ABSTRACT Nonignorable missing data is common in studies where the outcome is relevant to the subject's behaviour. Ibrahim, Lipsitz, and Horton [(2001), ‘Using Auxiliary Data for Parameter Estimation with Non-ignorably Missing Outcomes’, Journal of the Royal Statistical Society: Series C (Applied Statistics), 50, 361–373] fitted a logistic regression for a binary outcome subject to nonignorable missing data, and they proposed to replace the outcome in the mechanism model with an auxiliary variable that is completely observed. They had to correctly specify a model for the auxiliary variable; unfortunately the outcome variable subject to nonignorable missingness is still involved. The correct specification of this model is mysterious. Instead, we propose two unconventional likelihood-based estimation procedures where the nonignorable missingness mechanism model could be completely bypassed. We apply our proposed methods to the children's mental health study and compare their performance with existing methods. The large sample properties of the proposed estimators are rigorously justified, and their finite sample behaviours are examined via comprehensive simulation studies.

中文翻译：

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基于具有不可忽略缺失数据的非常规可能性的估计及其在儿童心理健康研究中的应用

摘要 不可忽略的缺失数据在结果与受试者行为相关的研究中很常见。Ibrahim、Lipsitz 和 Horton [(2001)，“使用辅助数据进行具有不可忽视缺失结果的参数估计”，皇家统计学会杂志：C 系列（应用统计），50, 361–373] 拟合了逻辑回归对于受不可忽略缺失数据影响的二元结果，他们建议用完全观察到的辅助变量替换机制模型中的结果。他们必须正确地为辅助变量指定一个模型；不幸的是，仍然涉及受不可忽略缺失影响的结果变量。这个模型的正确规格是神秘的。反而，我们提出了两种非常规的基于可能性的估计程序，其中可以完全绕过不可忽略的缺失机制模型。我们将我们提出的方法应用于儿童的心理健康研究，并将他们的表现与现有方法进行比较。所提出的估计器的大样本特性得到了严格的证明，并且通过综合模拟研究检查了它们的有限样本行为。