A matching framework to improve causal inference in interrupted time-series analysis

Interrupted time-series analysis (ITSA) is a popular evaluation methodology in which a single treatment unit's outcome is studied over time and the intervention is expected to "interrupt" the level and/or trend of the outcome, subsequent to its introduction. When ITSA is implemented without a comparison group, the internal validity may be quite poor. Therefore, adding a comparable control group to serve as the counterfactual is always preferred. This paper introduces a novel matching framework, ITSAMATCH, to create a comparable control group by matching directly on covariates and then use these matches in the outcomes model.

We evaluate the effect of California's Proposition 99 (passed in 1988) for reducing cigarette sales, by comparing California to other states not exposed to smoking reduction initiatives. We compare ITSAMATCH results to 2 commonly used matching approaches, synthetic controls (SYNTH), and regression adjustment; SYNTH reweights nontreated units to make them comparable to the treated unit, and regression adjusts covariates directly. Methods are compared by assessing covariate balance and treatment effects.

Both ITSAMATCH and SYNTH achieved covariate balance and estimated similar treatment effects. The regression model found no treatment effect and produced inconsistent covariate adjustment.

While the matching framework achieved results comparable to SYNTH, it has the advantage of being technically less complicated, while producing statistical estimates that are straightforward to interpret. Conversely, regression adjustment may "adjust away" a treatment effect. Given its advantages, ITSAMATCH should be considered as a primary approach for evaluating treatment effects in multiple-group time-series analysis.