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Ilya Shpitser develops foundations of causal inference. With Tyler J. VanderWeele, he compared formal definitions of a confounder by asking whether adjusting for all such variables removes confounding, and whether each variable can help in an appropriate adjustment context.^[ref]

This makes adjustment a problem about causal structure. A variable's observed correlation with treatment and outcome alone cannot determine whether conditioning on it is useful. Their analysis relates a confounder to membership in a minimally sufficient adjustment set.^[ref]

Tyler J. VanderWeele develops methods and foundations for causal inference. With Ilya Shpitser, he examined how to define a confounder so that the definition supports valid adjustment decisions.^[ref]

Their preferred definition concerns a pretreatment variable belonging to some minimally sufficient adjustment set. This connects the variable's role to elimination of confounding, rather than merely to prediction of exposure and outcome. The distinction matters because a predictive variable can be unsuitable for adjustment, and the contribution of one covariate depends on what else is adjusted for.^[ref]