Why Exclusion Requires a Pathway Audit
An instrumental variable can shift treatment receipt without being assigned like a treatment itself. For example, an encouragement may raise participation, eligibility may make a program available, or access may reduce the effort required to obtain care. The instrumental-variable argument requires more than a change in treatment: the instrument must not affect the outcome by another route. This is the exclusion restriction.
Exclusion is not established by showing that the instrument predicts treatment, nor by describing the instrument as an encouragement or a policy rule. It is a substantive claim about what could happen if the instrument changed while treatment receipt were held fixed. A pathway audit makes that claim concrete: list plausible consequences of the instrument, trace whether each could reach the outcome without passing through the defined treatment, and explain why each route is absent or negligible.
For binary \(Z\) and \(D\), the restriction says there is no causal effect of \(Z\) on \(Y\) at either fixed treatment level. It does not say that \(Z\) and \(Y\) must be unassociated in the observed data: a valid instrument can change \(Y\) by changing \(D\). The key question is whether any causal route from \(Z\) to \(Y\) remains when the route through treatment receipt is set aside.
The definition depends on what counts as treatment. If treatment is defined as receipt of a particular medication, an instrument-induced change in counseling could be a bypass pathway. If treatment is instead defined as a well-specified care package that includes that counseling, the pathway may run through the broader treatment. As the earlier material on multiple treatment versions emphasizes, changing the treatment definition changes the causal contrast being studied. Renaming a pathway as part of treatment is not enough: the revised treatment must be clearly defined and meaningful for the question.
How to Trace Alternative Pathways
A pathway audit starts with the instrument as it is actually assigned or experienced, not just with its label. Ask what the instrument changes, for whom, and at what point in the process. Then follow each plausible consequence toward the outcome. A path is a concern for exclusion if it can affect the outcome without changing the defined treatment receipt.
For example, an invitation to a screening program could increase screening attendance, but could also provide health information that changes diet. If the treatment is screening attendance, the information-to-diet-to-outcome route bypasses treatment receipt. Likewise, an eligibility rule could increase receipt of a named therapy while also changing insurance coverage, clinician contact, or access to other services. Whether any of these is a genuine concern depends on the setting and outcome; naming a possible route is the start of an audit, not proof that it operates.
Describe what \(Z\) changes and define exactly what counts as \(D\), including the relevant treatment versions and timing.
Consider information, money, time, stress, provider contact, service availability, and changes in other care—not only the intended change in treatment uptake.
Ask whether the outcome could change while the defined treatment receipt stayed fixed. If so, describe the bypass route and its plausibility.
Use design knowledge and subject-matter evidence to assess routes. Observed associations alone generally cannot verify that all such routes are absent.
A useful audit separates three claims. First, the instrument changes treatment receipt: this is relevance. Second, the instrument is independent of potential outcomes under the assumptions appropriate to the design. Third, the instrument affects the outcome only through treatment receipt: exclusion. Evidence for one claim does not establish the others. The earlier material on observable and unobservable implications of IV assumptions motivates this distinction; here the emphasis is on examining exclusion substantively.
Worked Pathway Audits
Worked Example: A Reminder That Also Provides Advice
Suppose a hypothetical randomized study sends a reminder encouraging patients to attend a vaccination appointment. Let \(Z=1\) indicate receiving the reminder, \(D=1\) indicate receiving the vaccine, and \(Y\) be a hypothetical health score measured later, in points. Among 200 patients in each randomized group, 120 of those sent a reminder and 60 of those not sent one receive the vaccine. The mean health scores are 72 and 68 points, respectively.
First-stage contrast. The vaccination proportions are \(120/200=0.60\) and \(60/200=0.30\). The difference is \(0.60-0.30=0.30\), or 30 percentage points. The reminder is relevant in this hypothetical sample.
Outcome contrast and Wald ratio. The mean outcome difference is \(72-68=4\) points. The ratio is \(4/0.30=13.33\) health-score points per additional vaccination induced by the reminder. This arithmetic is correct as a ratio of the observed contrasts, but its interpretation as a complier LATE requires the IV assumptions, including exclusion.
Pathway audit. Suppose the reminder also includes advice about hydration and when to seek care. That advice could affect the later health score whether or not a patient receives the vaccine. The route \(Z\) to advice to \(Y\) therefore bypasses the defined treatment \(D\). If this route is plausible, the Wald ratio cannot be justified as a vaccine effect by the IV argument alone. Randomization can support independence of the reminder, but it does not eliminate a direct effect of the reminder’s content.
The example illustrates why a strong first stage and a randomized instrument do not settle exclusion. The study team would need to examine what the reminder communicates and whether those messages could affect the measured outcome independently of vaccination.
Worked Example: Eligibility That Changes More Than Program Receipt
Consider a hypothetical income-eligibility rule used as an instrument for receiving a medication. Let \(Z=1\) denote eligibility, \(D=1\) medication receipt, and \(Y\) a blood-pressure measure in millimeters of mercury. Among 100 eligible people, 70 receive the medication and the mean blood-pressure reduction is 8 mmHg. Among 100 ineligible people, 40 receive it and the mean reduction is 5 mmHg.
