The average causal treatment effect (ATE) can be estimated from observational data based on covariate adjustment. Even if all confounding covariates are observed, they might not necessarily be reliably measured and may fail to obtain an unbiased ATE estimate. Instead of fallible covariates, the respective latent covariates can be used for covariate adjustment. But is it always necessary to use latent covariates? How well do analysis of covariance (ANCOVA) or propensity score (PS) methods estimate the ATE when latent covariates are used? We first analytically delineate the conditions under which latent instead of fallible covariates are necessary to obtain the ATE. Then we empirically examine the difference between ATE estimates when adjusting for fallible or latent covariates in an applied example. We discuss the issue of fallible covariates within a stochastic theory of causal effects and analyse data of a within‐study comparison with recently developed ANCOVA and PS procedures that allow for latent covariates. We show that fallible covariates do not necessarily bias ATE estimates, but point out different scenarios in which adjusting for latent covariates is required. In our empirical application, we demonstrate how latent covariates can be incorporated for ATE estimation in ANCOVA and in PS analysis.

中文翻译：

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协变量中的测量误差何时会影响因果效应估计？不同场景的解析推导和经验说明。

可以基于协变量调整从观察数据中估计平均因果治疗效果（ATE）。即使观察到所有混杂的协变量，也不一定可以对其进行可靠的测量，并且可能无法获得无偏的ATE估计。代替易变的协变量，可以将各个潜在的协变量用于协变量调整。但是是否总是有必要使用潜在协变量？当使用潜在协变量时，协方差分析（ANCOVA）或倾向得分（PS）方法如何估计ATE？我们首先分析性地描述了获得ATE所需的隐性协变量而不是易变协变量的条件。然后，在一个应用示例中，当调整易失或潜在协变量时，我们将根据经验检查ATE估计之间的差异。我们在因果关系随机理论中讨论了易错协变量的问题，并与最近开发的允许潜在协变量的ANCOVA和PS程序进行了研究内比较的数据。我们表明，易变协变量不一定会使ATE估计值产生偏差，而是指出了需要对潜在协变量进行调整的不同情况。在我们的经验应用中，我们演示了如何在ANCOVA和PS分析中将潜在协变量用于ATE估计。