The nonparametric analysis of interval-censored failure time data
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By interval-censored failure time data, we mean that the failure time of interest is observed to belong to some windows or intervals, instead of being known exactly. One would get an interval-censored observation for a survival event if a subject has not experienced the event at one follow-up time but had experienced the event at the next follow-up time. Interval-censored data include right-censored data (Kalbfleisch and Prentice, 2002) as a special case. Nonparametric comparison of survival functions is one of the main tasks in failure time studies such as clinical trials. For interval-censored failure time data, a few nonparametric test procedures have been developed. However, due to the strict restrictions of existing nonparametric tests and practical demands, some new nonparametric tests need to be developed. This dissertation consists of four parts. In the first part, we propose a new class of test procedures whose asymptotic distributions are established under both null and alternative hypotheses, since all of the existing test procedures cannot be used if one intends to perform some power or sample size calculation under the alternative hypothesis. Some numerical results have been obtained from a simulation study for assessing the finite sample performance of the proposed test procedure. Also we applied the proposed method to a real data set arising from an AIDS clinical trial concerning the opportunistic infection cytomegalovirus (CMV). The second part of this dissertation will focus on the nonparametric test for intervalcensored data with unequal censoring. As we know, one common drawback or restriction of the nonparametric test procedures given in the literature is that they can only apply to situations where the observation processes follow the same distribution among different treatment groups. To remove the restriction, a test procedure is proposed, which takes into account the difference between the distributions of the censoring variables. Also the asymptotic distribution of the test statistics is
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