Kernel Methods for Unobserved Confounding: Negative Controls, Proxies, and Instruments
This work provides a method for researchers to estimate causal treatment effects in observational studies where unmeasured confounding is a significant challenge, particularly useful in fields like public health and social sciences.
This paper proposes a family of kernel ridge regression algorithms to learn nonparametric treatment effects in the presence of unmeasured confounding, using negative control treatments and outcomes. The method is applied to estimate the dose response curve of cigarette smoking on infant birth weight, adjusting for unobserved household income confounding, using Pennsylvania birth data from 1989-1991.
Negative control is a strategy for learning the causal relationship between treatment and outcome in the presence of unmeasured confounding. The treatment effect can nonetheless be identified if two auxiliary variables are available: a negative control treatment (which has no effect on the actual outcome), and a negative control outcome (which is not affected by the actual treatment). These auxiliary variables can also be viewed as proxies for a traditional set of control variables, and they bear resemblance to instrumental variables. I propose a family of algorithms based on kernel ridge regression for learning nonparametric treatment effects with negative controls. Examples include dose response curves, dose response curves with distribution shift, and heterogeneous treatment effects. Data may be discrete or continuous, and low, high, or infinite dimensional. I prove uniform consistency and provide finite sample rates of convergence. I estimate the dose response curve of cigarette smoking on infant birth weight adjusting for unobserved confounding due to household income, using a data set of singleton births in the state of Pennsylvania between 1989 and 1991.