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PurposeNon-linear mixed effect models are widely used and increasingly integrated into decision-making processes. Propagating uncertainty is an important element of this process, and while standard errors (SE) on pa- rameters are most often computed using asymptotic approaches, alternative methods such as the bootstrap are also available. In this article, we propose a modified residual parametric bootstrap taking into account the different levels of variability involved in these models.MethodsThe proposed approach uses samples from the individual conditional distribution, and was implemented in R using the saemix algorithm. We performed a simulation study to assess its performance in different scenarios, comparing it to the asymptotic approximation and to standard bootstraps in terms of coverage, also looking at bias in the parameters and their SE.ResultsSimulations with an Emax model with different designs and sigmoidicity factors showed a similar coverage rate to the parametric bootstrap, while requiring less hypotheses. Bootstrap improved coverage in several scenarios compared to the asymptotic method especially for the variance param-eters. However, all bootstraps were sensitive to estimation bias in the original datasets.ConclusionsThe conditional bootstrap provided better coverage rate than the traditional residual bootstrap, while preserving the structure of the data generating process.

We modeled the viral dynamics of 13 untreated patients infected with severe acute respiratory syndrome‐coronavirus 2 to infer viral growth parameters and predict the effects of antiviral treatments. In order to reduce peak viral load by more than two logs, drug efficacy needs to be > 90% if treatment is administered after symptom onset; an efficacy of 60% could be sufficient if treatment is initiated before symptom onset. Given their pharmacokinetic/pharmacodynamic properties, current investigated drugs may be in a range of 6–87% efficacy. They may help control virus if administered very early, but may not have a major effect in severely ill patients.

Parallel designs with an end-of-treatment analysis are commonly used for randomised trials, but they remain challenging to conduct in rare diseases due to small sample size and heterogeneity. A more powerful alternative could be to use model-based approaches. We investigated the performance of longitudinal modelling to evaluate disease-modifying treatments in rare diseases using simulations. Our setting was based on a model describing the progression of the standard clinician-reported outcome SARA score in patients with ARCA (Autosomal Recessive Cerebellar Ataxia), a group of ultra-rare, genetically defined, neurodegenerative diseases. We performed a simulation study to evaluate the influence of trials settings on their ability to detect a treatment effect slowing disease progression, using a previously published non-linear mixed effect logistic model. We compared the power of parallel, crossover and delayed start designs, investigating several trial settings: trial duration (2 or 5 years); disease progression rate (slower or faster); magnitude of residual error ( =2 or =0.5); number of patients (100 or 40); method of statistical analysis (longitudinal analysis with non-linear or linear models; standard statistical analysis), and we investigated their influence on the type 1 error and corrected power of randomised trials. In all settings, using non-linear mixed effect models resulted in controlled type 1 error and higher power (88% for a parallel design) than a rich (75% for a parallel design) or sparse (49% for a parallel design) linear mixed effect model or standard statistical analysis (36% for a parallel design). Parallel and delayed start designs performed better than crossover designs. With slow disease progression and high residual error, longer durations are needed for power to be greater than 80%, 5 years for slower progression and 2 years for faster progression ataxias. In our settings, using non-linear mixed effect modelling allowed all three designs to have more power than a standard end-of-treatment analysis. Our analysis also showed that delayed start designs are promising as, in this context, they are as powerful as parallel designs, but with the advantage that all patients are treated within this design.

Where there are a limited number of patients, such as in a rare disease, clinical trials in these small populations present several challenges, including statistical issues. This led to an EU FP7 call for proposals in 2013. One of the three projects funded was the Innovative Methodology for Small Populations Research (InSPiRe) project. This paper summarizes the main results of the project, which was completed in 2017. The InSPiRe project has led to development of novel statistical methodology for clinical trials in small populations in four areas. We have explored new decision-making methods for small population clinical trials using a Bayesian decision-theoretic framework to compare costs with potential benefits, developed approaches for targeted treatment trials, enabling simultaneous identification of subgroups and confirmation of treatment effect for these patients, worked on early phase clinical trial design and on extrapolation from adult to pediatric studies, developing methods to enable use of pharmacokinetics and pharmacodynamics data, and also developed improved robust meta-analysis methods for a small number of trials to support the planning, analysis and interpretation of a trial as well as enabling extrapolation between patient groups. In addition to scientific publications, we have contributed to regulatory guidance and produced free software in order to facilitate implementation of the novel methods.

The development of new treatments for rare neurological diseases (RNDs) may be very challenging due to limited natural history data, lack of relevant biomarkers and clinical endpoints, small and heterogeneous patient populations, and other complexities. A systematic approach is needed for comparing various design and analysis strategies to identify “optimal” approaches for a clinical trial in a chosen RND with the given resource constraints. For this purpose, we propose a pharmacometrics‐informed clinical scenario evaluation framework (CSE‐PMx), which includes some important research hallmarks relevant to RND clinical trials: a disease progression model for simulating individual longitudinal outcomes, the choice of a suitable randomization method for trial design, and an option to perform subsequent statistical analysis with randomization tests. We illustrate the utility of CSE‐PMx for an exemplary randomized trial to compare the disease‐modifying effect of an experimental treatment versus control in patients with Autosomal‐Recessive Spastic Ataxia Charlevoix Saguenay (ARSACS). In the considered example, our simulation evidence suggests that a nonlinear mixed‐effects model (NLMEM) with a population‐based likelihood ratio test analysis is valid, robust, and more powerful than some conventional methods such as two‐sample t‐test, analysis of covariance (ANCOVA), or a mixed model with repeated measurements (MMRM). Our proposed framework is very flexible and generalizable to clinical research in other rare disease indications.

