Order restricted assumption is usual common choice for any methodology used, primary to increase the power of inference. Typically, it reduces to monotonicity assumption and inference against simple order alternatives.
In this presentation, we will review various aspects of order restricted dose-response modelling: approaches to tackle the inference, model selection, estimation, model averaging, etc. We will focus on early drug development stage, with only small dataset available. Specifically, multiple contrast tests will be introduced, together with their Bayesian alternative: Bayesian variable selection method.
Bornkamp, B. and Pinheiro, J. C. and Bretz, F. (2009) MCPMod - An R Package for the Design and Analysis of Dose-Finding Studies. Journal of Statistical Software, 29(7):1-23
Kuiper, Rebecca M., and Gerhard, Daniel, and Hothorn, Ludwig A. (2014) Identification of the Minimum Effective Dose for Normally Distributed Endpoints Using a Model Selection Approach. Statistics in Biopharmaceutical Research. 6(1):55-66
Otava, Martin and Shkedy, Ziv and Lin, Dan and Goehlmann, Hinrich W.H. and Bijnens, Luc and Talloen, Willem and Kasim, Adetayo (2014) Dose-Response Modeling Under Simple Order Restrictions Using Bayesian Variable Selection Methods. Statistics in Biopharmaceutical Research, 6(3):252-262
Whitney, Melissa, and Ryan, Louise (2009) Quantifying Dose-Response Uncertainty Using Bayesian Model Averaging. In book: Uncertainty Modeling in Dose Response: Bench Testing Environmental Toxicity. Editor: Cooke, Roger C. John Wiley & Sons, Inc., p 165-179.