SEMIPARAMETRIC ESTIMATION WITH DATA MISSING NOT AT RANDOM USING AN INSTRUMENTAL VARIABLE
SEMIPARAMETRIC ESTIMATION WITH DATA MISSING NOT AT RANDOM USING AN INSTRUMENTAL VARIABLE
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DOI：
10.5705/ss.202016.0324
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发表时间：
2018-10-01
影响因子：
1.4
通讯作者：
Tchetgen, Eric J. Tchetgen
中科院分区：
文献类型：
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作者：
Sun, BaoLuo;Liu, Lan;Tchetgen, Eric J. Tchetgen
数据缺失在健康和社会科学的实证研究中经常发生，并且可能会损害我们获得有效推论的能力。如果以观察到的变量为条件，缺失数据机制仍然取决于未观察到的结果，则称结果不是随机缺失 (MNAR)。在这种情况下，如果不施加额外的假设，通常不可能进行识别。然而，如果所有受试者都观察到工具变量 (IV) 满足排除限制，即 IV 影响缺失过程而不直接影响结果，则有时可以进行识别。在本文中，我们借助 IV 提供了 MNAR 下完整数据分布的非参数识别的充分必要条件。此外，我们给出了足够的识别条件，在实践中更容易验证。为了进行推理，我们专注于总体结果均值的估计，为此我们开发了一套半参数估计器，扩展了之前为随机丢失数据开发的方法。具体来说，我们提出了一种新颖的双稳健估计器，用于评估 MNAR 的结果均值。为了说明这一点，这些方法用于解释在评估博茨瓦纳莫丘迪的艾滋病毒血清阳性率时因拒绝艾滋病毒检测而引起的选择偏差，使用访谈者特征（例如性别、年龄和经验年限）作为 IV。
Missing data occur frequently in empirical studies in the health and social sciences, and can compromise our ability to obtain valid inference. An outcome is said to be missing not at random (MNAR) if, conditional on the observed variables, the missing data mechanism still depends on the unobserved outcome. In such settings, identification is generally not possible without imposing additional assumptions. Identification is sometimes possible, however, if an instrumental variable (IV) is observed for all subjects that satisfies the exclusion restriction that the IV affects the missingness process without directly influencing the outcome. In this paper, we provide necessary and sufficient conditions for nonparametric identification of the full data distribution under MNAR with the aid of an IV. In addition, we give sufficient identification conditions that are more straightforward to verify in practice. For inference, we focus on estimation of a population outcome mean, for which we develop a suite of semiparametric estimators that extend methods previously developed for data missing at random. Specifically, we propose a novel doubly robust estimator of the mean of an outcome subject to MNAR. For illustration, the methods are used to account for selection bias induced by HIV testing refusal in the evaluation of HIV seroprevalence in Mochudi, Botswana, using interviewer characteristics such as gender, age and years of experience as IVs.