A joint modeling framework was developed using data from 75 patients of early amcenestrant phase I–II AMEERA‐1‐2 dose escalation and expansion cohorts. A semi‐mechanistic tumor growth inhibition (TGI) model was developed. It accounts for the dynamics of sensitive and resistant tumor cells, an exposure‐driven effect on tumor proliferation of sensitive cells, and a delay in the initiation of treatment effect to describe the time course of target lesion tumor size (TS) data. Individual treatment exposure overtime was introduced in the model using concentrations predicted by a population pharmacokinetic model of amcenestrant. This joint modeling framework integrated complex RECISTv1.1 criteria information, linked TS metrics to progression‐free survival (PFS), and was externally evaluated using the randomized phase II trial AMEERA‐3. We demonstrated that the instantaneous rate of change in TS (TS slope) was an important predictor of PFS and the developed joint model was able to predict well the PFS of amcenestrant phase II monotherapy trial using only early phase I–II data. This provides a good modeling and simulation tool to inform early development decisions.

Postpartum hypocalcemia is a problem in dairy cows. Both the Jersey vs. Holstein breed and increasing parity are known risk factors. Our objectives were: (1) to evaluate a simple approach to provide dietary acidogenic salts suitable for application on small dairies and (2) to evaluate the combined effects of degree of acidification and oral Ca supplementation along with breed and parity group on periparturient Ca status of Holstein and Jersey cows. Cows were moved weekly from the far-off dry pen at 260 days pregnant to the close-up pen, where all cows received the acidogenic diets. The diet was offered as a total mixed ration and CaCl2, and our source of acidogenic salts was top-dressed in liquid form and mixed in by hand. Thirty-six cows were blocked by parity group (parity = 2 vs. parity ≥ 3) and breed (Holstein vs. Jersey) and assigned to one of two treatments (no intervention or postpartum oral Ca bolus supplementation) in an alternating fashion, based on expected date of parturition. Urinary acidification appeared complete within 3–4 days. Increased urinary Ca excretion was >93% of maximum from 7–21 days before falling to <5% of maximum by 28 days. Serum Ca concentrations 12–24 h postpartum were lower for Jerseys vs. Holsteins and for parity ≥ 3 vs. parity = 2 cows. Serum Ca over 6–48 h postpartum decreased and increased, respectively, with oral Ca supplementation for parity = 2 and parity ≥ 3 cows. Decreased prepartum urinary Ca excretion and increased colostrum yield appear to be independent risk factors of hypocalcemia for parity ≥ 3 Jerseys.

The treatment of respiratory tract infections is threatened by the emergence of bacterial resistance. Immunomodulatory drugs, which enhance airway innate immune defenses, may improve therapeutic outcome. In this concept paper, we aim to highlight the utility of pharmacometrics and Bayesian inference in the development of immunomodulatory therapeutic agents as an adjunct to antibiotics in the context of pneumonia. For this, two case studies of translational modelling and simulation frameworks are introduced for these types of drugs up to clinical use. First, we evaluate the pharmacokinetic/pharmacodynamic relationship of an experimental combination of amoxicillin and a TLR4 agonist, monophosphoryl lipid A, by developing a pharmacometric model accounting for interaction and potential translation to humans. Capitalizing on this knowledge and associating clinical trial extrapolation and statistical modelling approaches, we then investigate the TLR5 agonist flagellin. The resulting workflow combines expert and prior knowledge on the compound with the in vitro and in vivo data generated during exploratory studies in order to construct high-dimensional models considering the pharmacokinetics and pharmacodynamics of the compound. This workflow can be used to refine preclinical experiments, estimate the best doses for human studies, and create an adaptive knowledge-based design for the next phases of clinical development.

The SO is based on a hierarchical structure defined to separate independent output information or results obtained from different modeling tasks (e.g., estimation, simulation, and optimal design), whereas standardizing and providing consistent definition of output structure from different estimation methods and tools (e.g., for maximum likelihood and stochastic or sample-based estimation). AIC, Akaike information criterion; BIC, Bayesian information criteria; CI, confidence interval; DIC, Deviance Information Criterion; FIM, Fisher Information Matrix; MLE, maximum likelihood estimation; OF, Objective Function; PDF, probability density function VPC, Visual Predictive Check. [...]the element contains the values of various estimated objective function measures, such as the likelihood, log-likelihood, tool-specific objective function, deviance, and individual contributions to likelihood, as well as the calculated values of the most common information criteria used for model selection purpose (i.e., Akaike information criterion, Bayesian information criteria, and Deviance Information Criterion). [...]any level below (e.g., occasion) or above (e.g., country or center) the subject level can be considered.

The aim of this study is to define and illustrate metrics for the external evaluation of a population model. In this paper, several types of metrics are defined: based on observations (standardized prediction error with or without simulation and normalized prediction distribution error); based on hyperparameters (with or without simulation); based on the likelihood of the model. All the metrics described above are applied to evaluate a model built from two phase II studies of gliclazide. A real phase I dataset and two datasets simulated with the real dataset design are used as external validation datasets to show and compare how metrics are able to detect and explain potential adequacies or inadequacies of the model. Normalized prediction errors calculated without any approximation, and metrics based on hyperparameters or on objective function have good theoretical properties to be used for external model evaluation and showed satisfactory behaviour in the simulation study. For external model evaluation, prediction distribution errors are recommended when the aim is to use the model to simulate data. Metrics through hyperparameters should be preferred when the aim is to compare two populations and metrics based on the objective function are useful during the model building process.