Persistent threats to validity in single-group interrupted time series analysis with a cross over design

The basic single-group interrupted time series analysis (ITSA) design has been shown to be susceptible to the most common threat to validity-history-the possibility that some other event caused the observed effect in the time series. A single-group ITSA with a crossover design (in which the intervention is introduced and withdrawn 1 or more times) should be more robust. In this paper, we describe and empirically assess the susceptibility of this design to bias from history.

Time series data from 2 natural experiments (the effect of multiple repeals and reinstatements of Louisiana's motorcycle helmet law on motorcycle fatalities and the association between the implementation and withdrawal of Gorbachev's antialcohol campaign with Russia's mortality crisis) are used to illustrate that history remains a threat to ITSA validity, even in a crossover design.

Both empirical examples reveal that the single-group ITSA with a crossover design may be biased because of history. In the case of motorcycle fatalities, helmet laws appeared effective in reducing mortality (while repealing the law increased mortality), but when a control group was added, it was shown that this trend was similar in both groups. In the case of Gorbachev's antialcohol campaign, only when contrasting the results against those of a control group was the withdrawal of the campaign found to be the more likely culprit in explaining the Russian mortality crisis than the collapse of the Soviet Union.

Even with a robust crossover design, single-group ITSA models remain susceptible to bias from history. Therefore, a comparable control group design should be included, whenever possible.