零膨胀作为缺失数据问题：一种基于代理变量的方法
Zero Inflation as a Missing Data Problem: a Proxy-based Approach
AI总结：
本文将零膨胀数据重新表述为缺失数据问题，利用缺失指示变量的代理变量修改效应恢复方法，实现参数识别、估计及未知关系下的部分识别敏感性分析。
摘要：
一类常见的零膨胀数据中，由于数据记录惯例（罕见结果被假定为不存在）或数据记录设备的细节（例如基因表达数据中的人为零值），某些真实值被错误地替换为零。现有的零膨胀数据方法要么通过显式表示超额零值的参数混合模型拟合观测数据似然，要么旨在用插补值替换超额零值。如果分析目标依赖于获知真实数据实现，零膨胀数据的一个特殊挑战是可识别性，因为很难正确判断哪些观测零值是真实的、哪些是膨胀的。本文将零膨胀数据视为一种一般类型的缺失数据问题：每当记录到零时，潜在删失变量的可观测性指示变量本身也是未观测的。我们表明，在没有附加假设的情况下，涉及零膨胀变量的目标参数不可识别。然而，如果观测到缺失指示变量的代理变量，在代理变量与指示变量之间关系已知的条件下，对 Kuroki 和 Pearl 的效应恢复方法进行修改，即可实现识别与估计。如果该关系未知，我们的方法给出一种用于敏感性分析的部分识别策略。具体而言，我们表明只有某些代理变量—指示变量关系与观测数据分布相容。对于分类结局情形，我们给出该关系的解析界，该界在某些模型中是尖锐的。对于更复杂的情形，可使用 Duarte 等人[2023]中的方法计算尖锐数值界。我们通过模拟研究以及一项关于中心静脉导管相关血流感染（CLABSIs）的数据应用来说明所提方法。
英文摘要：
A common type of zero-inflated data has certain true values incorrectly replaced by zeros due to data recording conventions (rare outcomes assumed to be absent) or details of data recording equipment (e.g. artificial zeros in gene expression data). Existing methods for zero-inflated data either fit the observed data likelihood via parametric mixture models that explicitly represent excess zeros, or aim to replace excess zeros by imputed values. If the goal of the analysis relies on knowing true data realizations, a particular challenge with zero-inflated data is identifiability, since it is difficult to correctly determine which observed zeros are real and which are inflated. This paper views zero-inflated data as a general type of missing data problem, where the observability indicator for a potentially censored variable is itself unobserved whenever a zero is recorded. We show that, without additional assumptions, target parameters involving a zero-inflated variable are not identified. However, if a proxy of the missingness indicator is observed, a modification of the effect restoration approach of Kuroki and Pearl allows identification and estimation, given the proxy-indicator relationship is known. If this relationship is unknown, our approach yields a partial identification strategy for sensitivity analysis. Specifically, we show that only certain proxy-indicator relationships are compatible with the observed data distribution. We give an analytic bound for this relationship in cases with a categorical outcome, which is sharp in certain models. For more complex cases, sharp numerical bounds may be computed using methods in Duarte et al.[2023]. We illustrate our method via simulation studies and a data application on central line-associated bloodstream infections (CLABSIs).
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