A Study of the Minimum p-value and Related Methods for the Identification of Treatment-Sensitive Groups

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Li, Na
predictive classification , cutpoint , minimum p-value method , bootstrap , profile method
In clinical practices, a fundamentally important problem is to identify a subgroup of patients who may benefit more in terms of a clinical outcome from a certain treatment based on a specific clinical variable or biomarker, which is referred as predictive classification in this thesis. The clinical variable or biomarker used for predictive classification is usually continuous and, therefore, a cutpoint needs to be determined for the definition of the subgroup. The commonly adopted methods, the minimum p-value method and the profile method, suffer from the type I error inflation and/or the identifiability issue. In this thesis research, we first propose bootstrap-based methods for the adjustment of the minimum p-value method for predictive classifications with respect to a continuous clinical outcome in both identifiable and non-identifiable cases under random designs and fixed designs, respectively. Since the minimum p-value test statistics diverge at a rate sqrt(n) (n is the sample size) under the framework of the generalized linear model with non-identity link function and the Cox model for respectively categorical and time to event clinical outcomes, bootstrap-based methods are proposed to adjust the profile methods for predictive classifications in both identifiable and non-identifiable cases. The theoretical properties of the proposed adjustments are investigated and simulation studies are conducted to evaluate their fixed sample size performance. In addition, the proposed methods are applied to analyze the data from a cancer clinical trial.
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