论文标题
连续结果的累积概率模型的渐近特性
Asymptotic Properties for Cumulative Probability Models for Continuous Outcomes
论文作者
论文摘要
连续结果的回归模型通常需要对结果进行转换，用户可以将其指定为{\ it先验}或从参数家族中估算。累积概率模型（CPM）非参数估计转换，因此是连续结果的灵活分析方法。但是，由于可能无限制的转换范围，很难为CPMS建立渐近特性。在这里，当将结果应用于末端的结果时，我们显示了CPM的渐近性能。我们证明了估计的回归系数的一致性和在非审核区域上的估计转换函数，并描述了它们的关节渐近分布。我们通过模拟显示了这种审查方法的结果，而在审查一小部分数据时，来自原始数据的CPM的方法相似。我们重新分析了患有CPM的HIV阳性患者的数据集，以说明和比较方法。
Regression models for continuous outcomes often require a transformation of the outcome, which the user either specify {\it a priori} or estimate from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation and are thus a flexible analysis approach for continuous outcomes. However, it is difficult to establish asymptotic properties for CPMs due to the potentially unbounded range of the transformation. Here we show asymptotic properties for CPMs when applied to slightly modified data where the outcomes are censored at the ends. We prove uniform consistency of the estimated regression coefficients and the estimated transformation function over the non-censored region, and describe their joint asymptotic distribution. We show with simulations that results from this censored approach and those from the CPM on the original data are similar when a small fraction of data are censored. We reanalyze a dataset of HIV-positive patients with CPMs to illustrate and compare the approaches.
