Inverse probability weights are increasingly used in epidemiological analysis, and estimation and application of weights to address a single bias are well discussed in the literature. Weights to address multiple biases simultaneously (i.e. a combination of weights) have almost exclusively been discussed related to marginal structural models in longitudinal settings where treatment weights (estimated first) are combined with censoring weights (estimated second). In this work, we examine two examples of combined weights for confounding and missingness in a time-fixed setting in which outcome or confounder data are missing, and the estimand is the marginal expectation of the outcome under a time-fixed treatment. We discuss the identification conditions, construction of combined weights and how assumptions of the missing data mechanisms affect this construction. We use a simulation to illustrate the estimation and application of the weights in the two examples. Notably, when only outcome data are missing, construction of combined weights is straightforward; however, when confounder data are missing, we show that in general we must follow a specific estimation procedure which entails first estimating missingness weights and then estimating treatment probabilities from data with missingness weights applied. However, if treatment and missingness are conditionally independent, then treatment probabilities can be estimated among the complete cases.

中文翻译：

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对现代方法的反思：结合权重以处理混杂和缺失数据

逆概率权重越来越多地用于流行病学分析，并且在文献中很好地讨论了权重的估计和应用以解决单一偏差。同时处理多个偏差的权重（即权重的组合）几乎完全被讨论与纵向设置中的边际结构模型相关，其中治疗权重（首先估计）与审查权重（估计其次）相结合。在这项工作中，我们检查了在时间固定的环境中混合和缺失的组合权重的两个示例，其中缺少结果或混杂数据，并且估计是在固定时间处理下结果的边际期望。我们讨论识别条件，组合权重的构建以及缺失数据机制的假设如何影响这种构建。我们使用模拟来说明两个示例中权重的估计和应用。值得注意的是，当仅缺少结果数据时，组合权重的构建很简单；然而，当混杂数据缺失时，我们表明通常我们必须遵循特定的估计程序，该程序首先需要估计缺失权重，然后根据应用了缺失权重的数据估计治疗概率。但是，如果治疗和缺失是条件独立的，则可以在完整病例中估计治疗概率。组合权重的构造很简单；然而，当混杂数据缺失时，我们表明通常我们必须遵循特定的估计程序，该程序首先需要估计缺失权重，然后根据应用了缺失权重的数据估计治疗概率。但是，如果治疗和缺失是条件独立的，则可以在完整病例中估计治疗概率。组合权重的构造很简单；然而，当混杂数据缺失时，我们表明通常我们必须遵循特定的估计程序，该程序首先需要估计缺失权重，然后根据应用了缺失权重的数据估计治疗概率。但是，如果治疗和缺失是条件独立的，则可以在完整病例中估计治疗概率。