CRTgeeDR: An R Package for Doubly Robust Generalized Estimating Equations Estimations in Cluster Randomized Trials with Missing Data

International audienceSemi-parametric approaches based on generalized estimating equation (GEE) are widelyused to analyse correlated outcomes. Most available softwares had been developed forlongitudinal settings. In this paper, we present a R package CRTgeeDR for estimatingparameters in marginal regression in cluster randomized trials (CRTs). Theory for adjustingfor missing at random outcomes by inverse-probability weighting methods (IPW)based on the use of a propensity score had been largely studied and implemented. Weexhibit that in CRTs most of the available softwares use an implementation of weightsthat lead to a bias in estimation if a non-independence working correlation structure ischosen. In CRTgeeDR, we solve this problem by using a different implementation whilekeeping the consistency properties of the IPW. Moreover, in CRTs using an augmentedGEE (AUG) allow to improve efficiency by adjusting for treatment-covariate interactionsand imbalance in baseline covariates between treatment groups using an outcome model.In CRTgeeDR, we extend the abilities of existing packages such as geepack and geeMto allow such data augmentation. Finally, one may want to combine IPW and AUG ina Doubly Robust (DR) estimator, which lead to consistent estimation when either thepropensity score or the outcome model corresponds to the true data generation process(Prague, Wang, Stephens, Tchetgen Tchetgen, and De gruttola 2015). The DR approachis implemented in CRTgeeDR. Simulations studies demonstrate the consistency of IPWimplemented in CRTgeeDR and the gains associated with the use of the DR for analyzinga binary outcome using a logit regression. Finally, we reanalyzed data from a sanitationCRT in developing countries (Guiteras, Levinsohn, and Mobarak 2015a) with the DRapproach compared to classical GEE and demonstrated a signiffcant intervention effect

Accounting for Interactions and Complex Inter-Subject Dependency in Estimating Treatment Effect in Cluster Randomized Trials with Missing Outcomes

Semi-parametric methods are often used for the estimation of intervention effects on correlated outcomes in cluster-randomized trials (CRTs). When outcomes are missing at random (MAR), Inverse Probability Weighted (IPW) methods incorporating baseline covariates can be used to deal with informative missingness. Also, augmented generalized estimating equations (AUG) correct for imbalance in baseline covariates but need to be extended for MAR outcomes. However, in the presence of interactions between treatment and baseline covariates, neither method alone produces consistent estimates for the marginal treatment effect if the model for interaction is not correctly specified. We propose an AUG-IPW estimator that weights by the inverse of the probability of being a complete case and allows different outcome models in each intervention arm. This estimator is doubly robust (DR), it gives correct estimates whether the missing data process or the outcome model is correctly specified. We consider the problem of covariate interference which arises when the outcome of an individual may depend on covariates of other individuals. When interfering covariates are not modeled, the DR property prevents bias as long as covariate interference is not present simultaneously for the outcome and the missingness. An R package is developed implementing the proposed method. An extensive simulation study and an application to a CRT of HIV risk reduction-intervention in South Africa illustrate the method.Comment: 27 pages, 5 table

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: An optimal control approach

We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The method presented here aims at regularizing the estimation problem in presence of model misspecifications, practical identifiability issues and unknown initial conditions. For doing so, we define our estimator as the minimizer of a cost function which incorporates a possible gap between the assumed model at the population level and the specific individual dynamic. The cost function computation leads to formulate and solve optimal control problems at the subject level. This control theory approach allows to bypass the need to know or estimate initial conditions for each subject and it regularizes the estimation problem in presence of poorly identifiable parameters. Comparing to maximum likelihood, we show on simulation examples that our method improves estimation accuracy in possibly partially observed systems with unknown initial conditions or poorly identifiable parameters with or without model error. We conclude this work with a real application on antibody concentration data after vaccination against Ebola virus coming from phase 1 trials. We use the estimated model discrepancy at the subject level to analyze the presence of model misspecification.European Union’s Horizon 2020 research and innovation programm

