Interrupted time series analysis

When ITS fits

Three conditions define the design’s home ground [1, 2]:

1. A population-level intervention — a policy, fee change, guideline, or system-wide programme that affects (nearly) everyone producing the outcome data, rather than a subset that opted in.
2. A clearly defined start date. The interruption must be locatable in time. Phased or creeping rollouts blur the break the analysis depends on; if implementation ramped up over months, model that explicitly rather than pretending a single switch.
3. An adequate series of consistent measurements before and after. ITS earns its counterfactual from the pre-intervention trend, so the pre-period must be long enough to characterise that trend — including any seasonality — and the outcome must be measured the same way throughout. There is no universal minimum number of data points; the requirement depends on the trend’s stability, the outcome’s variability and the expected effect size, and Lopez Bernal, Cummins and Gasparrini’s tutorial is the reference for thinking it through rather than reaching for a rule of thumb [1].

This combination — population-level, dated, routinely measured — is why ITS is the workhorse for health-system and public-policy questions: user-fee removals, treatment-guideline changes, road-safety laws, facility-payment reforms, all evaluated from HMIS or service-statistics series that already exist. Where routine data are the source, their quality is a design input, not a footnote: run the data-quality assessment before trusting the series (see the data cluster), and where the series lives in DHIS2, the systems cluster covers what that platform does and does not guarantee about completeness.

Segmented regression: level and slope

The standard analysis fits a segmented regression: one model over the whole series with terms for the pre-existing trend, an indicator for the post-intervention period, and the time elapsed since the intervention. Two effect parameters result [1]:

• Level change — an immediate jump or drop in the outcome at the intervention point, relative to what the pre-trend predicted.
• Slope change — a change in the outcome’s direction or rate of change thereafter.

These are different substantive claims. A stock-out-ending supply intervention should produce a level change; a training programme whose effects accumulate should bend the slope; some interventions produce both, and some produce a temporary jump that decays. Specify the expected impact model in advance — which parameters, in which direction, over what horizon — because with two parameters and flexible timing, an unconstrained search will find something significant in noise [1].

Threats, and what answers them

Co-interventions and history. The design’s counterfactual is the projected pre-trend, so anything else that changed around the intervention date — a parallel campaign, a funding shift, an epidemic, a price shock — is a rival explanation the single-series analysis cannot separate from the programme [1, 3]. The strongest defence is a controlled ITS: add a comparison series that shares the confounders but not the intervention — the same outcome in a region the policy did not reach, or an outcome the intervention could not affect in the same population. A break in the treated series that does not appear in the comparison series is far harder to explain away [1, 2]. Where only one treated unit exists and several plausible comparison units do, the synthetic control page describes the natural next step; where comparison data exist before and after for both groups, difference-in-differences may fit better.

Seasonality. Outcomes with annual rhythm — malaria, births, enrolment — will fake a level change for any intervention that starts at the right point in the cycle. Model seasonality explicitly, and ensure the pre-period covers enough full cycles to estimate it [1].

Autocorrelation. Adjacent months resemble each other, so residuals are serially correlated and naive standard errors are too small — the same failure that plagues difference-in-differences inference. Test for autocorrelation and use methods that adjust for it [1].

Selection artefacts in routine data. The most treacherous rival explanation in development practice is not epidemiological but administrative: the intervention changes reporting, not reality. A programme that improves facility reporting completeness will raise counts of everything reported; a new register or revised indicator definition introduced alongside the intervention moves the series by construction. Check reporting rates over the same period, and treat any definitional change mid-series as a break in the instrument, not a finding [1, 2]. The data-quality assessment page covers how to verify a routine series can carry an evaluation.

Reporting: plot the raw series, always

An ITS result that cannot be seen in a plot of the raw data points with the fitted segments overlaid should be treated with suspicion, and a report that shows only coefficients should be sent back. The plot is also where honest uncertainty lives: readers can see the noise, the seasonality, the outliers and the size of the break relative to all three. Alongside it, report the impact model chosen in advance, the level and slope estimates with intervals, the autocorrelation handling, reporting-completeness checks, and any comparison series [1].

The wider debate in this cluster bears on ITS directly: a single-series ITS is a counterfactual design with a modelled — not observed — comparison, which is precisely why theory matters here. An explicit account of how and how fast the intervention should move the outcome converts the level/slope choice from a fishing licence into a test [1, 3].

Checklist before you commit to ITS

• The intervention is population-level with a documented start date (or a modelled ramp-up).
• The outcome series is long enough pre-intervention to establish trend and seasonality, and the measurement instrument was stable throughout.
• The expected impact model — level, slope, or both; immediate or lagged — is specified before analysis.
• Seasonality and autocorrelation are handled explicitly.
• Co-interventions in the window are catalogued; a comparison series is used where one exists.
• Reporting completeness and indicator definitions are verified stable across the series.
• The report leads with the raw-series plot and fitted segments.