Zhang Jiameng, Heitjan Daniel F
Genentech, Inc., South San Francisco, CA 94080, USA.
Biostatistics. 2007 Oct;8(4):722-43. doi: 10.1093/biostatistics/kxm001. Epub 2007 Jan 10.
The coarse data model of Heitjan and Rubin (1991) generalizes the missing data model of Rubin (1976) to cover other forms of incompleteness such as censoring and grouping. The model has 2 components: an ideal data model describing the distribution of the quantity of interest and a coarsening mechanism that describes a distribution over degrees of coarsening given the ideal data. The coarsening mechanism is said to be nonignorable when the degree of coarsening depends on an incompletely observed ideal outcome, in which case failure to properly account for it can spoil inferences. A theme in recent research is to measure sensitivity to nonignorability by evaluating the effect of a small departure from ignorability on the maximum likelihood estimate (MLE) of a parameter of the ideal data model. One such construct is the "index of local sensitivity to nonignorability" (ISNI) (Troxel and others, 2004), which is the derivative of the MLE with respect to a nonignorability parameter evaluated at the ignorable model. In this paper, we adapt ISNI to Bayesian modeling by instead defining it as the derivative of the posterior expectation. We propose the application of ISNI as a first step in judging the robustness of a Bayesian analysis to nonignorable coarsening. We derive formulas for a range of models and apply the method to evaluate sensitivity to nonignorable coarsening in 2 real data examples, one involving missing CD4 counts in an HIV trial and the other involving potentially informatively censored relapse times in a leukemia trial.
海特扬和鲁宾（1991年）的粗数据模型将鲁宾（1976年）的缺失数据模型进行了推广，以涵盖其他形式的不完整性，如删失和分组。该模型有两个组成部分：一个描述感兴趣量分布的理想数据模型，以及一个在给定理想数据的情况下描述粗化程度分布的粗化机制。当粗化程度取决于未完全观测到的理想结果时，就称粗化机制是不可忽略的，在这种情况下，若未能正确考虑它，可能会破坏推断。近期研究的一个主题是通过评估与可忽略性的微小偏离对理想数据模型参数的最大似然估计（MLE）的影响，来衡量对不可忽略性的敏感性。一种这样的构建是“对不可忽略性的局部敏感性指数”（ISNI）（特罗克塞尔等人，2004年），它是在可忽略模型处评估的MLE关于不可忽略性参数的导数。在本文中，我们通过将其定义为后验期望的导数，使ISNI适用于贝叶斯建模。我们建议将ISNI的应用作为判断贝叶斯分析对不可忽略粗化的稳健性的第一步。我们推导了一系列模型的公式，并将该方法应用于两个实际数据示例中，以评估对不可忽略粗化的敏感性，一个示例涉及艾滋病病毒试验中缺失的CD4计数，另一个示例涉及白血病试验中可能提供信息的删失复发时间。
