Bayesian Estimation Research Articles

Getting Tacrolimus Dosing Right.

Tacrolimus (TAC) dosing is typically guided by the trough concentration (C0). Yet, significant relationships between TAC C0 and clinical outcomes have seldom been reported or only with adverse events. Large retrospective studies found a moderate correlation between TAC C0 and the area under the curve (AUC), where, for any given C0 value, the AUC varied 3- to 4-fold between patients (and vice versa). However, no randomized controlled trial evaluating the dose adjustment based on TAC AUC has been conducted yet. A few observational studies have shown that the AUC is associated with efficacy and, to a lesser extent, adverse effects. Other studies showed the feasibility of reaching predefined target ranges and reducing underexposure and overexposure. TAC AUC0-12 h is now most often assessed using Bayesian estimation, but machine learning is a promising approach. Microsampling devices are well accepted by patients and represent a valuable alternative to venous blood sample collection during hospital visits, especially when a limited sampling strategy is required. As AUC monitoring cannot be proposed very frequently, C0 monitoring has to be used in the interim, which has led to fluctuating doses in patients with an AUC/C0 ratio far from the population mean, because of different dose recommendations between the 2 biomarkers. We proposed estimating the individual AUC/C0 ratio and derived individual C0 targets to be used in between or as a replacement for AUC monitoring. Existing technology and evidence are now sufficient to propose AUC monitoring interspersed with individualized-C0 monitoring for all patients with kidney transplants while collecting real-world data to strengthen the evidence.

Analysis of dependent complementary competing risks data from a generalized inverted family of lifetime distributions under a maximum ranked set sampling procedure with unequal samples

This paper explores analysis of a dependent complementary competing risks model when the failure causes are distributed by the proposed generalized inverted family of lifetime distributions. Under maximum ranked set sampling with unequal samples (MRSSU), statistical inference of model parameters and reliability indices is discussed under classical frequentist and Bayesian approaches, respectively. Maximum likelihood estimators along with their existence and uniqueness are obtained for model parameters, and associated approximate confidence intervals are constructed in consequence. Bayesian estimation is also performed with respect to general flexible priors, and the Markov Chain Monte Carlo (MCMC) algorithm is proposed for complex posterior computation. The study further examines classical and Bayesian estimations with order restriction of parameters when additional historical information is available in the MRSSU scenario. Finally, the performance of different results is evaluated through numerical simulations and a real data example is presented for demonstrating the application of our methods.

Bayesian estimation of trunk-leg coordination during walking using phase oscillator models

In human walking, the legs and other body parts coordinate to produce a rhythm with appropriate phase relationships. From the point of view for rehabilitating gait disorders, such as Parkinson Disorders, it is important to understand the control mechanism of the gait rhythm. A previous study showed that the antiphase relationship of the two legs during walking is not strictly controlled using the reduction of the motion of the legs during walking to coupled phase oscillators. However, the control mechanisms other than those of the legs remains unknown. In particular, the trunk moves in tandem with the legs and must play an important role in stabilizing walking because it is above the legs and accounts for more than half of the mass of the human body. This study aims to uncover the control mechanism of the leg-trunk coordination in the sagittal plane using the coupled phase oscillators model and Bayesian estimation. We demonstrate that the leg-trunk coordination is not strictly controlled, as well as the interleg coordination.

Bayesian and E-Bayesian Estimation for Odd Generalized Exponential Inverted Weibull Distribution

Bayesian and E-Bayesian Estimation for Odd Generalized Exponential Inverted Weibull Distribution

