Robust designs in longitudinal studies accounting for parameter and model uncertainties – application to count data

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.

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.

Optimized Rhombic Experimental Dynamic Checkerboard Designs to Elucidate Pharmacodynamic Drug Interactions of Antibiotics

PURPOSE

Quantification of pharmacodynamic interactions is key in combination therapies, yet conventional checkerboard experiments with up to 10 by 10 combinations are labor-intensive. Therefore, this study provides optimized experimental rhombic checkerboard designs to enable an efficient interaction screening with significantly reduced experimental workload.

METHODS

Based on the general pharmacodynamic interaction (GPDI) model implemented in Bliss Independence, a novel rhombic 'dynamic' checkerboard design with quantification of bacteria instead of turbidity as endpoint was developed. In stochastic simulations and estimations (SSE), the precision and accuracy of interaction parameter estimations and classification rates of conventional reference designs and the newly proposed rhombic designs based on effective concentrations (EC) were compared.

RESULTS

Although a conventional rich design with 20-times as many combination scenarios provided estimates of interaction parameters with higher accuracy, precision and classification rates, the optimized rhombic designs with one natural growth scenario, three monotherapy scenarios per combination partner and only four combination scenarios were still superior to conventional reduced designs with twice as many combination scenarios. Additionally, the rhombic designs were able to identify whether an interaction occurred as a shift on maximum effect or EC50 with > 98%. Overall, effective concentration-based designs were found to be superior to traditional standard concentrations, but were more challenged by strong interaction sizes exceeding their adaptive concentration ranges.

CONCLUSION

The rhombic designs proposed in this study enable a reduction of resources and labor and can be a tool to streamline higher throughput in drug interaction screening.

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.