Mathematical Sciences: Asymptotic Methods for Order Restricted Inference in Survival Analysis

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Proposal: DMS 9504891 PI: Jens Praestgaard Institution: University of Iowa Title: Asymptotic Methods for Order Restricted Inference in Survival Analysis ABSTRACT: The purpose of the research is to develop large-sample theory for inference from survival data when the unknown parameters exhibit order restrictions. Such restrictions occur frequently in survival analysis. For example, if a clinical trial involves administering a drug in increasing doses to the cohorts under study, then the survival curves computed for each group should be ordered according to dose level. In linkage analysis, for the purpose of mapping a quantitative genetic trait, it may be known that the trait under study is more prevalent for one genotype than for others. Although appropriate estimators in these settings are known, their distributional properties have not been studied. Thus, order restricted methods are often not used when it would potentially help the data analysis. For estimation purposes it would give estimators with higher degree of accuracy. For testing purposes it would give higher power to be able to consider order restricted alternatives. The research centers on investigating statistical methods in the presence of order restrictions. These restrictions occur often in biotechnological problems. For instance, in a clinical trial to determine drug efficacy, it is often the case that the drug is administered in increasing doses. In genetical linkage analysis it is often known that a certain genotype lowers the time until the onset of a disease more than do other possible genotypes. If the interest is on determining the drug efficacy (in the first case) or finding out where the gene is located (second case), then the statistical methods, which separate the noise in the data from the signal, must incorporate these known orderings. The investigators study ways of incorporating such information. They believe that the resulting statistical method ology will be more appropriate than present methods for dealing with biotechnological data where such orderings are present.