Bounding the Effects of Continuous Treatments for Hidden Confounders

Observational studies often seek to infer the causal effect of a treatment even though both the assigned treatment and the outcome depend on other confounding variables. An effective strategy for dealing with confounders is to estimate a propensity model that corrects for the relationship between covariates and assigned treatment. Unfortunately, the confounding variables themselves are not always observed, in which case we can only bound the propensity, and therefore bound the magnitude of causal effects. In many important cases, like administering a dose of some medicine, the possible treatments belong to a continuum. Sensitivity models, which are required to tie the true propensity to something that can be estimated, have been explored for binary treatments. We propose one for continuous treatments. We develop a framework to compute ignorance intervals on the partially identified dose-response curves, enabling us to quantify the susceptibility of an inference to hidden confounders. We show with simulations and three real-world observational studies that our approach can give non-trivial bounds on causal effects from continuous treatments in the presence of hidden confounders.