An Efficiency Comparison between Concentration-Response Analysis and Dose-Response Analysis through Simulation
Alienor Berges, Bart Laurijssens, Chao Chen
GlaxoSmithkline, Clinical Pharmacology Modelling & Simulation, Greenford, UK
Background: Identifying the dose of optimal benefit-risk ratio is crucial in drug development, therefore confident and efficient characterisation of efficacy or toxicity as a function of dose is important. Using concentration-response relationship as a potentially more powerful tool for dose finding is increasingly appreciated. However, PK sampling is inconvenient; drug assays are costly; and PKPD analysis is labour intensive and time consuming. In this investigation, we attempted to quantify the incremental value of concentration-response analysis (CR) over dose-response analysis (DR).
Objectives: The objective of the current work is to compare the accuracy and precision of ED50 estimation directly through DR and indirectly through CR analyses in common dose-finding scenarios.
Methods: Response of a hypothetical drug as a function of steady-state concentration was described by a direct Emax model with a fixed Emax. Three hundred replicate parallel dose-ranging trials were simulated using R software to investigate the impact of the following drug and design properties on bias and imprecision of ED50 estimation as a function of sample size: inter-individual variability in CL/F, inter-individual variability in EC50, response measurement error, top dose and the number of dose groups. For each replicate, CR and DR models were fitted in R. Mean bias and imprecision for ED50 in each scenario were calculated for CR and DR. To allow comparison between the two analyses, the typical value of ED50 from the CR approach was calculated using CL/F and EC50 estimates.
Results: Under the scenarios investigated, higher variability in EC50 and less dose groups were the most important causes for greater bias and imprecision in ED50 estimation for both CR and DR. CR consistently out-performed DR, although the difference was not large under all circumstances. As expected, higher variability in CL/F differentially increased bias and imprecision for DR analysis over CR analysis. The difference in these metrics between CR and DR was not sensitive to response measurement error, top dose or variability in EC50.
Conclusions: The work reported here forms a simulation frame work for assessing the value added by PK sampling and PKPD analysis in dose finding. In practice, simulation parameters can be modified based on drug prior and potential design options to suit specific project needs. These preliminary results are limited to a parallel design with fixed Emax. Ongoing further investigation includes situations of cross-over design and the needs to estimate Emax.
