Imputation approaches for potential outcomes in causal inference

Abstract

Background: The fundamental problem of causal inference is one of missing data, and specifically of missing potential outcomes: if potential outcomes were fully observed, then causal inference could be made trivially. Though often not discussed explicitly in the epidemiological literature, the connections between causal inference and missing data can provide additional intuition.

Methods: We demonstrate how we can approach causal inference in ways similar to how we address all problems of missing data, using multiple imputation and the parametric g-formula.

Results: We explain and demonstrate the use of these methods in example data, and discuss implications for more traditional approaches to causal inference.

Conclusions: Though there are advantages and disadvantages to both multiple imputation and g-formula approaches, epidemiologists can benefit from thinking about their causal inference problems as problems of missing data, as such perspectives may lend new and clarifying insights to their analyses.

Keywords: Causal inference; g-formula; multiple imputation; potential outcomes.

Figure 1.

Expected realization for 10 000 participants from example data, by stratum of Z and overall.(Color online).