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Use of Simultaneous Inference Under Order Restriction, Stepdown Testing Procedure and Stage-wise Sequential Optimal Design in Clinical Dose Study

This dissertation discusses the design approaches of adaptive dose escalation study and the analysis methods of dose study data, and the relationship between the study design approach and data analysis methods.A general max-min approach to construct simultaneous confidence Intervals for the monotone means of correlated and normally istributed random samples is proposed to analyze correlated dose response data. The approach provides an accurate, flexible and computationally easy way to obtain critical values of simultaneous confidence intervals under monotone order restriction.Stepdown testing procedure for analyzing dose study data is examined and an modified stepdown testing approach is proposed to incorporate the adaptive sampling nature of the study data. An approximate mixture normal distribution of the dose response is proposed to analyze the binary outcome with small sample size at the first stage of the adaptive design.Finally, an optimal stage-wise adptive clinical dose study design is proposed to be applied in dose escalation study with binary outcome and correlated dose response. The study design criteria is defined as a weighted average power to identify all effective dose levels. A back induction algorithm is used to obtain the design parameters. The values of optimal design parameters vary when different analysis methods are used to analyze the study data.Simulation studies are performed to illustrate the two proposed analysis methods and the proposed optimal design approach.