Interrupted Time Series (ITS) Analysis

A Simple Guide to Interrupted Time Series Analysis

What is a Time Series?

A time series is a sequence of data points collected over time. For example, the number of crimes reported each month in a city, or the number of stop and searches performed in a ward each week, are both examples of time series data.

In these examples, the data is ordered in time, and each point depends on what happened before.

What is Interrupted Time Series Analysis (ITSA)?

Interrupted Time Series Analysis (ITSA) is a method used to measure the effect of an event or intervention on a time series. It helps us understand how a change (like a policy, program, or external event) impacts a certain outcome over time.

In other words, ITSA helps answer the question: “Did this intervention really make a difference?”

Why Use Interrupted Time Series Analysis?

ITSA is valuable for understanding how interventions impact social phenomena, such as crime rates. It allows us to:

• Assess the effect of a policy or event by examining data points before and after the interruption.
• Analyse trends over time, helping to distinguish between natural fluctuations and the effects of the intervention.

Key Components of ITSA

• Time Series Data: A sequence of data points collected over time. In the context of crime, this might involve monthly crime rates over several years.
• Intervention Point: The moment when the intervention occurs, such as the implementation of a new law or policy.
• Baseline Trend: The trend in the data prior to the intervention. Understanding this helps to assess how the intervention has changed the trend.
• Post-Intervention Trend: The trend after the intervention, allowing us to see if there’s a significant difference compared to the baseline trend.

How Does Interrupted Time Series Analysis Work?

1. Baseline Trend (Before the Intervention)

   The first step in ITSA is to observe the data before the intervention. This is called the baseline trend. It shows how things were progressing without any external influence. For example, if we are measuring crime rates, we look at how crime was changing before a new policy was introduced.

2. Intervention or Event

   An interruption happens when something changes. This could be the introduction of a new policy, a public awareness campaign, or any significant event that might influence the data. This interruption splits the time series into before and after segments.

3. Post-Intervention Trend

   After the interruption, we observe the post-intervention trend. We want to see if the data changes after the intervention, either immediately or gradually over time.

4. Measuring the Impact

   ITSA measures two things:

   • Level Change: Did the value of the outcome (e.g., crime rate, sales, etc.) jump up or down immediately after the intervention? This is called the immediate impact.
   • Slope Change: Did the long-term trend change after the intervention? For instance, was there a steady decline in crime rates after the policy was introduced? This is known as the sustained impact.

Together, these help us understand both the short-term and long-term effects of an intervention.

Example of ITSA in Action

Imagine a city introduces a new policy to reduce speeding by installing more speed cameras. We might observe the number of speeding tickets issued each month before and after the cameras were installed:

• Before the intervention: The number of speeding tickets was steadily rising.
• Intervention: More cameras were installed in March.
• After the intervention: The number of speeding tickets dropped immediately and continued to decline slowly over time.

By applying ITSA, we can measure whether the cameras had a lasting effect on reducing speeding incidents.

Strengths and Limitations of ITSA

Strengths:

• Clear Impact Measurement: ITSA can show both the immediate and long-term effects of an intervention, making it a valuable tool for policy evaluation.
• Real-World Data: ITSA uses real-world data collected over time, making the results highly relevant to practical decision-making.

Limitations:

• Requires Consistent Data: ITSA works best when there is consistent data over a long period before and after the intervention.
• Confounding Variables: Other factors (like economic changes or community programs) may also influence crime rates, making it difficult to attribute changes solely to the intervention.
• Data Quality: Accurate, consistent data over time is crucial for reliable results. Any gaps or inconsistencies can affect the analysis.
• Assumption of Linear Trends: ITSA assumes that trends are linear and that any changes are directly attributable to the intervention, which may not always be the case.

Summary

Interrupted Time Series Analysis is a valuable method for evaluating the impact of interventions in the crime domain. By analysing trends before and after an intervention, analysts can gain insights into the effectiveness of policies or programs aimed at reducing crime rates.

Key Takeaways

• Interrupted Time Series Analysis (ITSA) is a method used to assess the impact of an intervention or event on time series data.
• ITSA measures two main changes: level change (immediate impact) and slope change (long-term trend) by comparing the baseline trends (before the intervention) to post-intervention trends to assess the effect.
• ITSA helps decision-makers understand whether a policy, campaign, or event had a lasting effect.
• ITSA is valuable for evaluating public policies, business strategies, and health interventions, but it relies on consistent data and careful interpretation to account for external factors.

Glossary of Key Terms

• Time Series: Data points collected at regular intervals over time (e.g., monthly crime rates, daily sales).
• Interrupted Time Series Analysis (ITSA): A statistical method used to evaluate the impact of an event or intervention on a time series.
• Baseline Trend: The trend observed in the time series before the intervention.
• Interruption: The event or intervention that occurs at a specific point in time and is expected to impact the time series.
• Post-Intervention Trend: The trend observed in the time series after the intervention.
• Level Change:The immediate change in the value of the time series following the intervention.
• Slope Change: The change in the long-term trend of the time series after the intervention.
• Counterfactual: The estimated trend of what would have happened to the time series if the intervention hadn’t occurred.