Collaborative Seismic Impedance Inversion under Bayesian Parameter Estimation

Abstract At present, the industry mainly divides seismic inversion methods into deterministic inversion and deterministic inversion based on the methods and principles used in inversion. There are two types of geostatistical inversion. Deterministic inversion is the process of directly modifying the model quantity through optimization algorithms under given initial constraint conditions to obtain a definite solution; Geostatistical inversion uses random simulation methods to obtain inversion results through simulation and selection. The seismic data did not participate in the direct modification of the model, but rather served as a matching optimization constraint for the random model. Starting from the Bayesian formula, this article unifies deterministic inversion and geostatistical inversion within the Bayesian parameter estimation framework. From a theoretical framework, it analyzes the similarities and differences between deterministic inversion and geostatistical inversion, and proposes a method that combines deterministic inversion and geostatistical inversion - seismic wave impedance co inversion. Sequential Gaussian simulation and model constrained inversion are used as examples of the two major methods, The correctness of the research results and the feasibility and effectiveness of the proposed new inversion method and process have been verified through the application of the Marmousi theoretical model and actual data from Fudong, Fukang Depression, Xinjiang. It has been proven that the proposed method can improve the accuracy and precision of inversion. The inversion method and process used in this study obtained high-resolution and high-precision inversion results, which have good application prospects.

Toward Accelerated Nuclear-physics Parameter Estimation from Binary Neutron Star Mergers: Emulators for the Tolman–Oppenheimer–Volkoff Equations

Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman–Oppenheimer–Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: multilayer perceptrons (MLPs), Gaussian processes, and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms, whereas the RBM results in the largest speedup with respect to the full high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.

Kinematic calibration of industrial robot using Bayesian modeling framework

Positioning accuracy of an end-effector is a crucial metric for evaluating industrial robot performance. Uncertainties in joint angles and joint backlash deviate actual angles from the designed nominal values to negate positioning accuracy. Most existing parameter identification methods overlook or not properly account for such uncertainties, leading to usually overconfident identification results. To this gap, the present study introduces a kinematic calibration methodology employing Bayesian parameter estimation to achieve identification of joint variables. New formulas based on data features of industrial robots for constructing the likelihood function are proposed, and model selection is applied to assess various likelihood functions for a tradeoff balance between complexity and accuracy. To evaluate the robustness of the proposed approach, identification of joint variables is conducted under different measurement noises. The position response of kinematic model is predicted based on the identified joint uncertainty information. The efficacy is verified through rigorous scrutiny involving both a numerical example and an engineering application. Results indicate that the proposed method exhibits satisfactory kinematic parameter identification accuracy and robustness. In addition, the uncertainty of parameters can be measured and the prediction of trajectory uncertainty intervals is realized simultaneously, which promotes the application of industrial robots in high-precision scenes.

MEFDPN: Mixture exponential family distribution posterior networks for evaluating data uncertainty

The computation of uncertainty are crucial for developing a reliable machine learning model. The natural posterior network (NatPN) provides uncertainty estimation for any single exponential family distribution, but real-world data is often complex. Therefore, we introduce a mixture exponential family posterior network (MEFDPN), which extends the prior distribution to a mixture of exponential family distributions, aiming to fit complex distributions that better represent real data. During network training, MEFDPN independently updates the posterior Bayesian estimates for each prior distribution, and the weights of these distributions are updated based on the forward propagation results. Furthermore, MEFDPN calculates two types of uncertainty (aleatoric and epistemic) and combines them using entropy weighting to obtain a comprehensive confidence measure for each data point. Theoretically, MEFDPN achieves higher prediction accuracy, and experimental results demonstrate its capability to compute high-quality data comprehensive confidence. Moreover, it shows encouraging accuracy in Out-of-Distribution(OOD) detection and validation experiments. Finally, we apply MEFDPN to a materials dataset, efficiently filtering out OOD data. This results in a significant enhancement of prediction accuracy for machine learning models. Specifically, removing only 5% of outlier data leads to a 2%–5% improvement in accuracy.

