Multiple Imputation, Maximum Likelihood and Fully Bayesian methods are the three most commonly used model-based approaches in missing data problems. Although it is easy to show that when the responses are missing at random (MAR), the complete case analysis is unbiased and efficient, the aforementioned methods are still commonly used in practice for this setting. To examine the performance of and relationships between these three methods in this setting, we derive and investigate small sample and asymptotic expressions of the estimates and standard errors, and fully examine how these estimates are related for the three approaches in the linear regression model when the responses are MAR. We show that when the responses are MAR in the linear model, the estimates of the regression coefficients using these three methods are asymptotically equivalent to the complete case estimates under general conditions. One simulation and a real data set from a liver cancer clinical trial are given to compare the properties of these methods when the responses are MAR.

中文翻译：

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关于线性回归模型中缺失响应的多重插补、最大似然和完全贝叶斯方法之间关系的说明

多重插补、最大似然和完全贝叶斯方法是缺失数据问题中最常用的三种基于模型的方法。虽然很容易证明，当响应随机缺失 (MAR) 时，完整的案例分析是无偏的和有效的，但上述方法在实践中仍然普遍用于这种设置。为了检查这三种方法在这种情况下的性能和关系，我们推导出并研究了估计和标准误的小样本和渐近表达式，并充分检查了这些估计与线性回归模型中的三种方法之间的关系，当回复是 MAR。我们表明，当线性模型中的响应为 MAR 时，使用这三种方法对回归系数的估计与一般条件下的完整案例估计渐近等效。给出了一个模拟和来自肝癌临床试验的真实数据集，以比较这些方法在响应为 MAR 时的特性。