Multiply Robust Causal Inference with Double-Negative Control Adjustment for Categorical Unmeasured Confounding

Abstract

Summary Unmeasured confounding is a threat to causal inference in observational studies. In recent years, the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity. Negative controls have a long‐standing tradition in laboratory sciences and epidemiology to rule out non‐causal explanations, although they have been used primarily for bias detection. Recently, Miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non‐parametrically the average treatment effect (ATE) from observational data subject to uncontrolled confounding. We establish non‐parametric identification of the ATE under weaker conditions in the case of categorical unmeasured confounding and negative control variables. We also provide a general semiparametric framework for obtaining inferences about the ATE while leveraging information about a possibly large number of measured covariates. In particular, we derive the semiparametric efficiency bound in the non‐parametric model, and we propose multiply robust and locally efficient estimators when non‐parametric estimation may not be feasible. We assess the finite sample performance of our methods in extensive simulation studies. Finally, we illustrate our methods with an application to the post‐licensure surveillance of vaccine safety among children.

Zostavax vaccine effectiveness among US elderly using real‐world evidence: Addressing unmeasured confounders by using multiple imputation after linking beneficiary surveys with Medicare claims

“…We intend to continue our investigation into alternate methods to address potential unmeasured confounding factors such as health-seeking behavior. 8,25,30 Surveys are susceptible to measurement error and response rate variability. 31 As expected, we found that responses to less time variant questions (eg, education level) were consistent when asked to the same individual in different years, while responses to questions about impaired mobility and health-seeking behaviors varied.…”

On Semiparametric Instrumental Variable Estimation of Average Treatment Effects through Data Fusion

“…In this paper, we focused on the canonical case of binary Z and D; extension of the proposed methodology to the case of general Z or D is an interesting topic for future research. It will also be of interest to investigate the use of negative controls under data fusion to mitigate unmeasured confounding and identify causal effects, which has gained increasing recognition and popularity in recent years (Miao and Tchetgen Tchetgen, 2017;Shi et al, 2018).…”

An Introduction to Proximal Causal Learning

“…We refer the reader to Miao et al for a technical exposition of required regularity conditions. In the categorical case, as established in Shi et al 16 condition (14) along with a rank condition for a certain matrix defined in terms of the conditional distribution of W given (Z, A, X) suffices for equation (12) to admit a solution 16 . It is important to note that h (a, x, w) satisfying (12) need not be unique, any solution to this equation yields the same value of the proximal g-formula.…”

“…A generalization of the above closed-form expression for proximal g-formula with categorical variables is given in Shi et al 16 for the average causal effect β (1) − β (0) of a binary treatment on the additive scale. Unfortunately, unlike the g-formula, the proximal g-formula is not always available in closed-form and requires solving equation (12) numerically, which might be computationally intensive and unstable due to its potential to be empirically ill-posed.…”

“…In this case, completeness requires that which states that Z and W must each have at least as many categories as U . Intuitively, condition (14) states that proximal causal learning can potentially account for unmeasured confounding in the categorical case as long as the number of categories of U is no larger than that of either proxies Z and W 16 . This further provides a rationale for measuring a rich set of baseline characteristics in observational studies as a potential strategy for mitigating unmeasured confounding via the proximal approach we now describe.…”