Contrasts. The treatment-receipt difference is \(70/100-40/100=0.70-0.40=0.30\). The outcome difference is \(8-5=3\) mmHg of additional mean reduction. The Wald ratio is \(3/0.30=10\) mmHg of reduction per induced medication receipt. These are hypothetical group summaries; the ratio is not automatically a causal effect.
Pathway audit. Suppose eligibility also confers access to nurse visits that include blood-pressure monitoring and lifestyle counseling, even for people who do not receive the medication. Eligibility could then affect \(Y\) through those services while \(D\) remains fixed. The route from eligibility to nurse services to blood pressure is a potential exclusion violation for medication receipt as defined here.
A narrower audit might find that nurse visits are available only after medication initiation and are part of a consistently defined medication-care package. That evidence could change the substantive assessment, but it does not mechanically prove exclusion. Alternatively, defining \(D\) as receipt of the full package changes the treatment from medication receipt to package receipt, and the causal effect of interest changes accordingly. The analysis must state which treatment is being evaluated.
Worked Example: A Transport Voucher and Access to Other Care
Suppose a hypothetical hospital offers some patients a transport voucher intended to increase receipt of a planned procedure. Let \(Z=1\) indicate voucher availability, \(D=1\) indicate receiving the procedure, and \(Y\) be the number of days alive and outside hospital during the following month. Among 150 patients with a voucher, 90 receive the procedure and the average outcome is 24.0 days. Among 150 without a voucher, 60 receive it and the average is 23.0 days.
Contrasts. The treatment proportions are \(90/150=0.60\) and \(60/150=0.40\), giving a first-stage difference of \(0.20\). The outcome difference is \(24.0-23.0=1.0\) day. The Wald ratio is \(1.0/0.20=5.0\) days per additional procedure receipt. This is a ratio of the reported differences, not a verified procedure effect.
Pathway audit. A voucher might enable a patient to travel to primary-care visits or collect medication, not only attend the procedure. If those additional trips change health or hospital use without changing receipt of the procedure, they are bypass pathways. Their plausibility depends on voucher rules: a voucher restricted to a single procedure trip raises a different concern from one usable for any medical travel.
The outcome also matters. A transport effect on another service may alter days outside hospital even if it does not affect the procedure. A pathway audit should therefore connect specific instrument-induced changes to the particular outcome being analyzed, rather than treating “access” as either automatically harmless or automatically disqualifying.
What the Wald Ratio Can and Cannot Tell Us
For a binary instrument, the Wald ratio is the difference in mean outcomes across instrument groups divided by the difference in treatment proportions. Under the relevant IV assumptions, including exclusion and monotonicity, it identifies the complier LATE. But the ratio is computed from observed contrasts; the calculation itself does not verify its assumptions.
The source of the problem is visible from the exclusion definition. The outcome contrast across instrument values can reflect both any change in treatment receipt and any effect of changing the instrument at fixed treatment receipt. If a bypass pathway exists, the observed outcome contrast includes a contribution that is not solely due to the treatment change. Dividing by the first-stage contrast does not, by itself, remove that contribution.
This is a substantive assessment, not generally a test with a definitive pass-or-fail result. In many settings, exclusion is not empirically identified from the observed instrument, treatment, and outcome alone. Researchers can make the case more credible by documenting instrument implementation, examining what else it changes, using subject-matter evidence about plausible mechanisms, and explaining why particular bypass routes are unlikely to affect the outcome. If a route is credible, report it as a limitation and avoid presenting the Wald ratio as an established treatment effect.
Common Mistakes
- “The instrument was randomized, so exclusion holds.” Randomization can support independence, but an assigned instrument may itself change information, attention, resources, or behavior directly.
- “The instrument strongly predicts treatment, so it is valid.” A large first-stage contrast supports relevance only. It says nothing by itself about bypass pathways.
- “There is no statistically significant outcome difference among nonrecipients, so exclusion is proven.” A comparison among observed nonrecipients is not generally a comparison of groups made comparable by treatment receipt; selection into nonreceipt can matter. A nonsignificant result is not proof that a causal direct effect is absent.
- “Any pathway can be absorbed into the treatment.” Redefining treatment may be appropriate only if the broader treatment is well specified and matches the scientific question. It changes the estimand and needs a new justification.
- “The Wald ratio is the treatment effect because its units look reasonable.” The ratio has a numerical value even when exclusion is doubtful. Numerical calculation and causal interpretation are separate steps.
Check Your Understanding
For each question, distinguish a pathway concern from evidence that establishes or refutes the exclusion restriction.
- A text reminder increases receipt of a therapy and also tells patients how to manage symptoms at home. If treatment is defined as therapy receipt, describe a possible bypass pathway.
- An eligibility rule increases medication uptake. Why does that first-stage result not establish exclusion?
- In a hypothetical study, the instrument-group outcome difference is 2 units and the treatment-receipt difference is 0.25. Calculate the Wald ratio and state why the calculation alone does not identify a LATE.
- A travel voucher can be used for both the planned procedure and unrelated medical visits. What additional information would help assess exclusion for an outcome affected by healthcare use?
- What changes when treatment is redefined from receipt of a medication to receipt of a medication-plus-counseling package?