional form such as the Sigmoidal Mixed Model and the Piecewise Mixed Model (or Changepoint Mixed Model) with abrupt or smooth random change allows the interpretation of the defined parameters to understand longitudinal trajectories. Currently, there are no interface R packages that can easily fit the Sigmoidal Mixed Model allowing the inclusion of covariates or incorporating recent developments to fit the Piecewise Mixed Model with random change.ResultsTo facilitate the modeling of the Sigmoidal Mixed Model, and Piecewise Mixed Model with abrupt or smooth random change, we have created an R package called nlive. All needed pieces such as functions, covariance matrices, and initials generation were programmed. The package was implemented with recent developments such as the polynomial smooth transition of the piecewise mixed model with improved properties over Bacon-Watts, and the stochastic approximation expectation-maximization (SAEM) for efficient estimation. It was designed to help interpretation of the output by providing features such as annotated output, warnings, and graphs. Functionality, including time and convergence, was tested using simulations. We provided a data example to illustrate the package use and output features and interpretation. The package implemented in the R software is available from the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=nlive.ConclusionsThe nlive package for R fits the Sigmoidal Mixed Model and the Piecewise Mixed: abrupt and smooth. The nlive allows fitting these models with only five mandatory arguments that are intuitive enough to the less sophisticated users.

Limited sampling strategy and population pharmacokinetic model of mycophenolic acid in pediatric patients with systemic lupus erythematosus: application of a double gamma absorption model with SAEM algorithm.

Mycophenolic acid (MPA), the active metabolite of mycophenolate mofetil (MMF), is widely used in the treatment of systemic lupus erythematosus (SLE). It has been shown that its therapeutic drug monitoring based on the area under the curve (AUC) improves treatment efficacy. MPA exhibits a complex bimodal absorption, and a double gamma distribution model has been already proposed in the past to accurately describe this phenomenon. These previous population pharmacokinetics models (POPPK) have been developed using iterative two stage Bayesian (IT2B) or non-parametric adaptive grid (NPAG) methods. However, non-linear mixed effect (NLME) approaches based on stochastic approximation expectation-maximization (SAEM) algorithms have never been published so far for this particular model. The objectives of this study were (i) to implement the double absorption gamma model in Monolix, (ii) to compare different absorption models to describe the pharmacokinetics of MMF, and (iii) to develop a limited sampling strategy (LSS) to estimate AUC in pediatric SLE patients. A data splitting of full pharmacokinetic profiles sampled in 67 children extracted either from the expert system ISBA (n = 34) or the hospital Saint Louis (n = 33) was performed into train (75%) and test (25%) sets. A POPPK was developed for MPA in the train set using a NLME and the SAEM algorithm and different absorption models were implemented and compared (first order, transit, or simple and double gamma). The best limited sampling strategy was then determined in the test set using a maximum-a-posteriori Bayesian method to estimate individual PK parameters and AUC based on three blood samples compared to the reference AUC calculated using the trapezoidal rule applied on all samples and performances were assessed in the test set. Mean patient age and dose was 13years old (5-18) and 18.1mg/kg (7.9-47.6), respectively. MPA concentrations (764) from 107 occasions were included in the analysis. A double gamma absorption with a first-order elimination from the central compartment best fitted the data. The optimal LSS with samples at 30min, 2h, and 3h post-dose exhibited good performances in the test set (mean bias - 0.32% and RMSE 21.0%). The POPPK developed in this study adequately estimated the MPA AUC in pediatric patients with SLE based on three samples. The double absorption gamma model developed with the SAEM algorithm showed very accurate fit and reduced computation time.

MSAEM Estimation for Confirmatory Multidimensional Four‐Parameter Normal Ogive Models

AbstractIn this paper, we develop a mixed stochastic approximation expectation‐maximization (MSAEM) algorithm coupled with a Gibbs sampler to compute the marginalized maximum a posteriori estimate (MMAPE) of a confirmatory multidimensional four‐parameter normal ogive (M4PNO) model. The proposed MSAEM algorithm not only has the computational advantages of the stochastic approximation expectation‐maximization (SAEM) algorithm for multidimensional data, but it also alleviates the potential instability caused by label‐switching, and then improved the estimation accuracy. Simulation studies are conducted to illustrate the good performance of the proposed MSAEM method, where MSAEM consistently performs better than SAEM and some other existing methods in multidimensional item response theory. Moreover, the proposed method is applied to a real data set from the 2018 Programme for International Student Assessment (PISA) to demonstrate the usefulness of the 4PNO model as well as MSAEM in practice.

