Randomized Encouragement Designs and Treatment Uptake

Why Encourage Rather Than Assign Treatment?

In some studies, researchers cannot or do not want to compel people to receive a treatment. They may instead randomize an offer, reminder, referral, or other encouragement intended to increase uptake. A reminder to attend a counseling appointment, for example, can be randomly assigned even though attendance remains each participant’s choice. The resulting design has two distinct events: being assigned an encouragement and actually receiving the treatment.

That distinction is central to causal inference. Randomization governs the encouragement assignment; it does not automatically randomize who takes up treatment. Comparing people who received treatment with those who did not can therefore reintroduce selection: their decisions to take up treatment may reflect health, motivation, resources, or other factors that also relate to the outcome. An encouragement design uses random assignment as a possible source of variation in treatment uptake, but the design must also be assessed for other requirements.

The encouragement may be an invitation, reminder, subsidy, access offer, referral, or other intervention intended to change treatment uptake. It is not itself the treatment merely because it is designed to promote treatment. Whether a particular activity counts as the treatment or as an encouragement depends on the study’s precise definitions and causal question. Those definitions should be fixed before looking at outcomes.

Assignment, Receipt, and Noncompliance

Assignment describes what randomization allocated. Receipt describes what a participant actually experienced. In a fully enforced treatment assignment, these may coincide. In an encouragement design, they commonly differ: some people assigned an offer do not take up treatment, while some not assigned the offer obtain treatment through another route. This mismatch is called noncompliance with the intended treatment status or encouragement pathway.

A participant assigned an encouragement is not necessarily treated. Likewise, a participant not assigned an encouragement is not necessarily untreated. For that reason, the study should record \(Z\) and \(D\) separately rather than replacing one with the other. The distinction also applies when \(D\) is not a simple yes-or-no event: treatment receipt may require an operational definition, such as attending at least one session or completing a specified course.

The assignment may be randomized even when receipt is not. A participant who accepts a treatment may differ from one who declines it in ways that matter for \(Y\). Thus a comparison by \(D\) is not automatically protected by the randomization that was used to allocate \(Z\). Randomization supports a comparison by assigned encouragement; a causal interpretation involving treatment receipt requires additional reasoning about how assignment affects outcomes.

The Causal Pathways an Encouragement Design Requires

A simple causal map helps distinguish the design’s intended mechanism from competing explanations. The desired pathway is from randomized encouragement \(Z\) to treatment receipt \(D\), and then from \(D\) to outcome \(Y\). Other variables can create additional paths. Let \(X\) represent measured characteristics recorded before assignment, and let \(U\) represent other causes that may not be measured.

The \(U\)-paths illustrate why treatment receipt can be confounded with the outcome. For example, motivation might affect both attendance and later health. Random assignment of \(Z\) is intended to break systematic links between assignment and pre-existing causes of the outcome. But it does not erase the \(U\)-paths between receipt and outcome, and it does not guarantee that every effect of \(Z\) on \(Y\) travels through \(D\).

The exclusion condition is substantive, not a consequence of randomization. A reminder might change attendance and thereby affect the outcome through counseling. But it might also increase patients’ attention to their health, prompt medication adherence, or create additional contact with clinicians. If any of these routes affect \(Y\) without operating through the defined treatment \(D\), the encouragement has a direct or alternative pathway to the outcome. Calling an intervention an “encouragement” does not make those pathways disappear.

The study’s definitions matter here. If \(D\) is defined narrowly as attending one counseling session, but the reminder also causes people to complete a separate clinical service, that separate service is not automatically part of \(D\). The researcher must ask whether it is a consequence of the defined treatment or a distinct route from \(Z\) to \(Y\). Clear definitions and a realistic account of how participants experience the encouragement are essential to that assessment.

What Randomization Does—and Does Not—Guarantee

Randomization means assignment is generated by a chance mechanism rather than chosen according to participants’ characteristics. In expectation over that mechanism, assignment is independent of pre-assignment characteristics and potential outcomes. This is a statement about the assignment process, not a promise that every realized sample will have identical groups or that all other instrumental-variable conditions hold.

A short justification makes the scope clear. Suppose \(Z\) is assigned with probability \(q\), independently of a fixed pre-assignment quantity \(W\), where \(W\) might be a potential outcome or a baseline characteristic. Let \(I(Z=1)\) equal 1 when \(Z=1\) and 0 otherwise. Independence gives

Since \(P(Z=1)=q\), it follows that

provided \(q>0\). The same reasoning applies to \(Z=0\) when that assignment has positive probability. Thus the two assignment groups have the same expected value of \(W\) under the randomization mechanism. In a particular finite sample, their observed averages can still differ by chance.

This argument concerns variables determined before assignment and potential outcomes under the assignment mechanism. It does not show that \(D\) is randomized: treatment receipt occurs after assignment and may depend on participant choices and circumstances. Nor does it show that \(Z\) affects \(Y\) only through \(D\), or that \(Z\) changes \(D\). These are separate design questions.

Practical Design Questions and Common Pitfalls

Before interpreting an encouragement study, specify what is assigned, what counts as treatment receipt, and what outcome is measured. Also describe the timing: assignment should precede the uptake it is meant to influence, and outcome measurement should follow the relevant treatment period. These details help prevent ambiguous classifications, such as counting a referral as treatment in one part of the analysis and as encouragement in another.

A useful pathway audit asks whether assignment is genuinely randomized; whether the encouragement could plausibly change receipt; and whether it could affect the outcome through attention, cointerventions, access, or any other route that bypasses the defined treatment. The study should also state how receipt and outcome are measured and consider whether participants’ assignment could influence one another’s receipt or outcomes. Those checks do not establish validity mechanically; they make the assumptions and design choices visible.

Common mistake: “The offer was randomized, so treatment receipt was randomized and any difference between treated and untreated participants is causal.” The first clause concerns \(Z\), not \(D\). Participants may select into receipt, and their reasons for doing so may also predict the outcome. Randomization of \(Z\) does not by itself remove that selection or rule out a direct path from \(Z\) to \(Y\). The correction is to preserve the distinction between assignment and receipt, then assess the assumptions needed for the intended instrumental-variable interpretation.