NPJ Vaccines

The persistence of the long-term immune response induced by the heterologous Ad26.ZEBOV, MVA-BN-Filo two-dose vaccination regimen against Ebola has been investigated in several clinical trials. Longitudinal data on IgG-binding antibody concentrations were analyzed from 487 participants enrolled in six Phase I and Phase II clinical trials conducted by the EBOVAC1 and EBOVAC2 consortia. A model based on ordinary differential equations describing the dynamics of antibodies and short- and long-lived antibody-secreting cells (ASCs) was used to model the humoral response from 7 days after the second vaccination to a follow-up period of 2 years. Using a population-based approach, we first assessed the robustness of the model, which was originally estimated based on Phase I data, against all data. Then we assessed the longevity of the humoral response and identified factors that influence these dynamics. We estimated a half-life of the long-lived ASC of at least 15 years and found an influence of geographic region, sex, and age on the humoral response dynamics, with longer antibody persistence in Europeans and women and higher production of antibodies in younger participants.Initiative for the creation of a Vaccine Research InstituteHorizon 2020 research and innovation programm

Temporal trends of population viral suppression in the context of Universal Test and Treat: the ANRS 12249 TasP trial in rural South Africa

Introduction: The universal test-and-treat (UTT) strategy aims to maximize population viral suppression (PVS), that is, the proportion of all people living with HIV (PLHIV) on antiretroviral treatment (ART) and virally suppressed, with the goal of reducing HIV transmission at the population level. This article explores the extent to which temporal changes in PVS explain the observed lack of association between universal treatment and cumulative HIV incidence seen in the ANRS 12249 TasP trial conducted in rural South Africa. Methods: The TasP cluster-randomized trial (2012 to 2016) implemented six-monthly repeat home-based HIV counselling and testing (RHBCT) and referral of PLHIV to local HIV clinics in 2 9 11 clusters opened sequentially. ART was initiated according to national guidelines in control clusters and regardless of CD4 count in intervention clusters. We measured residency status, HIV status, and HIV care status for each participant on a daily basis. PVS was computed per cluster among all resident PLHIV (≥16, including those not in care) at cluster opening and daily thereafter. We used a mixed linear model to explore time patterns in PVS, adjusting for sociodemographic changes at the cluster level. Results: 8563 PLHIV were followed. During the course of the trial, PVS increased significantly in both arms (23.5% to 46.2% in intervention, +22.8, p < 0.001; 26.0% to 44.6% in control, +18.6, p < 0.001). That increase was similar in both arms (p = 0.514). In the final adjusted model, PVS increase was most associated with increased RHBCT and the implementation of local trial clinics (measured by time since cluster opening). Contextual changes (measured by calendar time) also contributed slightly. The effect of universal ART (trial arm) was positive but limited. Conclusions: PVS was improved significantly but similarly in both trial arms, explaining partly the null effect observed in terms of cumulative HIV incidence between arms. The PVS gains due to changes in ART-initiation guidelines alone are relatively small compared to gains obtained by strategies to maximize testing and linkage to care. The achievement of the 90-90-90 targets will not be met if the operational and implementational challenges limiting access to care and treatment, often context-specific, are not properly addressed. Clinical trial number: NCT01509508 (clinicalTrials.gov)/DOH-27-0512-3974 (South African National Clinical Trials Register)

Modelling the response to vaccine in non-human primates to define SARS-CoV-2 mechanistic correlates of protection

The definition of correlates of protection is critical for the development of next-generation SARS-CoV-2 vaccine platforms. Here, we propose a model-based approach for identifying mechanistic correlates of protection based on mathematical modelling of viral dynamics and data mining of immunological markers. The application to three different studies in non-human primates evaluating SARS-CoV-2 vaccines based on CD40-targeting, two-component spike nanoparticle and mRNA 1273 identifies and quantifies two main mechanisms that are a decrease of rate of cell infection and an increase in clearance of infected cells. Inhibition of RBD binding to ACE2 appears to be a robust mechanistic correlate of protection across the three vaccine platforms although not capturing the whole biological vaccine effect. The model shows that RBD/ACE2 binding inhibition represents a strong mechanism of protection which required significant reduction in blocking potency to effectively compromise the control of viral replication.Initiative for the creation of a Vaccine Research InstituteInfrastructure nationale pour la modélisation des maladies infectieuses humaine