Significant Effects of Renal Function on Mycophenolic Acid Total Clearance in Pediatric Kidney Transplant Recipients with Population Pharmacokinetic Modeling.

Mycophenolic acid (MPA) is an immunosuppressant commonly prescribed in pediatric kidney transplantation to prevent graft rejection. Large variabilities in MPA plasma exposures have been observed in this population, which could result in severe adverse effects. The majority of the MPA pharmacokinetic data have been reported in adult populations, whereas information in pediatric patients is still very limited. The objective of this study was to establish a novel, nonlinear mixed-effects model for MPA and investigate the clinical variables affecting MPA population pharmacokinetics in pediatric kidney transplant recipients. Data were collected retrospectively from pediatric kidney transplant patients (≤ 18 years when MPA concentrations were initially collected; on oral administration of mycophenolate mofetil) in Calgary, Alberta, Canada. Nonlinear mixed-effect modeling was conducted using stochastic approximation expectation-maximization in Monolix 2021R2 (Lixoft SAS, France) to determine population pharmacokinetic estimates, interindividual variabilities, and interoccasional variabilities. Covariate models were constructed using the Model Proposal function in Monolix in conjunction with a systematic stepwise inclusion/elimination protocol. The best model was selected based on objective function values, relative standard errors, goodness-of-fit plots, prediction-corrected visual predictive checks, and numerical predictive checks. A total of 50 pediatric kidney transplant patients (25 female) with 219 MPA plasma concentration-time profiles were included. The average age (± standard deviation) and posttransplant time for the sample population were 12.8 ± 4.8 years and 762 ± 1160 days, respectively. The majority of study subjects (i.e., > 85% based on all occasions) were co-administered tacrolimus. A two-compartment, first-order absorption with lag time and linear elimination structural model with lognormal distributed proportional residual errors best described the MPA concentration-time data. The absorption rate constant (2.52 h-1 or 0.042 min-1), lag time (0.166 h or 9.96 min), volumes of distributions of the central (22.8 L) and peripheral (216 L) compartments, and intercompartment clearance (17.6 Lh-1 or 0.293 Lmin-1) were consistent with literature values; whereas total MPA clearance (0.72 Lh-1 or 0.012 Lmin-1) was relatively reduced, likely due to the general lack of cyclosporine interactions and the stabilized graft functions from significantly longer posttransplant time in our sample population. Of the clinical variables tested, only estimated glomerular filtration rate (eGFR) was identified a significant covariate affecting total MPA clearance with a positive, exponential relationship. The final population pharmacokinetic model was successfully evaluated/validated using a variety of complementary methods. We have successfully constructed and validated a novel population pharmacokinetic model of MPA in pediatric kidney transplant patients. A positive, nonlinear relationship between eGFR and total MPA clearance identified in our model is likely attributed to multiple concurrent mechanisms, which warrant further systematic investigations.

Stochastic Expectation Maximization Algorithm for Linear Mixed-Effects Model with Interactions in the Presence of Incomplete Data.

The purpose of this paper is to propose a new algorithm based on stochastic expectation maximization (SEM) to deal with the problem of unobserved values when multiple interactions in a linear mixed-effects model (LMEM) are present. We test the effectiveness of the proposed algorithm with the stochastic approximation expectation maximization (SAEM) and Monte Carlo Markov chain (MCMC) algorithms. This comparison is implemented to highlight the importance of including the maximum effects that can affect the model. The applications are made on both simulated psychological and real data. The findings demonstrate that our proposed SEM algorithm is highly preferable to the other competitor algorithms.