Incorporating multi-source uncertainties in fast building wall thermal resistance estimation through physics-based and multi-fidelity statistical learning models

Meta-modeling and Bayesian inversion technique are proposed for fast and accurate in-situ estimation of the total thermal resistance (RTot) of walls using non-intrusive wall instrumentation. Various sources of uncertainties are taken into account to provide an enhanced credible interval for the thermal resistance estimate. In the considered protocol, a small zone of the internal surface of the wall is excited by a prototype to get faster in situ estimation and to limit the influence of external weather conditions. To be independent of the heat transfer coefficients and of the misknown layer thicknesses, which are difficult to estimate, we use herein the measurements of internal and external surface temperatures as boundary conditions in a thermal direct problem reformulated. A meta-model of the thermal model is created based on a statistical multi-fidelity approach with two levels of fidelity, Resistance-Capacitance (RC) and 1D models, to achieve the Bayesian estimation of the total thermal resistance in a reasonable computation time. The RTot estimation method is applied to realistic internal insulated walls (IIW), from poorly to highly insulated, under different weather conditions. Several numerical tests are carried out and credible intervals are provided to study the importance of the wall initial condition, the excitation time and the instrumentation. Finally, an experimental application is conducted using real measurements on an internal insulated wall (IIW) in Nancy (France). The obtained experimental results show that, in a short excitation time (10h) with a reduced instrumentation, the proposed method accurately estimates the minimum wall thermal resistance. For a standard wall of about 4 m2.K/W, a relevant estimate of RTot with a relative deviation less than 10% can be achieved by using a polynomial initial temperature profile proposed in this study, sufficient measurements and an excitation time of 3 days. This study thus offers prospects for improved energy assessment of buildings before and after renovation.

Bayesian Optimization for Sparse Neural Networks With Trainable Activation Functions.

In the literature on deep neural networks, there is considerable interest in developing activation functions that can enhance neural network performance. In recent years, there has been renewed scientific interest in proposing activation functions that can be trained throughout the learning process, as they appear to improve network performance, especially by reducing overfitting. In this paper, we propose a trainable activation function whose parameters need to be estimated. A fully Bayesian model is developed to automatically estimate from the learning data both the model weights and activation function parameters. An MCMC-based optimization scheme is developed to build the inference. The proposed method aims to solve the aforementioned problems and improve convergence time by using an efficient sampling scheme that guarantees convergence to the global maximum. The proposed scheme has been tested across a diverse datasets, encompassing both classification and regression tasks, and implemented in various CNN architectures to demonstrate its versatility and effectiveness. Promising results demonstrate the usefulness of our proposed approach in improving models accuracy due to the proposed activation function and Bayesian estimation of the parameters.

Genetic programming-based algorithms application in modeling the compressive strength of steel fiber-reinforced concrete exposed to elevated temperatures

Steel-fiber-reinforced concrete (SFRC) has replaced traditional concrete in the construction sector, improving fracture resistance and post-cracking performance. However, extreme temperatures degrade concrete's material characteristics including stiffness and strength. The construction industry increasingly embraces machine learning (ML) to estimate concrete properties and optimize cost and time accurately. This study employs independent ML methods, gene expression programming (GEP), multi-expression programming (MEP), XGBoost, and Bayesian estimation model (BES) to predict SFRC compressive strength (CS) at high temperatures. 307 experimental data points from published studies were utilized to develop the models. The models were trained using 70 % of the dataset, with 15 % for validation and 15 % for testing. Iterative hyperparameter adjustment and trial-and-error refining achieved optimum predictions. All the models were evaluated using correlation (R) values for training, validation, and testing datasets. MEP showed slightly lower R-values of 0.923, 0.904, and 0.949 than GEP, which performed consistently with 0.963, 0.967, and 0.961. XGBoost had the greatest training R-value of 0.997 but dropped in validation (0.918) and testing (0.896). BES model exhibited commendable performance with scores of 0.986, 0.944, and 0.897. GEP and XGBoost exhibited great accuracy, with GEP sustaining constant accuracy across all datasets, highlighting its potency in predicting CS. Interpreting model predictions using SHapley Additive exPlanation (SHAP) highlighted temperature over heating rate. CS improved significantly as the steel fiber volume fraction (Vf) reached 1.5 %, plateauing thereafter. The proposed models are valid and accurate, providing designers and builders with a practical and adaptable method for estimating strength in SFRC structural applications, particularly under high-temperature conditions.

