Proxy Variables and the Generalizability of Study Results

When individuals self-select (or are selected) into a study based on factors that influence the outcome, conclusions may not generalize to the full population. To compensate for this, results may be adjusted, for example, by standardization on the set of common causes of participation and outcome. Although such standardization is useful in some contexts, the common causes of participation and outcome may in practice not be fully observed. Instead, the researcher may have access to one or several variables related to the common causes, that is, to proxies for the common causes. This article defines and examines different types of proxy variables and shows how these can be used to obtain generalizable study results. First of all, the researcher may exploit proxies that influence only participation or outcome but which still allow for perfect generalizability by rendering participation and outcome conditionally independent. Further, generalizability can be achieved by leveraging 2 proxies, one of which is allowed to influence participation and one of which is allowed to influence the outcome, even if participation and outcome do not become independent conditional on these. Finally, approximate generalizability may be obtained by exploiting a single proxy that does not itself influence participation or outcome.

Automated summary

When individuals self-select or are selected into a study based on factors that affect the outcome, the conclusions may not be applicable to the entire population. To address this issue, researchers may adjust the results by standardizing on common causes of participation and outcome. However, these common causes may not be fully observed, and proxies for these causes are used instead. This article explores different types of proxy variables and demonstrates how they can be employed to achieve generalizable study results. Researchers can use proxies that only influence participation or outcome, but still maintain conditional independence to ensure generalizability. Additionally, leveraging two proxies, one for participation and one for the outcome, can also achieve generalizability even if participation and outcome are not conditionally independent. Finally, approximate generalizability can be obtained using a single proxy that does not directly influence participation or outcome.