MULTIVARIATE SURVIVAL CURVE ANALYSIS

估计生存函数和预测未来的寿命 病人是重要的医学问题。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了规定的 研究结束前的终点。此外，超过一个 单次时间测量通常是感兴趣的，例如，时间 直到疾病复发和直到死亡的时间可能都是 被认为重要的变量。统计方法的发展 对这种多变量删失数据的分析是本文提出的目标 研究。 该研究将包括开发、测试和研究 三个新过程的最优性性质，以及测试和 研究最有前途的现有分析技术。这个 建议的过程是非参数的，因为参数形式可以是 在多个方面都有相当大的限制。对于其中的每个过程 测试阶段将包括对实际生物医学的分析 审查数据，比较估计器的相对优劣。这个 多变量分析比现行单变量分析方法的优越性 还将说明分析的重要性。测试阶段还将包括 一项计算机模拟研究，这将有助于表明优势 以及提出的每个估计器的弱点，通过允许测试 在各种已知正确答案的情况下。 提出的第一个程序是对存活率的贝叶斯估计。 曲线。该估计量难以计算，且样本不大 最优性属性是已知的。估算值的近似值为 它允许计算中等样本量的估计值。 这将通过将数据拆分为三个子类型来实现 审查数据，这将简化分析。大样本 我们将利用一种简化方法来研究估计量的性质 涉及到单变量的多变量概率分布 分配。 第二个过程是贝叶斯预测方法，它概括了 已知的单变量方法。该方法的优点是 适用于新观测的预测，比目前的任何 使用的方法。此估计器开发过程中的攻击技术 有点投机性。 第三种方法是单变量Kaplan-Meier方法的推广 基于关联概率的重分布的估计器 被审查的观察结果。非参数平滑技术允许 这种重新分布以类似于单变量情况的方式发生 通过利用从附近数据获得的信息。大样本 将使用适用于以下方面的方法来研究估计量的性质 单变量估计量。 最后，给出了非参数极大似然估计的大样本性质 将研究估计器。初步研究将通过模拟进行 结果旨在确定估计器如何合理地 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 因为估计值是相似的。

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.