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Unmeasured confounding

Estimating propensity scores assumes we have identified and measured all the important confounders. But what if we can’t measure all the confounders? For example, what if some confounders are not captured in our data source? This is likely – there are always some confounders of interest that we can’t measure and those are called unmeasured confounders.

Proxy variables

If we have an unmeasured confounder, a proxy can offer an alternative. A proxy is a variable that’s highly correlated with the confounder of interest. By adjusting for the proxy, we are indirectly adjusting for the unmeasured confounder. For example, smoking is an important confounder in some research questions and we often can’t measure it in data sources such as the administrative databases. Chronic obstructive pulmonary disease (COPD) is a valid proxy; it has been used in population-based studies as a smoking proxy because smoking is the leading cause of COPD (up to 80-90% of the cases are attributable to smoking) and COPD can be captured in administrative databases such as physician visits and hospital abstracts. So by including COPD in a propensity score estimation we are indirectly including smoking.

Many proxies are available in the rich administrative databases; they either individually or collectively measure some of the unmeasured confounding. The stronger the relationship between the proxies and the confounder of interest, the more we can adjust for the unmeasured confounder.