Using group-based trajectory modelling to enhance causal inference in interrupted time series analysis

Several enhancements have been proposed for interrupted time series analysis (ITSA) to improve causal inference. Presently, group-based trajectory modelling (GBTM) is introduced as a complement to ITSA. GBTM assumes a certain number of discrete groups in the sample have unique trajectories of the outcome. GBTM is used herein for 2 purposes: (1) to compare outcomes across all trajectory groups via a stand-alone GBTM and (2) to identify comparable non-treated units to serve as controls in the ITSA outcome model. Examples of each are offered.

The effect of California's Proposition 99 (passed in 1988) for reducing cigarette sales is evaluated by comparing California to other states not exposed to smoking reduction initiatives. In the stand-alone GBTM, distinct trajectory groups are identified based on cigarette sales for the entire observation period (1970-2000). In the second approach, a GBTM is generated using only baseline period observations (1970-1988), and treatment effects (difference in post-intervention trends) are then estimated for the treatment unit versus non-treated units in the treated unit's trajectory group.

In the stand-alone GBTM, 3 distinct trajectory groups were identified: low-decreasing, medium-decreasing, and high-decreasing (California and 26 other states were in the low-decreasing group). When using baseline data for matching, California and 19 non-treated states comprised the low group. California had a significantly larger decrease in post-intervention cigarette sales than these controls (P < 0.01).

GBTM enhances ITSA by providing perspective for the outcome trajectory in the treated unit's group versus all others and can identify non-treated units to be used for estimating treatment effects.