Abstract: Negative controls can be used to adjust for unobserved confounders in an observational study.  A negative control is a variable that is known a priori to be (1) unaffected by treatment, and (2) affected by the unobserved confounders.  Any observed variation in a negative control may be attributed to the confounders, but not to treatment.  Thus, negative controls can be used to partially identify the unobserved confounders.  A similar situation arises when a single observational unit is observed multiple times, under varying conditions of the confounders.  The multiple observations are referred to as replicates.  Any observed variation between the replicates may be attributed purely to the confounders.  Thus, like negative controls, replicates can be used to partially identify the confounding variables.  Importantly, in a high-dimensional setting, the partial identification provided by negative controls and the partial identification provided by the replicates are in some sense dual to one another.  More to the point, these two partial identifications are not redundant, but rather complimentary, and therefore negative controls and replicates can be used together to more fully identify and control for unobserved confounders.

 

Johann Gagnon-Bartsch is an Assistant Professor in the Department of Statistics at the University of Michigan.