When does measurement error in covariates impact causal effect estimates? Analytic derivations of different scenarios and an empirical illustration.

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.