MULTIVARIATE SURVIVAL CURVE ANALYSIS

估计生存函数并预测未来的寿命 患者是重要的医疗问题。 临床研究中的数据是 经常被审查，因为不是所有的研究成员都达到规定的 研究结束前的终点。 此外，超过一个 单一的时间测量通常是感兴趣的，例如，时间 直到疾病复发和死亡的时间都可能是 被视为重要的变量。 统计方法的发展 本文的目的是对这种多元删失数据进行分析， research. 该研究将包括开发，测试和研究 三个新程序的最优性，以及测试和 研究最有前途的现有分析技术。 的 提出的程序是非参数的，因为参数形式可以是 在多个维度上都有很大的限制 对于每一个程序， 测试阶段将包括对实际生物医学 删失数据比较估计量的相对优点。 的 多变量分析优于当前的单变量方法 分析也将被提及。 测试阶段还将包括 计算机模拟研究将有助于表明优势 和弱点的每一个估计建议，通过允许测试 在已知正确答案的广泛条件下。 提出的第一个程序是生存的贝叶斯估计 曲线 该估计量计算困难，且不需要大样本 最优性质是已知的。 估计数的近似值为 发现允许计算中等样本量的估计。 这将通过将数据分为三个子类型来实现， 删失数据将简化分析。 大样本 估计量的性质将研究利用简化 涉及到单变量的多变量概率分布 分布。 第二个过程是贝叶斯预测方法，它概括了 已知单变量方法。 本发明的优点是： 更适合于预测新的观测结果， 使用的方法。 该估计器开发中的攻击技术 都是推测性的 第三种方法是单变量Kaplan-Meier方法的推广 估计的基础上重新分配的概率与 审查意见。 非参数平滑技术允许 这种重新分配以与单变量情况类似的方式发生 通过利用从附近数据获得的信息。 大样本 估计量的性质将使用适用于 单变量估计量 最后，讨论了非参数极大似然估计的大样本性质 估计将被研究。 初步研究将通过模拟 结果旨在确定如何估计行为合理 大样本。 数学大样本属性将是 与贝叶斯估计量的类似研究一起开发 因为估计量是相似的。

Estimating a survival function and predicting the lifetimes of future patients are important medical problems. Data in clinical studies is often censored because not all members of the study reach a prescribed endpoint before the conclusion of the study. In addition, more than a single time measurement is often of interest, for instance, the time until recurrence of a disease and the time until death may both be variables deemed important. Development of methods of statistical analysis for this multivariate censored data is the aim of this proposed research. The research will consist of the development, testing, and study of optimality properties for three new procedures, and the testing and study of the most promising existing technique of analysis. The procedures proposed are nonparametric since parametric forms can be quite restrictive in multiple dimensions. For each of these procedures the testing phase will include the analysis of actual biomedical censored data comparing the relative merits of the estimators. The superiority of multivariate analysis over the current univariate methods of analysis will also be indicated. The testing phase will also include a computer simulation study which will help to indicate the strengths and weaknesses of each of the estimators proposed, by allowing testing over a wide range of conditions where the correct answer is known. The first procedure proposed is a Bayesian estimate of the survival curve. The estimator is difficult to compute and no large sample optimality properties are known. Approximations to the estimate will be found which allow computation of the estimate for moderate sample sizes. This will be accomplished by splitting the data into three subtypes of censored data which will simplify the analysis. The large sample properties of the estimator will be studied utilizing a simplification of the multivariate probability distributions involved to univariate distributions. The second procedure is a Bayesian predictive method which generalizes a known univariate method. The method has the advantage of being more suitable for prediction of new observations than any of the currently used methods. Techniques of attack in the development of this estimator are somewhat speculative. The third method is a generalization of the univariate Kaplan-Meier estimator based on the redistribution of probability associated with censored observations. The techniques of nonparametric smoothing allow this redistribution to occur in a similar manner to the univariate case by utilizing information obtained from nearby data. Large sample properties of the estimator will be studied using methods applicable to the univariate estimator. Finally, large sample properties of the nonparametric maximum likelihood estimator will be studied. Preliminary study will be via simulation results designed to determine how the estimator behaves for reasonably large samples. The mathematical large sample properties will be developed in conjunction with similar studies on the Bayesian estimator since the estimators are similar.