Influence of additive and maternal effects on growth traits in Deccani sheep through Bayesian inference

The aim of this study was to estimate genetic parameters for growth traits in Deccani sheep using Bayesian inference. A dataset comprising pedigree information and growth trait records from 2590 Deccani animals, born to 127 sires and 836 dams between 2011 and 2020, was analyzed. The growth traits considered included birth weight (BWT), weaning weight (WWT), and weights at six (SWT), nine (NWT), and twelve (YWT) months of age. Genetic evaluation employed six univariate animal models incorporating direct and maternal effects, implemented through THRGIBBS1F90 and POSTGIBBSF90 programs. Fixed factors adjusted in the analysis included year of birth, sex of lamb, season of lambing, and dam’s age and weight at lambing. Bayesian estimates of direct heritability, under the best model, revealed values of 0.14±0.05, 0.13±0.01, 0.20±0.04, 0.15±0.06, and 0.18±0.05 for BWT, WWT, SWT, NWT, and YWT traits, respectively. Corresponding maternal heritability estimates were 0.07±0.02, 0.08±0.01, 0.02±0.01, 0.10±0.02, and 0.17±0.06. Negative genetic correlations between additive and maternal genetic effects ranged from -0.14 to 0.07, while maternal permanent environmental influences were negligible. Positive and moderate to high genetic correlations among growth traits suggest potential relationships between them. These findings suggested selection based on WWT because it measured early in life, and has high correlation with other body weight especially SWT trait.

Bayesian estimation and comparison of idiographic network models.

Idiographic network models are estimated on time series data of a single individual and allow researchers to investigate person-specific associations between multiple variables over time. The most common approach for fitting graphical vector autoregressive (GVAR) models uses least absolute shrinkage and selection operator (LASSO) regularization to estimate a contemporaneous and a temporal network. However, estimation of idiographic networks can be unstable in relatively small data sets typical for psychological research. This bears the risk of misinterpreting differences in estimated networks as spurious heterogeneity between individuals. As a remedy, we evaluate the performance of a Bayesian alternative for fitting GVAR models that allows for regularization of parameters while accounting for estimation uncertainty. We also develop a novel test, implemented in the tsnet package in R, which assesses whether differences between estimated networks are reliable based on matrix norms. We first compare Bayesian and LASSO approaches across a range of conditions in a simulation study. Overall, LASSO estimation performs well, while a Bayesian GVAR without edge selection may perform better when the true network is dense. In an additional simulation study, the novel test is conservative and shows good false-positive rates. Finally, we apply Bayesian estimation and testing in an empirical example using daily data on clinical symptoms for 40 individuals. We additionally provide functionality to estimate Bayesian GVAR models in Stan within tsnet. Overall, Bayesian GVAR modeling facilitates the assessment of estimation uncertainty which is important for studying interindividual differences of intraindividual dynamics. In doing so, the novel test serves as a safeguard against premature conclusions of heterogeneity. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test.

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

Reliability inference of a multicomponent stress-strength model for exponentiated Pareto distribution based on progressive first failure censored samples

Multicomponent stress-strength (MC-SS) analysis is crucial for risk management and decision-making in various fields such as engineering, manufacturing, and quality control. It helps in identifying vulnerable components and areas where improvements can enhance overall system reliability. A primary contribution of this research is the implementation of the progressive first-Failure censored (PFIF-C) scheme. This scheme offers a novel and efficient approach to time and cost censoring, surpassing many existing censoring schemes found in the literature. The current study investigates the issue of MC-SS reliability inference under PFIF-C from the exponentiated Pareto distribution. The reliability of the MC-SS system is considered under the condition that both stress and strength follow an exponentiated Pareto distribution with a common second shape parameter. The parameter estimates and reliability estimate of the MC-SS system is produced using the maximum likelihood and Bayesian procedures. The asymptotic confidence intervals and highest posterior density credible intervals for the MC-SS system reliability are produced. Bayesian estimates are yielded using Markov Chain Monte Carlo under both informative and non-informative priors, considering symmetric and asymmetric loss functions. In order to assess the efficacy of the suggested methodology, simulation analyses are conducted. According to the simulation data Bayesian estimates of the MC-SS reliability, employing both symmetric and asymmetric loss functions, consistently outperform maximum likelihood estimates in terms of estimated risks. In general, Bayesian estimates based on asymmetric loss function perform better than the other competing loss function. The procedure is further shown with one real-world data example about failure times of a specific software model to show how the recommended approach may be applied to assess the strength and stress of a multicomponent model.