A mixed effects changepoint quantile regression model for longitudinal data with application on COVID-19 data

IntroductionLongitudinal individual response profiles could exhibit a mixture of two or more phases of increase or decrease in trend throughout the follow-up period, with one or more unknown transition points (changepoints). The detection and estimation of these changepoints is crucial. Most of the proposed statistical methods for detecting and estimating changepoints in literature rely on distributional assumptions that may not hold. In this case, a good alternative is to use a robust approach; the quantile regression model. There are methods in the literature to deal with quantile regression models with a changepoint. These methods ignore the within-subject dependence of longitudinal data.MethodsWe propose a mixed effects quantile regression model with changepoints to account for dependence structure in the longitudinal data. Fixed effects parameters, in addition to the location of the changepoint, are estimated using the profile estimation method. The stochastic approximation EM algorithm is proposed to estimate the fixed effects parameters exploiting the link between an asymmetric Laplace distribution and the quantile regression. In addition, the location of the changepoint is estimated using the usual optimization methods.Results and discussionA simulation study shows that the proposed estimation and inferential procedures perform reasonably well in finite samples. The practical use of the proposed model is illustrated using COVID-19 data. The data focus on the effect of global economic and health factors on the monthly death rate due to COVID-19 from 1 April 2020 to 30th April 2021. the results show a positive effect on the monthly number of patients with COVID-19 in intensive care units (ICUs) for both 0.5th and 0.8th quantiles of new monthly deaths per million. The stringency index, hospital beds, and diabetes prevalence have no significant effect on both 0.5th and 0.8th quantiles of new monthly deaths per million.

Computational model of CAR T-cell immunotherapy dissects and predicts leukemia patient responses at remission, resistance, and relapse

BackgroundAdaptive CD19-targeted chimeric antigen receptor (CAR) T-cell transfer has become a promising treatment for leukemia. Although patient responses vary across different clinical trials, reliable methods to dissect and predict patient...

A stochastic approximation expectation maximization algorithm for estimating Ramsay-curve three-parameter normal ogive model with non-normal latent trait distributions.

In the estimation of item response models, the normality of latent traits is frequently assumed. However, this assumption may be untenable in real testing. In contrast to the conventional three-parameter normal ogive (3PNO) model, a 3PNO model incorporating Ramsay-curve item response theory (RC-IRT), denoted as the RC-3PNO model, allows for flexible latent trait distributions. We propose a stochastic approximation expectation maximization (SAEM) algorithm to estimate the RC-3PNO model with non-normal latent trait distributions. The simulation studies of this work reveal that the SAEM algorithm produces more accurate item parameters for the RC-3PNO model than those of the 3PNO model, especially when the latent density is not normal, such as in the cases of a skewed or bimodal distribution. Three model selection criteria are used to select the optimal number of knots and the degree of the B-spline functions in the RC-3PNO model. A real data set from the PISA 2018 test is used to demonstrate the application of the proposed algorithm.

Joint modeling under competing risks: Application to survival prediction in patients admitted in Intensive Care Unit for sepsis with daily Sequential Organ Failure Assessment score assessments.

Joint models of longitudinal process and time-to-event data have recently gained attention, notably to provide individualized dynamic predictions. In the presence of competing risks, models published mostly involve cause-specific hazard functions jointly estimated with a linear or generalized linear model. Here we propose to extend the modeling to full parametric joint estimation of a nonlinear mixed-effects model and a subdistribution hazard model. We apply this approach on 6046 patients admitted in intensive care unit (ICU) for sepsis with daily Sequential Organ Failure Assessment (SOFA) score measurements. The joint model is built on a randomly selected training set of two thirds of patients and links the current predicted SOFA measurement to the instantaneous risks of ICU death and discharge from ICU, both adjusted on the patient age. Stochastic Approximation Expectation Maximization algorithm in Monolix is used for estimation. SOFA evolution is significantly associated with both risks: 0.37, 95% confidence interval (CI)=[0.35, 0.39] for the risk of death and -0.38, 95% CI=[-0.39, -0.36] for the risk of discharge. A simulation study, inspired from the real data, shows the good estimation properties of the parameters. We assess on the validation set the added value of modeling the longitudinal SOFA follow-up for the prediction of death compared with a model that includes only SOFA at baseline. Time-dependent receiver operating characteristic area under the curve and Brier scores show that when enough longitudinal individual information is available, joint modeling provides better predictions. The methodology can easily be applied to other clinical applications because of the general form of the model.

