Statistical inference for normal means with order restrictions and applications to dose-response studies

Davis, Karelyn Alexandrea (2004) Statistical inference for normal means with order restrictions and applications to dose-response studies. Masters thesis, Memorial University of Newfoundland.

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Abstract

Scientific experiments often compare several treatment means with a control mean. In particular, such multiple comparisons arise in biopharmaceutical studies in which it is desirable to conduct the inferences in a specified order and failure to achieve the desired inference at any step renders subsequent comparisons unnecessary. In clinical trials, an important dosing quantity is the minimum effective dose (MED), defined as the minimum dose such that the mean response is clinically significantly better than the mean response of the control by a practical significant difference. In relation to MED estimation, previous authors have either failed to account for the monotonicity of the dose-response means or considered the case of a zero clinically significant difference. In this thesis, an innovative approach using Kuhn-Tucker conditions to evaluate the optimal confidence lower bound at each step in a closed step-down testing procedure is derived and simulation results are presented.

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