Mathematical Sciences: Topics in Semiparametric Inference, with Special Reference to Survival Analysis

对半参数推理问题的统计研究将进行，其中大多数与生存分析有关，还有一些具有序列性质。在双样本加速寿命模型中，将基于生存分析数据，对相对尺度参数进行序贯检验。该模型是半参数的，即相对尺度参数是一个参数分量，而基线分布是非参数分量。将针对这个问题开发顺序有效分数测试，作为顺序logrank测试的替代方案。更一般的版本也将被分析。我们还将研究使用截尾数据的加速寿命模型的估计。设置将包括对生存数据的顺序临床试验中经过时间的研究，对由脆弱性引起的双变量模型的推断，对比例平均剩余寿命模型的推断，半参数模型中的加权U统计，大样本“完整性”和蒙特卡洛试验的顺序停止规则。

Statistical research on problems in semiparametric inference will be conducted with most relating to survival analysis and several with a sequential nature. Sequential tests will be constructed for the relative-scale parameter based on survival analysis data with censoring in a two-sample accelerated-life model. The model is semiparametric in that the relative scale parameter is a parametric component while the baseline distribution is a nonparametric component. Sequential effective score tests will be developed for this problem as an alternative to sequential logrank tests. More general versions of this will also be analyzed. Estimation will also be studied in accelerated- life models with censored data. The settings will include the study of elapsed time in sequential clinical trials on survival data, inference for bivariate models induced by frailties, inference for proportional-mean-residual-life models, weighted U- statistics in semiparametric models, large-sample "completeness", and sequential stopping rules for Monte Carlo tests.