Expectation-Maximization-Based Simultaneous Localization and Mapping for Millimeter-Wave Communication Systems.

In this paper, we proposed a novel expectation–maximization-based simultaneous localization and mapping (SLAM) algorithm for millimeter-wave (mmW) communication systems. By fully exploiting the geometric relationship among the access point (AP) positions, the angle difference of arrival (ADOA) from the APs and the mobile terminal (MT) position, and regarding the MT positions as the latent variable of the AP positions, the proposed algorithm first reformulates the SLAM problem as the maximum likelihood joint estimation over both the AP positions and the MT positions in a latent variable model. Then, it employs a feasible stochastic approximation expectation–maximization (EM) method to estimate the AP positions. Specifically, the stochastic Monte Carlo approximation is employed to obtain the intractable expectation of the MT positions’ posterior probability in the E-step, and the gradient descent-based optimization is used as a viable substitute for estimating the high-dimensional AP positions in the M-step. Further, it estimates the MT positions and constructs the indoor map based on the estimated AP topology. Due to the efficient processing capability of the stochastic approximation EM method and taking full advantage of the abundant spatial information in the crowd-sourcing ADOA data, the proposed method can achieve a better positioning and mapping performance than the existing geometry-based mmW SLAM method, which usually has to compromise between the computation complexity and the estimation performance. The simulation results confirm the effectiveness of the proposed algorithm.

A Mixed Stochastic Approximation EM (MSAEM) Algorithm for the Estimation of the Four-Parameter Normal Ogive Model.

In recent years, the four-parameter model (4PM) has received increasing attention in item response theory. The purpose of this article is to provide more efficient and more reliable computational tools for fitting the 4PM. In particular, this article focuses on the four-parameter normal ogive model (4PNO) model and develops efficient stochastic approximation expectation maximization (SAEM) algorithms to compute the marginalized maximum a posteriori estimator. First, a data augmentation scheme is used for the 4PNO model, which makes the complete data model be an exponential family, and then, a basic SAEM algorithm is developed for the 4PNO model. Second, to overcome the drawback of the SAEM algorithm, we develop an improved SAEM algorithm for the 4PNO model, which is called the mixed SAEM (MSAEM). Results from simulation studies demonstrate that: (1) the MSAEM provides more accurate or comparable estimates as compared with the other estimation methods, while computationally more efficient; (2) the MSAEM is more robust to the choices of initial values and the priors for item parameters, which is a valuable property for practice use. Finally, a real data set is analyzed to show the good performance of the proposed methods.

Nonlinear mixed-effects models for HIV viral load trajectories before and after antiretroviral therapy interruption, incorporating left censoring.

Characterizing features of the viral rebound trajectories and identifying host, virological, and immunological factors that are predictive of the viral rebound trajectories are central to HIV cure research. We investigate if key features of HIV viral decay and CD4 trajectories during antiretroviral therapy (ART) are associated with characteristics of HIV viral rebound following ART interruption. Nonlinear mixed effect (NLME) models are used to model viral load trajectories before and following ART interruption, incorporating left censoring due to lower detection limits of viral load assays. A stochastic approximation EM (SAEM) algorithm is used for parameter estimation and inference. To circumvent the computational intensity associated with maximizing the joint likelihood, we propose an easy-to-implement three-step method. We evaluate the performance of the proposed method through simulation studies and apply it to data from the Zurich Primary HIV Infection Study. We find that some key features of viral load during ART (e.g., viral decay rate) are significantly associated with important characteristics of viral rebound following ART interruption (e.g., viral set point). The proposed three-step method works well. We have shown that key features of viral decay during ART may be associated with important features of viral rebound following ART interruption.

