Model identification for dose response signal detection

Abstract

We consider the problem of detecting a dose response signal if several competing regression models are available to describe the dose response relationship. In particular, we re-analyze the MCP-Mod approach from Bretz et al. (2005), which has become a very popular tool for this problem in recent years. We propose an improvement based on likelihood ratio tests and prove that in linear models this approach is always at least as powerful as the MCP-Mod method. This result remains valid in nonlinear regression models with identi able parameters. However, for many commonly used nonlinear dose response models the regression parameters are not identi able and standard likelihood ratio test theory is not applicable. We thus derive the asymptotic distribution of likelihood ratio tests in regression models with a lack of identifiability and use this result to simulate the quantiles based on Gaussian processes. The new method is illustrated with a real data example and compared to the MCP-Mod procedure using theoretical investigations as well as simulations.