标题： 逆概率加权方法的不稳定性及处理不可忽略缺失数据的方法 显示英文标题

标题： Instability of inverse probability weighting methods and a remedy for non-ignorable missing data

摘要： 逆概率加权（IPW）方法通常用于在缺失概率服从逻辑模型的假设下分析不可忽略的缺失数据。 然而，当样本量适中且缺失概率较高时，数值求解IPW方程可能会遇到不收敛的问题。 此外，这些方程通常有多个根，确定最佳根具有挑战性。 因此，IPW方法可能效率低下，甚至产生偏差结果。 我们病理学地识别了这些方法中的缺陷：它们涉及矩生成函数的估计，而这类函数在一般情况下非常不稳定。 作为补救措施，我们对完全观测个体的协变量给定的结果分布进行半参数建模。 在为结果和协变量的缺失状态形成一个诱导的逻辑回归模型后，我们开发了一种最大条件似然方法来估计潜在参数。 所提出的方法避免了矩生成函数的估计，从而克服了IPW方法的不稳定性。 我们的理论和模拟结果表明，所提出的方法大大优于现有的竞争方法。 两个实际数据例子被分析以说明我们方法的优势。 我们得出结论，如果仅假设参数逻辑回归但结果回归模型保持任意，则在涉及不可忽略缺失数据的问题中使用任何现有统计方法时都必须谨慎。 显示英文摘要

摘要： Inverse probability weighting (IPW) methods are commonly used to analyze non-ignorable missing data under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve non-convergence problems when the sample size is moderate and the missingness probability is high. Moreover, those equations often have multiple roots, and identifying the best root is challenging. Therefore, IPW methods may have low efficiency or even produce biased results. We identify the pitfall in these methods pathologically: they involve the estimation of a moment-generating function, and such functions are notoriously unstable in general. As a remedy, we model the outcome distribution given the covariates of the completely observed individuals semiparametrically. After forming an induced logistic regression model for the missingness status of the outcome and covariate, we develop a maximum conditional likelihood method to estimate the underlying parameters. The proposed method circumvents the estimation of a moment-generating function and hence overcomes the instability of IPW methods. Our theoretical and simulation results show that the proposed method outperforms existing competitors greatly. Two real data examples are analyzed to illustrate the advantages of our method. We conclude that if only a parametric logistic regression is assumed but the outcome regression model is left arbitrary, then one has to be cautious in using any of the existing statistical methods in problems involving non-ignorable missing data.