An optimized multi-layer ensemble model for airborne networks intrusion detection

In view of the characteristics of airborne networks, such as the traffic data of 1553B data bus and public networks, numerous redundant and irrelevant data, and fewer but more types of attack behaviors, a highly representative balanced data subset is generated by combining K-means with synthetic minority oversampling technique (SMOTE). A feature selection (FS) method of fast correlation-based filter combined with information gain (IG-FCBF) is proposed to filter the key characteristics with 90 % cumulative importance. Aiming at the problem that it is not easy for a single classifier to accurately classify various types of attacks, as well as the difficulty in obtaining the best prediction results by adjusting default and manual parameters, a multi-layer ensemble model based on Bayesian optimization tree-structured Parzen estimator (BO-TPE) is proposed for airborne networks intrusion detection, combining the advantages of supervised learning, stacking ensemble method and hyperparameter optimization (HPO). The experimental results show the superiority and effectiveness of the model, as well as its universality in Integrated Avionics Systems (IAS) and onboard public networks, which provides a new approach for airborne networks intrusion identification and protection.

Model Estimation Approaches for Fully-Latent Principal Stratification with Small Samples

This study investigated the performance of Bayesian fully-latent principal stratification (FLPS) models in estimating causal and principal effects in small-sample randomized control trials (RCTs) and compared their robustness with three maximum likelihood estimation (MLE)-based models. The impact of prior choices on principal effect estimation in the Bayesian FLPS framework was also explored. Simulation results showed that Bayesian estimation with informative priors consistently outperformed three MLEs and Bayesian estimation with diffuse priors, especially in small samples. The choice of priors played a critical role in estimation accuracy and bias. The study highlights the advantages of Bayesian FLPS with informative priors for RCT research with limited sample sizes and encourages future research to explore complex latent structures, robustness to different measurement models, and guidelines for selecting appropriate priors in the Bayesian FLPS framework.

Assays of Variant Effect and Automated Patch Clamping Improve KCNH2-LQTS Variant Classification and Cardiac Event Risk Stratification.

Long QT syndrome is a lethal arrhythmia syndrome, frequently caused by rare loss-of-function variants in the potassium channel encoded by KCNH2. Variant classification is difficult, often because of lack of functional data. Moreover, variant-based risk stratification is also complicated by heterogenous clinical data and incomplete penetrance. Here we sought to test whether variant-specific information, primarily from high-throughput functional assays, could improve both classification and cardiac event risk stratification in a large, harmonized cohort of KCNH2 missense variant heterozygotes. We quantified cell-surface trafficking of 18 796 variants in KCNH2 using a multiplexed assay of variant effect (MAVE). We recorded KCNH2 current density for 533 variants by automated patch clamping. We calibrated the strength of evidence of MAVE data according to ClinGen guidelines. We deeply phenotyped 1458 patients with KCNH2 missense variants, including QTc, cardiac event history, and mortality. We correlated variant functional data and Bayesian long QT syndrome penetrance estimates with cohort phenotypes and assessed hazard ratios for cardiac events. Variant MAVE trafficking scores and automated patch clamping peak tail currents were highly correlated (Spearman rank-order ρ=0.69; n=433). The MAVE data were found to provide up to pathogenic very strong evidence for severe loss-of-function variants. In the cohort, both functional assays and Bayesian long QT syndrome penetrance estimates were significantly predictive of cardiac events when independently modeled with patient sex and adjusted QT interval (QTc); however, MAVE data became nonsignificant when peak tail current and penetrance estimates were also available. The area under the receiver operator characteristic curve for 20-year event outcomes based on patient-specific sex and QTc (area under the curve, 0.80 [0.76-0.83]) was improved with prospectively available penetrance scores conditioned on MAVE (area under the curve, 0.86 [0.83-0.89]) or attainable automated patch clamping peak tail current data (area under the curve, 0.84 [0.81-0.88]). High-throughput KCNH2 variant MAVE data meaningfully contribute to variant classification at scale, whereas long QT syndrome penetrance estimates and automated patch clamping peak tail current measurements meaningfully contribute to risk stratification of cardiac events in patients with heterozygous KCNH2 missense variants.

