03 · What You Need to Know
How Controlled Interrupted Time Series Strengthens Causal Inference
What Is an Uncontrolled Interrupted Time-Series Design?
An uncontrolled interrupted time-series (ITS) design examines repeated outcome measurements before and after an intervention within a single population or system.
The pre-intervention trajectory is used to estimate what the outcome might have looked like if the intervention had not occurred. The observed post-intervention outcomes are compared with this projected counterfactual.
For example, a university may examine monthly withdrawal rates for two years before introducing a retention policy and two years afterward. Segmented regression can estimate whether the policy coincided with an immediate change in withdrawal rates, a change in their trend, or both.
This approach can address several weaknesses of a simple before-and-after comparison because it explicitly models the outcome's earlier trajectory.
However, it remains vulnerable to events occurring near the intervention date that independently affect the outcome. This problem is often described as history bias.
What Is a Controlled Interrupted Time-Series Design?
A controlled interrupted time-series design, also called a comparative interrupted time series (CITS), extends the basic ITS approach by incorporating one or more comparison series.
The comparison series is generally drawn from a population, institution, geographical area, or outcome that was not exposed to the intervention of interest but may have experienced relevant background influences.
Researchers examine whether the intervention series changed differently from the comparison series after implementation, accounting for their pre-intervention trajectories.
The resulting counterfactual draws on both the intervention population's historical pattern and information about changes occurring in the comparison series.
| Feature |
Uncontrolled ITS |
Controlled ITS |
| Primary comparison |
Observed outcomes versus the projected historical trend |
Intervention-series changes relative to comparison-series changes |
| Number of series |
One intervention series |
Intervention series plus one or more controls |
| Concurrent common events |
May be difficult to distinguish from the intervention |
May be partially accounted for when they affect both series comparably |
| Between-group differences |
No external comparison-group selection problem |
Requires assessment of comparison suitability and differential trends |
| Statistical requirements |
Appropriate time-series modeling |
Time-series modeling plus between-series dependence and interaction structure |
| Main limitation |
Unmeasured events coinciding with intervention |
Invalid controls or differential changes may distort the estimated effect |
The controlled design is potentially more informative because it offers an additional source of evidence about the counterfactual. Whether that additional evidence is trustworthy depends on how the comparison series was selected.
Why Is History Bias a Major Concern in Uncontrolled ITS?
History bias occurs when an event other than the intervention influences the outcome around the intervention period.
Consider a school district introducing a digital attendance system. Recorded absenteeism decreases after implementation. During the same period, the government introduces a transportation subsidy that makes school attendance easier.
An uncontrolled ITS may detect a change in absenteeism relative to its earlier trajectory. Yet the observed interruption could reflect the digital system, the transportation subsidy, or both.
If a comparable district without the digital system experiences a similar reduction, that pattern may indicate a broader influence rather than an effect specific to the technology.
Conversely, if absenteeism decreases only in the intervention district while the comparison district continues along its expected trajectory, the evidence for an intervention-specific effect may become more convincing.
Neither pattern is conclusive by itself. The comparison is informative only if the control adequately represents relevant background influences and does not experience other differential changes.
What Makes a Comparison Series Credible?
A credible comparison series should be chosen because it can help approximate the intervention population's counterfactual, not simply because data are available.
Several characteristics deserve attention.
Exposure: The comparison population should not receive the intervention or experience meaningful spillover effects that undermine its role as an untreated reference.
Outcome comparability: Measurements should represent sufficiently similar constructs and use compatible definitions, collection procedures, and time intervals.
Pre-intervention behavior: The comparison series should provide useful information about relevant historical patterns. Identical baseline levels are not always necessary, but unexplained differences in trends or responses to background conditions may be problematic.
Shared influences: The control should plausibly experience the secular trends, seasonal conditions, or concurrent events that the researcher wants to account for.
Stability: Changes in population composition, reporting procedures, institutional policies, or intervention exposure should be documented and evaluated.
Importantly, a control can resemble the intervention population on observable characteristics while responding differently to important events. Baseline similarity alone does not establish counterfactual validity.
The broader principles of selecting a credible quasi-experimental comparison group remain relevant, although ITS introduces additional requirements concerning temporal patterns and concurrent influences.
What Types of Comparison Series Can Be Used?
Different control strategies address different sources of bias. Lopez Bernal and colleagues distinguish several approaches to selecting controls for interrupted time-series evaluations.
| Control type |
Illustrative example |
Principal concern |
| Geographical control |
Another school district without the policy |
Regional differences and location-specific events |
| Institutional control |
A comparable university without the intervention |
Differences in students, resources, and institutional policies |
| Within-institution control |
An unaffected department or eligible population |
Spillovers and shared institutional changes |
| Control outcome |
An outcome not expected to respond to the intervention but sensitive to relevant background conditions |
The outcome may respond differently to concurrent events or may actually be affected by the intervention |
A control outcome is not interchangeable with an untreated population. It may be useful for identifying common disturbances, but differences in causal mechanisms and outcome dynamics can limit the comparison.
