Model identification for dose response signal detection
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Date
2012-08-28
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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.
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Keywords
contrast tests, dose response studies, likelihood ratio test, model identification, nonlinear regression