On the Nondifferential Misclassification of a Binary Confounder

Abstract Consider a study with binary exposure, outcome, and confounder, where the confounder is nondifferentially misclassified. Epidemiologists have long accepted the unproven but oft-cited result that, if the confounder is binary, odds ratios, risk ratios, and risk differences which control for the mismeasured confounder will lie between the crude and the true measures. In this paper the authors provide an analytic proof of the result in the absence of a qualitative interaction between treatment and confounder, and demonstrate via counterexample that the result need not hold when there is a qualitative interaction between treatment and confounder. They also present an analytic proof of the result for the effect of treatment amount the treated, and describe extensions to measures conditional on or standardized over other covariates

Causal inference for social network data

We describe semiparametric estimation and inference for causal effects using observational data from a single social network. Our asymptotic result is the first to allow for dependence of each observation on a growing number of other units as sample size increases. While previous methods have generally implicitly focused on one of two possible sources of dependence among social network observations, we allow for both dependence due to transmission of information across network ties, and for dependence due to latent similarities among nodes sharing ties. We describe estimation and inference for new causal effects that are specifically of interest in social network settings, such as interventions on network ties and network structure. Using our methods to reanalyze the Framingham Heart Study data used in one of the most influential and controversial causal analyses of social network data, we find that after accounting for network structure there is no evidence for the causal effects claimed in the original paper

Identifying effects of multiple treatments in the presence of unmeasured confounding

Identification of treatment effects in the presence of unmeasured confounding is a persistent problem in the social, biological, and medical sciences. The problem of unmeasured confounding in settings with multiple treatments is most common in statistical genetics and bioinformatics settings, where researchers have developed many successful statistical strategies without engaging deeply with the causal aspects of the problem. Recently there have been a number of attempts to bridge the gap between these statistical approaches and causal inference, but these attempts have either been shown to be flawed or have relied on fully parametric assumptions. In this paper, we propose two strategies for identifying and estimating causal effects of multiple treatments in the presence of unmeasured confounding. The auxiliary variables approach leverages auxiliary variables that are not causally associated with the outcome; in the case of a univariate confounder, our method only requires one auxiliary variable, unlike existing instrumental variable methods that would require as many instruments as there are treatments. An alternative null treatments approach relies on the assumption that at least half of the confounded treatments have no causal effect on the outcome, but does not require a priori knowledge of which treatments are null. Our identification strategies do not impose parametric assumptions on the outcome model and do not rest on estimation of the confounder. This work extends and generalizes existing work on unmeasured confounding with a single treatment, and provides a nonparametric extension of models commonly used in bioinformatics

Augmented balancing weights as linear regression

We provide a novel characterization of augmented balancing weights, also known as Automatic Debiased Machine Learning (AutoDML). These estimators combine outcome modeling with balancing weights, which estimate inverse propensity score weights directly. When the outcome and weighting models are both linear in some (possibly infinite) basis, we show that the augmented estimator is equivalent to a single linear model with coefficients that combine the original outcome model coefficients and OLS; in many settings, the augmented estimator collapses to OLS alone. We then extend these results to specific choices of outcome and weighting models. We first show that the combined estimator that uses (kernel) ridge regression for both outcome and weighting models is equivalent to a single, undersmoothed (kernel) ridge regression; this also holds when considering asymptotic rates. When the weighting model is instead lasso regression, we give closed-form expressions for special cases and demonstrate a ``double selection'' property. Finally, we generalize these results to linear estimands via the Riesz representer. Our framework ``opens the black box'' on these increasingly popular estimators and provides important insights into estimation choices for augmented balancing weights