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A comparative study of doubly robust estimators of the mean with missing data

机译：缺失数据的均值双稳健估计量的比较研究

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摘要

Doubly robust (DR) estimators of the mean with missing data are compared. An estimator is DR if either the regression of the missing variable on the observed variables or the missing data mechanism is correctly specified. One method is to include the inverse of the propensity score as a linear term in the imputation model [D. Firth and K.E. Bennett, Robust models in probability sampling, J. R. Statist. Soc. Ser. B. 60 (1998), pp. 3-21; D.O. Scharfstein, A. Rotnitzky, and J.M. Robins, Adjusting for ntmignorable drop-out using semiparametric nonresponse models (with discussion), J. Am. Statist. Assoc. 94 (1999), pp. 1096-1146; H. Bang and J.M. Robins, Doubly robust estimation in missing data and causal inference models, Biometrics 61 (2005), pp. 962-972]. Another method is to calibrate the predictions from a parametric model by adding a mean of the weighted residuals [J.M Robins, A. Rotnitzky, and L.P. Zhao, Estimation of regression coefficients when some regressors are not always observed, J. Am. Statist. Assoc. 89 (1994), pp. 846-866; DO. Scharfstein, A. Rotnitzky, and J.M. Robins, Adjusting for nonignorable drop-out using semiparametric nonresponse models (with discussion), J. Am. Statist. Assoc. 94 (1999), pp. 1096-1146]. The penalized spline propensity prediction (PSPP) model includes the propensity score into the model non-parametrically [R.J.A. Little and H. An, Robust likelihood-based analysis of multivariate data with missing values. Statist. Sin. 14 (2004), pp. 949-968; G. Zhang and R.J. Little, Extensions of the penalized spline propensity prediction method of imputation, Biometrics, 65(3) (2008), pp. 911-918]. All these methods have consistency properties under misspecification of regression models, but their comparative efficiency and confidence coverage in finite samples have received little attention. In this paper, we compare the root mean square error (RMSE), width of confidence interval and non-coverage rate of these methods under various mean and response propensity functions. We study the effects of sample size and robustness to model misspecification. The PSPP method yields estimates with smaller RMSE and width of confidence interval compared with other methods under most situations. It also yields estimates with confidence coverage close to the 95% nominal level, provided the sample size is not too small.
机译：比较具有缺失数据的均值的双稳健（DR）估计量。如果正确指定了缺失变量对观察变量的回归或缺失数据机制，则估计量为DR。一种方法是将倾向得分的倒数作为线性项包括在插补模型中[D. Firth和K.E. Bennett，概率抽样中的Robust模型，J。R. Statist。 Soc。老师B.60（1998），第3-21页;做。 Scharfstein，A.Rodnitzky和J.M.Robins，《使用半参数无响应模型调整可迁移的辍学（有讨论）》，J.Am。统计员。副会长94（1999），第1096-1146页； H. Bang和J.M. Robins，缺失数据和因果推论模型中的双稳健估计，Biometrics 61（2005），第962-972页]。另一种方法是通过添加加权残差的平均值来校准参数模型中的预测[J.M Robins，A.Rotnitzky和L.P. Zhao，当某些回归变量并非总是被观察到时，估计回归系数，J.Am。统计员。副会长89（1994），第846-866页；做。 Scharfstein，A。Rotnitzky和J.M. Robins，《使用半参数无响应模型（讨论）调整不可忽略的辍学》，J。Am。统计员。副会长94（1999），第1096-1146页]。罚样条倾向预测（PSPP）模型将倾向得分非参数地包含到模型中[R.J.A. Little和H.基于缺失值的多元数据的基于稳健性的似然分析。统计员。罪。 14（2004），第949-968页； G.Zhang和R.J. Little，插补的惩罚样条曲线倾向性预测方法的扩展，Biometrics，65（3）（2008），第911-918页]。所有这些方法在回归模型的错误指定下都具有一致性属性，但是它们在有限样本中的比较效率和置信度覆盖率很少受到关注。在本文中，我们比较了在各种均值和响应倾向函数下这些方法的均方根误差（RMSE），置信区间宽度和非覆盖率。我们研究了样本量和健壮性对模型错误指定的影响。在大多数情况下，与其他方法相比，PSPP方法得出的估计具有较小的RMSE和置信区间宽度。只要样本量不太小，它也可以得出置信覆盖率接近标称值95％的估计值。

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