Design, optimization, and inference of biphasic decay of infectious virus particles.

Virus population dynamics are driven by counter-balancing forces of production and loss. Whereas viral production arises from complex interactions with susceptible hosts, the loss of infectious virus particles is often approximated as a first-order kinetic process. As such, experimental protocols to measure infectious virus loss are not typically designed to identify non-exponential decay processes. Here, we propose methods to evaluate if an experimental design is adequate to identify multiphasic virus particle decay and to optimize the sampling times of decay experiments, accounting for uncertainties in viral kinetics. First, we evaluate synthetic scenarios of biphasic decays, with varying decay rates and initial proportions of subpopulations. We show that robust inference of multiphasic decay is more likely when the faster decaying subpopulation predominates insofar as early samples are taken to resolve the faster decay rate. Moreover, design optimization involving non-equal spacing between observations increases the precision of estimation while reducing the number of samples. We then apply these methods to infer multiple decay rates associated with the decay of bacteriophage ('phage') Φ D 9 , an evolved isolate derived from phage Φ 21 . A pilot experiment confirmed that Φ D 9 decay is multiphasic, but was unable to resolve the rate or proportion of the fast decaying subpopulation(s). We then applied a Fisher information matrix-based design optimization method to propose non-equally spaced sampling times. Using this strategy, we were able to robustly estimate multiple decay rates and the size of the respective subpopulations. Notably, we conclude that the vast majority (94%) of the phage Φ D 9 population decays at a rate 16-fold higher than the slow decaying population. Altogether, these results provide both a rationale and a practical approach to quantitatively estimate heterogeneity in viral decay.

Macrophage-induced reduction of bacteriophage density limits the efficacy of in vivo pulmonary phage therapy.

The rise of antimicrobial resistance has led to renewed interest in evaluating phage therapy. In murine models highly effective treatment of acute pneumonia caused by Pseudomonas aeruginosa relies on the synergistic antibacterial activity of bacteriophages with neutrophils. Here, we show that depletion of alveolar macrophages (AM) shortens the survival of mice without boosting the P. aeruginosa load in the lungs. Unexpectedly, upon bacteriophage treatment, pulmonary levels of P. aeruginosa were significantly lower in AM-depleted than in immunocompetent mice. To explore potential mechanisms underlying the benefit of AM-depletion in treated mice, we developed a mathematical model of phage, bacteria, and innate immune system dynamics. Simulations from the model fitted to data suggest that AM reduce bacteriophage density in the lungs. We experimentally confirmed that the in vivo decay of bacteriophage is faster in immunocompetent compared to AM-depleted animals. These findings demonstrate the involvement of feedback between bacteriophage, bacteria, and the immune system in shaping the outcomes of phage therapy in clinical settings.

Robust and Adaptive Two-stage Designs in Nonlinear Mixed Effect Models.

To get informative studies for nonlinear mixed effect models (NLMEM), design optimization can be performed based on Fisher Information Matrix (FIM) using the D-criterion. Its computation requires knowledge about models and parameters, which are often prior guesses. Thus, adaptive designs composed of several stages may be used. Robust approach can also be used to account for various candidate models. In the estimation step of a given stage, model selection (MS) or model averaging (MA) can be performed. In this work we propose a new two-stage adaptive design strategy, based on the robust expected FIM and MA over several candidate models. The methodology is applied to a clinical trial simulation in ophthalmology to optimize doses and time measurements. A set of dose-response candidate models is defined, and one-stage designs are compared to two-stage 50/50 designs (i.e., each stage performed with half of the available subjects), using either local optimal design or robust design, and performing analysis with one model, MS or MA. Performing a two-stage design with MS at the interim analysis can correct the choice of a wrong model for designing the first stage. Overall, starting from a robust design (1- or 2-stage) is valuable and leads to reasonable bias and precision. The proposed robust adaptive design strategy is a new tool to design longitudinal studies that could be used in different therapeutic areas.

Combination of in vivo phage therapy data with in silico model highlights key parameters for pneumonia treatment efficacy.

The clinical (re)development of bacteriophage (phage) therapy to treat antibiotic-resistant infections faces the challenge of understanding the dynamics of phage-bacteria interactions in the in vivo context. Here, we develop a general strategy coupling in vitro and in vivo experiments with a mathematical model to characterize the interplay between phage and bacteria during pneumonia induced by a pathogenic strain of Escherichia coli. The model allows the estimation of several key parameters for phage therapeutic efficacy. In particular, it quantifies the impact of dose and route of phage administration as well as the synergism of phage and the innate immune response on bacterial clearance. Simulations predict a limited impact of the intrinsic phage characteristics in agreement with the current semi-empirical choices of phages for compassionate treatments. Model-based approaches will foster the deployment of future phage-therapy clinical trials.

Finding optimal design in nonlinear mixed effect models using multiplicative algorithms.

BACKGROUND AND OBJECTIVES: To optimize designs for longitudinal studies analyzed by nonlinear mixed effect models (NLMEMs), the Fisher information matrix (FIM) can be used. In this work, we focused on the multiplicative algorithms, previously applied in standard individual regression, to find optimal designs for NLMEMs. METHODS: We extended multiplicative algorithms to mixed models and implemented the algorithm both in R and in C. Then, we applied the algorithm to find D-optimal designs in two longitudinal data examples, one with continuous and one with binary outcome. RESULTS: For these examples, we quantified the improved speed when C is used instead of R. Design optimization using the multiplicative algorithm led to designs with D-efficiency gains between 13% and 25% compared to non-optimized designs. CONCLUSION: We found that the multiplicative algorithm can be used efficiently to design longitudinal studies.

Comparison of Various Phase I Combination Therapy Designs in Oncology for Evaluation of Early Tumor Shrinkage Using Simulations.

There is still a lack of efficient designs for identifying the dose response in oncology combination therapies in early clinical trials. The concentration response relationship can be identified using the early tumor shrinkage time course, which has been shown to be a good early response marker of clinical efficacy. The performance of various designs using an exposure-tumor growth inhibition model was explored using simulations. Different combination effects of new drug M and cetuximab (reference therapy) were explored first assuming no effect of M on cetuximab (to investigate the type I error (α)), and subsequently assuming additivity or synergy between cetuximab and M. One-arm, two-arm, and four-arm designs were evaluated. In the one-arm design, 60 patients received cetuximab + M. In the two-arm design, 30 patients received cetuximab and 30 received cetuximab + M. In the four-arm design, in addition to cetuximab and cetuximab + M as standard doses, combination arms with lower doses of cetuximab were evaluated (15 patients/arm). Model-based predictions or "simulated observations" of early tumor shrinkage at week 8 (ETS8) were compared between the different arms. With the same number of individuals, the one-arm design showed better statistical power than other designs but led to strong inflation of α in case of misestimated reference for ETS8 value. The two-arm design protected against this misestimation and, with the same total number of subjects, would provide higher statistical power than a four-arm design. However, a four-arm design would be helpful for exploring more doses of cetuximab in combination with M to better understand the interaction.

Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes.

To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.