Where multiple suitable comparison populations are available, researchers may consider approaches using several controls or constructing a weighted comparison series. These methods require additional assumptions and careful assessment of pre-intervention fit.
Does the Control Group Need the Same Baseline Outcome Level?
No. Two institutions can have different baseline outcome levels yet still provide a useful comparison if their temporal behavior and responses to relevant influences support the intended counterfactual model.
For example, University A may have a withdrawal rate of 12%, while University B has a rate of 8%. The difference in levels does not automatically invalidate University B as a control.
However, if withdrawal rates in the two institutions respond differently to economic conditions or student financial assistance, a simple comparison of changes may be misleading.
Researchers should examine historical trends, seasonal patterns, observable institutional characteristics, and the plausibility of comparable responses to concurrent events.
Different controlled ITS specifications permit different baseline levels and trends. What matters is whether the chosen model can credibly project the untreated intervention-series outcome using the historical and comparison information.
Must the Intervention and Control Series Have Parallel Pre-Intervention Trends?
Not necessarily in the same strict form as a conventional two-period difference-in-differences model.
Some controlled ITS models allow the intervention and comparison series to have different pre-intervention slopes and estimate whether their relative trajectories change after implementation.
Such models rely on assumptions about how those baseline differences would have evolved without intervention. For example, a linear comparative segmented-regression model may assume that the pre-intervention slope difference would have continued into the post-intervention period.
This is still a counterfactual assumption, and it may be implausible when trajectories are nonlinear or structurally unstable.
Researchers should distinguish a model that assumes parallel untreated trends from one that allows different baseline trends but assumes their relationship would remain stable.
The distinction is particularly relevant when comparing CITS with difference-in-differences, which also uses intervention and comparison groups but may impose different assumptions about counterfactual outcome changes.
How Is a Controlled Interrupted Time Series Analyzed?
A common approach extends segmented regression to include indicators for intervention-group membership and interactions with time and intervention-period variables.
For two groups, one illustrative linear specification is:
The interaction coefficients provide estimates of differential changes. They are not automatically causal effects unless the comparison series and counterfactual assumptions are credible.
The model also requires suitable treatment of autocorrelation, seasonality, heteroskedasticity, and clustering where relevant. A model fitted to aggregated institutional series may have different inferential requirements from one using repeated individual-level observations.
Nonlinear trends, delayed intervention effects, and changing implementation intensity may require alternative specifications. Researchers should define the expected impact model using substantive knowledge rather than selecting interactions solely on statistical significance.
Can Adding a Control Introduce Bias?
Yes. A comparison series may introduce bias when it differs from the intervention population in ways that affect the counterfactual.
Suppose a university implementing a retention program serves predominantly first-year students, while the comparison university serves a much larger proportion of working adults. The institutions may respond differently to changes in employment conditions or tuition assistance.
Even if both series have similar pre-intervention trends, a concurrent economic shock could affect them differently. Subtracting the comparison university's change might then overcorrect or undercorrect the intervention effect.
Spillover is another concern. If students at the comparison university gain access to the intervention's digital resources, the control no longer represents an unaffected population.
Adding controls can also reduce statistical precision when the comparison series is noisy or introduces additional parameters. The gain in potential bias reduction must be considered alongside these costs.
When Might an Uncontrolled ITS Be Preferable?
An uncontrolled ITS may be more defensible when the intervention series has a stable and well-characterized pre-intervention trajectory, important concurrent events are unlikely or can be addressed credibly, and no suitable comparison series exists.
For example, a highly specific institutional outcome may have no meaningful counterpart elsewhere. Introducing an unrelated control simply to satisfy a perceived methodological expectation could weaken rather than strengthen the analysis.
Researchers should not assume that a controlled design is always superior because it contains more groups. The value of the control depends on the causal problem it helps solve.
An uncontrolled analysis should nevertheless acknowledge the possibility of unmeasured concurrent influences and avoid overstating causal certainty.
How Can Researchers Evaluate Whether the Control Actually Helps?
Comparison-series selection should be informed by the likely sources of history bias before examining the estimated intervention effect.
Researchers can compare pre-intervention trajectories, examine relevant covariates, document concurrent policies, and investigate whether the control is exposed to intervention spillovers.
It is often useful to report both uncontrolled and controlled estimates. Agreement between them may strengthen confidence when the control is credible, while disagreement can reveal sensitivity to the counterfactual specification.
Disagreement does not automatically mean that the controlled estimate is correct. Researchers should investigate why the results differ, including whether the comparison series experienced a distinct shock or whether the model inadequately represents the historical relationship.
Where feasible, sensitivity analyses using alternative credible controls, different trend specifications, or prespecified intervention lags can help assess robustness.