Use of dynamical models for treatment optimization in HIV infected patients

La plupart des patients infectés par le VIH ont une charge virale qui peut être rendue indétectable par des combinaisons antirétrovirales hautement actives (cART); cependant, il existe des effets secondaires aux traitements. L'utilisation des modèles mécanistes dynamiques basés sur des équations différentielles ordinaires (ODE) a considérablement amélioré les connaissances de la dynamique HIV-système immunitaire et permet d'envisager une personnalisation du traitement. L'objectif de ces travaux de thèse est d'améliorer les techniques statistiques d'estimation de paramètres dans les modèles mécanistes dynamiques afin de proposer des stratégies de surveillance et d'optimisation des traitements. Après avoir introduit NIMROD un algorithme d'estimation bayésienne basé sur une maximisation de la vraisemblance pénalisée, nous montrons la puissance des approches mécanistes dynamiques pour l'évaluation des effets traitements par rapport aux méthodes descriptives d'analyse des trajectoires des biomarqueurs. Puis, nous définissons le « modèle à cellules cibles », un système ODE décrivant la dynamique du VIH et des CD4. Nous montrons qu'il possède de bonnes capacités prédictives. Nous proposons une preuve de concept de la possibilité de contrôler individuellement la dose de traitement. Cette stratégie adaptative réajuste la dose du patient en fonction de sa réaction à la dose précédente par une procédure bayésienne. Pour finir, nous introduisons la possibilité de l’'individualisation des changements de cART. Ce travail passe par la quantification in vivo d'effets de cART en utilisant des indicateurs d'activité antivirale in vitro. Nous discutons la validité des résultats et les étapes méthodologiques nécessaires pour l'intégration de ces méthodes dans les pratiques cliniques.Most HIV-infected patients viral loads can be made undetectable by highly active combination of antiretroviral therapy (cART), but there are side effects of treatments. The use of dynamic mechanistic models based on ordinary differential equations (ODE) has greatly improved the knowledge of the dynamics of HIV and of the immune system and can be considered for personalization of treatment. The aim of these PhD works is to improve the statistical techniques for estimating parameters in dynamic mechanistic models so as to elaborate strategies for monitoring and optimizing treatments. We present an algorithm and program called NIMROD using Bayesian inference based on the maximization of the penalized likelihood. Then, we show the power of dynamic mechanistic approaches for the evaluation of treatment effects compared to methods based on the descriptive analysis of the biomarkers trajectories. Next, we build the “target cells model “, an ODE system of the dynamics between the HIV and CD4. We demonstrate it has good predictive capabilities. We build a proof of concept for drug dose individualization. It consists in tuning the dose of the patient based on his reaction to the previous doses using a Bayesian update procedure. Finally, we introduce the possibility of designing an individualized change of cART. This work involves the quantification of in vivo effects of cART using in vitro antiviral activity indicators. We discuss the validity of the results and the further steps needed for the integration of these methods in clinical practice

SAMBA: a Novel Method for Fast Automatic Model Building in Nonlinear Mixed-Effects Models

The success of correctly identifying all the components of a nonlinear mixed-effects model is far from straightforward: it is a question of finding the best structural model, determining the type of relationship between covariates and individual parameters, detecting possible correlations between random effects, or also modeling residual errors. We present the SAMBA (Stochastic Approximation for Model Building Algorithm) procedure and show how this algorithm can be used to speed up this process of model building by identifying at each step how best to improve some of the model components. The principle of this algorithm basically consists in 'learning something' about the 'best model', even when a 'poor model' is used to fit the data. A comparison study of the SAMBA procedure with SCM and COSSAC show similar performances on several real data examples but with a much-reduced computing time. This algorithm is now implemented in Monolix and in the R package Rsmlx

Estimation for dynamical systems using a population-based Kalman filter - Applications to pharmacokinetics models

Many methods exist to identify parameters of dynamical systems. Unfortunately, in addition to the classical measurement noise and under-sampling drawbacks, mean and variance priors of the estimated parameters can be very vague. These difficulties can lead the estimation procedure to underfitting. In clinical studies, a circumvention consists in using the fact that multiple independent patients are observed as proposed by nonlinear mixed-effect models. However, these very effective approaches can turn to be time-consuming or even intractable when the model complexity increases. Here, we propose an alternative strategy of controlled complexity. We first formulate a population least square estimator and its associated a Kalman based filter, hence defining a robust large population sequential estimator. Then, to reduce and control the computational complexity, we propose a reduced-order version of this population Kalman filter based on a clustering technique applied to the observations. Using simulated pharmacokinetics data and the theophylline pharmacokinetics data, we compare the proposed approach with literature methods. We show that using the population filter improves the estimation performance compared to the classical and fast patient-by-patient Kalman filter and leads to estimation results comparable to state-of-the-art population-based approaches. Then, the reduced-order version allows to drastically reduce the computational time for equivalent estimation and prediction

Comparison of AUC in clinical trials with follow up censoring: Application to HIV therapeutic vaccines

International audienc