Evaluation of Intravenous Phenobarbital Pharmacokinetics in Critically Ill Patients With Brain Injury

Phenobarbital is still one of the drugs of choice in managing patients with brain injury in the intensive care unit (ICU). However, the impact of acute physiological changes on phenobarbital pharmacokinetic parameters is not well studied. This study aimed to evaluate the pharmacokinetic parameters of parenteral phenobarbital in critically ill patients with brain injury. Patients with severe traumatic or non-traumatic brain injury at high risk of seizure were included and followed for seven days. All patients initially received phenobarbital as a loading dose of 15 mg/kg over 30-minutes infusion, followed by 2 mg/kg/day divided into three doses. Blood samples were obtained on the first and fourth day of study at 1, 2, 5, 8, and 10 hours after the end of the infusion. Serum concentrations of phenobarbital were measured by high-pressure liquid chromatography (HPLC) with an ultraviolet (UV) detector. Pharmacokinetic parameters, including the volume of distribution (Vd), half-life (t1/2), and the drug clearance (CL), were provided by MonolixSuite 2019R1 software using stochastic approximation expectation-maximization (SAEM) algorithm and compared with previously reported parameters in healthy volunteers. Data from seventeen patients were analyzed. The mean value±standard deviation of pharmacokinetic parameters was calculated as follows: Vd: 0.81±0.15 L/kg; t1/2: 6.16±2.66 days; CL: 4.23±1.51 ml/kg/h. CL and Vd were significantly lower and higher than the normal population with the value of 5.6 ml/kg/h (P=0.002) and 0.7 L/kg (P=0.01), respectively. Pharmacokinetic behavior of phenobarbital may change significantly in critically ill brain-injured patients. This study affirms the value of early phenobarbital therapeutic drug monitoring (TDM) to achieve therapeutic goals.

Modeling serially correlated heavy-tailed data with some missing response values using stochastic EM algorithm

The linear regression model is a popular tool used by almost all in different areas of research. The model relies mainly on the assumption of uncorrelated errors from a Gaussian distribution. However, many datasets in practice violate this basic assumption, making inference in such cases invalid. Therefore, the linear regression model with structured errors driven by heavy-tailed innovations are preferred in practice. Another issue that occur frequently with real-life data is missing values, due to some reasons such as system breakdown and labor unrest. Despite the challenge these two issues pose to practitioners, there is scarcity of literature where they have jointly been studied. Hence, this article considers these two issues jointly, for the first time, and develops an efficient parameter estimation procedure for Student’s-t autoregressive regression model for time series with missing values of the response variable. The procedure is based on a stochastic approximation expectation–maximization algorithm coupled with a Markov chain Monte Carlo technique. The procedure gives efficient closed-form expressions for the parameters of the model, which are very easy to compute. Simulations and real-life data analysis show that the method is efficient for use with incomplete time series data.

Population Pharmacokinetics Modeling of Levofloxacin In Rabbit By Intravenous Bolus Injection and Peroral Administration

The population-based approach has been widely applied to describe the pharmacokinetic profile of many drugs. The aim of this current research was to study the implementation of the population-based pharmacokinetics of levofloxacin in rabbits administered by intravenous bolus injection and peroral delivery.&#x0D; Modeling analyses were performed using Monolix, one of the alternative tools for the population-based approach. Monolix works based on the Stochastic Approximation Expectation-Maximization (SAEM) method. The analysis was performed based on the population model using one-compartmental and two-compartmental disposition models. The combination error model was used during the analyses. Modeling appropriateness was determined based on the goodness of fit analyses, i.e., 1) the individual fit, 2) the observed versus population prediction values; and 3) the observed versus individual prediction values&#x0D; Plasma concentration profiles of levofloxacin by intravenous bolus injection and oral administration are better described by an appropriate model using a two-compartmental disposition model. All goodness of fit analyses demonstrates the power of the chosen model. However, the estimated disposition parameter values obtained based on the intravenous bolus injection and peroral administration are different for each subject. To confirm this phenomenon, we performed a simultaneous fitting of all intravenous bolus as well as peroral administration data. The goodness of fit analyses indicates an adequate fitting of all data.