Bayesian estimation of spatially varying mortality risk using tagged animal data

Abstract The survival of animals is impacted by landscapes of spatially varying mortality factors including habitat type, predation risk or harvest risk, among others. Characterization of these spatial mortality processes is important for managing animal populations and their habitats, yet this information has proved challenging to capture. Advances in telemetry now make it possible to monitor tagged individuals' locations through time for a wide range of taxa, providing opportunity to assess movement and mortality simultaneously through spatial time‐to‐event data. Existing time‐to‐event modelling frameworks have largely ignored spatially varying mortality processes or have treated an animal's location as fixed at a regional level. Here we present a general spatial survival model for analysing time‐to‐event data arising from animal telemetry. Our model has a flexible Cox regression form and can estimate the effects of conventional non‐spatial risk factors (size, seasonality, etc.), spatial covariates (e.g. habitat type) and spatial variation in risk not explained by covariates on mortality. We show how to fit our model using Bayesian methods and demonstrate applications of our model with several simulated examples and two animal telemetry case studies. Our model produced consistent and unbiased parameter estimates throughout simulations with a variety of spatial and non‐spatial hazards. In the first case study, data from 147 tagged caribou in British Columbia, Canada, revealed a spatially heterogeneous mortality landscape with caribou survival varying by elevation, likely in response to space use by predators. Our second case study involved a dataset of 390 acoustically tagged Atlantic cod in a southern Norwegian fjord where a marine protected area (MPA) was established during the study. We found that the MPA led to a shift from mostly fishing mortality to mostly natural mortality within the fjord and that these risks had markedly different spatial hazard patterns. Our spatial time‐to‐event model can make use of data from a variety of widely used telemetry technologies to characterize landscapes of mortality risks for different taxa. Our work provides new opportunities to inform the spatial ecology and management of fish and wildlife populations.

Population Pharmacokinetics and Exposure–Response Analysis of a Fixed‐Dose Combination of Ivermectin and Albendazole in Children, Adolescents, and Adults

Trichuris trichiura is a soil‐transmitted helminth causing intestinal disease. Albendazole is the standard treatment despite its moderate efficacy, which is improved when co‐administered with ivermectin. A fixed‐dose combination adds practical advantages mainly for mass drug administration. The aim of this article is to define the population pharmacokinetic models and exposure–response of an innovative albendazole/ivermectin combination. Data were obtained from a phase I clinical trial in healthy adults and from a phase II trial in children and adolescents infected with T. trichiura. Nonlinear mixed‐effects models were built for albendazole and ivermectin using NONMEM®. Area under the curve was calculated using the empirical Bayes estimates of the pharmacokinetic parameters of each individual and used for evaluation of exposure–response between cure rate and pharmacokinetic exposure. The pharmacokinetics of albendazole was described using a two‐compartmental model with first‐order absorption and the pharmacokinetics of ivermectin was described using a two‐compartmental model with zero‐order followed by first‐order absorption. Clearance and volume of distribution increased with body weight for both albendazole and ivermectin. Day 1 area under the curve of albendazole and ivermectin from the children and adolescents treated with the combination regimens were similar to the healthy adults treated with control drugs. A flat exposure–response relationship was observed between the cure rate and drug exposure. Population pharmacokinetic of a combination of albendazole and ivermectin in children, adolescents, and adults, either healthy or infected by T. trichiura was described. The dosage selected in the phase II trial was appropriate for the subsequent phase III.