The Data
A county launched a preventive screening program in 2019. Screening rates were already rising before the program started. The post-program data looks promising, but was the improvement already happening? Use the slider to adjust the post-program slope and see how ITS detects real effects. (Data are simulated for illustration.)
Screening Rate Over Time (ITS Analysis)
Next: How exactly does ITS separate the program effect from maturation that was already happening?
How ITS Works
ITS fits separate trend lines before and after the intervention. The key question is whether the post-program slope differs meaningfully from the pre-program slope. If improvement was already happening and continues at the same rate, the program added nothing.
What Is Interrupted Time Series?
An Interrupted Time Series (ITS) design tests whether an intervention changed the trajectory of an outcome. Rather than comparing before vs. after levels, it compares before vs. after slopes.
- Fits a regression line to pre-intervention data
- Fits a separate regression line to post-intervention data
- Tests whether the post-intervention slope differs from what the pre-intervention trend predicted
The Core Logic
A before-after comparison would credit the program for any improvement seen after launch. ITS asks a sharper question: Did the rate of improvement change?
- Pre-program slope = baseline rate of change (maturation)
- Post-program slope = rate of change after intervention
- Slope difference = program-attributable acceleration
The Counterfactual
ITS constructs a counterfactual by extending the pre-program trend forward. This shows what would have happened if the pre-existing rate of improvement continued.
Next: How do we formally test whether the slope change is statistically significant?
The Statistical Test
ITS uses regression with an interaction term to test whether the slope changed at the intervention point. The coefficient on this interaction term tells us whether the program accelerated improvement.
The ITS Regression Model
Where:
- B1 = Pre-program slope (baseline trend)
- B2 = Level change at intervention (immediate shift)
- B3 = Slope change (what we test)
Current Results
Conclusion
We fail to reject the null hypothesis. There is no statistically significant slope change. The program did not accelerate improvement beyond the pre-existing trend.
Next: What assumptions must hold for this ITS analysis to give valid conclusions?
Assumptions Audit
ITS is powerful but requires assumptions. The key threat is concurrent history: something else that changed at the same time as the program. ITS cannot distinguish your intervention from other simultaneous changes.
Key Assumptions
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✓
Pre-program data sufficient for slope estimationWe have 5 years of pre-program data (2014-2018), enough to establish a stable baseline trend.
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✓
Post-program data sufficient for slope estimationWe have 6 years of post-program data (2019-2024), enough to detect a new trajectory.
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?
No concurrent history threatITS cannot rule out that something else changed in 2019 that also affected screening rates (new state policy, insurance expansion, etc.).
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?
Linear trends appropriateWe assume outcomes follow linear trends. Non-linear patterns (acceleration, ceiling effects) could bias slope estimates.
Strengthening ITS
Single-group ITS is vulnerable to history threats. Adding a comparison group creates a more robust design.
- Add a comparison group that did not receive the intervention
- Document any other policy or environmental changes at intervention time
- Test for autocorrelation in residuals
- Check for seasonality that might confound trends
The History Threat
If a statewide policy also launched in 2019, ITS cannot determine whether your program or the state policy caused the slope change. This is why comparative ITS (with a control group) is stronger than single-group ITS.
Next: How much slope change would be needed for statistical and practical significance?
Sensitivity Analysis
ITS detects changes in trend slope, but not all statistically significant changes are practically meaningful. This table shows how different slope changes translate to effect sizes and statistical significance.
| Post-Program Slope | Slope Difference | Statistical Significance | Interpretation |
|---|---|---|---|
| 2.5% per year | 0% difference | Not significant (p > 0.05) | No effect beyond maturation |
| 3.0% per year | +0.5% difference | Marginally significant (p ~ 0.10) | Small acceleration (+0.5%/yr) |
| 3.5% per year | +1.0% difference | p ~ 0.05 | Program accelerated by 1%/yr |
| 4.5% per year | +2.0% difference | p < 0.01 | Program accelerated by 2%/yr |
What Economists Mean by "Identification"
ITS provides partial identification of the program effect. It controls for the maturation threat by accounting for pre-existing trends. However, it cannot rule out history threats (other simultaneous changes).
- What ITS controls: Pre-existing trends (maturation)
- What ITS cannot control: Concurrent events (history)
- Stronger design: Comparative ITS with a control group addresses both threats
Key Takeaway
ITS asks whether the rate of change shifted, not just whether levels improved. When pre-existing trends threaten validity, ITS separates program acceleration from natural maturation. The key test is whether the post-intervention slope differs from the pre-intervention slope. For stronger causal claims, combine ITS with a comparison group to also address history threats. This is what economists mean by "identification through design."