Defining a Fixed Target Population

Why Define the Population Before Adaptation?

An adaptive trial may change its enrollment pace, allocation, or eligible participant profile as information accumulates. The participants who eventually enter the trial are therefore not necessarily a stable description of the population the trial is intended to address. A clear target-population definition makes that distinction explicit: it says which people the intended conclusion concerns, rather than merely describing who happened to enroll.

This is a necessary part of specifying an adaptive-trial estimand. The target should be expressed in terms that can be checked using information available at baseline, before treatment assignment and before any participant-specific post-randomization events. It should not be defined retrospectively by the participants whose outcomes look most favorable or by the enrollment pattern produced by an adaptation.

It helps to distinguish four groups. The target population is the group the estimand concerns. The screened population consists of people assessed for possible participation. The enrolled population consists of those who enter the trial. The analysis population consists of the participants included in a particular analysis under its stated rules. These groups may overlap, but they are not interchangeable.

For a formal description, let \(X\) denote a vector of baseline characteristics and let \(E=1\) indicate that a person meets the specified baseline criteria. The target population can be described as people in a stated setting for whom \(E=1\). If the distribution of baseline characteristics within that group matters to the intended conclusion, denote the target distribution by \(F^*(x)\). Naming eligibility criteria identifies who qualifies; stating \(F^*(x)\), or otherwise defining the relevant population context, can also clarify how the eligible group is understood.

Writing Criteria That Fix Membership

A usable definition does more than say “patients with the disease” or “high-risk patients.” It identifies the condition, the relevant baseline assessment, the threshold or category, and the context in which membership is defined. The criteria should be clinically meaningful and sufficiently precise that two investigators would classify the same baseline record in the same way.

For example, a definition might specify adults aged 40 through 75 years with a confirmed diagnosis under a named clinical standard and a baseline laboratory measurement at or above a prespecified threshold, recruited from a stated type of care setting. In an actual protocol, the diagnosis standard, assay, timing window, treatment history if relevant, and handling of borderline or unavailable measurements should be made explicit. These details are not administrative decoration: they determine who belongs to the group.

Criteria for the target population should be based on characteristics measured before randomization. A criterion such as “people who remain adherent for six months” depends on events after treatment assignment and therefore does not define a baseline population. Likewise, a group defined by a response observed after treatment cannot be treated as if its membership had been known at trial entry. Such questions require distinct estimand choices; they should not be smuggled into the baseline target definition.

A fixed target is not a claim that every eligible person can be recruited, or that the trial will enroll a representative sample automatically. It is a stable reference for the intended conclusion. If adaptation narrows enrollment to a subset of that target, the estimand may still be stated for the original group, but the data may provide limited support for conclusions about people who are no longer enrolled. Defining the target does not solve that evidence problem.

Fixed Target and Changing Enrollment Are Different Objects

An adaptation may alter which eligible people are approached or randomized. For instance, an interim rule might favor enrollment of one baseline subgroup. That changes the composition of the enrolled cohort; it does not, by itself, revise the target definition. The target remains fixed if the estimand is still intended to concern the original baseline-defined group.

A simple calculation shows why the distinction matters. Suppose the target comprises two baseline categories, A and B, with equal shares. In a hypothetical outcome illustration, the mean outcome is 10 units in category A and 4 units in category B. A hypothetical early cohort enrolling 20 people from each category has a pooled mean of \(\frac{20(10)+20(4)}{40}=7\) units. After an enrichment adaptation, suppose a later cohort enrolls 30 people from A and 10 from B, with the same category-specific means. Its pooled mean is \(\frac{30(10)+10(4)}{40}=8.5\) units.

The pooled mean changed from 7 to 8.5 units because the enrolled category shares changed, even though the category-specific means in this illustration did not. The enrolled cohort’s average therefore reflects both outcomes within categories and the cohort’s composition. It should not automatically be described as the average for the fixed target, whose category shares in this example remain 50% and 50%.

Justification: Why Enrollment Counts Do Not Define the Target

The distinction follows from the definitions. Let \(E=1\) represent membership under fixed baseline criteria. Let \(A\) denote a trial adaptation, such as an enrollment rule that favors one category. The target membership rule is \(E=1\); the enrollment mechanism determines which members are observed. If \(A\) changes the chance of enrollment across categories, then the distribution of \(X\) among enrolled participants can change even while the rule \(E=1\) stays constant.

For a two-category illustration, let \(q_A\) be the share of category A among enrolled participants, and let \(m_A\) and \(m_B\) be the category-specific mean outcomes. The enrolled-cohort mean is \(q_A m_A+(1-q_A)m_B\). If adaptation changes \(q_A\) while \(m_A\) and \(m_B\) remain fixed, the pooled mean changes whenever \(m_A\ne m_B\). Specifically, a change from \(q_A\) to \(q'_A\) changes the pooled mean by \((q'_A-q_A)(m_A-m_B)\). Thus composition alone can change the pooled average. This arithmetic justifies treating target definition and enrollment composition as separate descriptions; it does not prescribe an analysis method.

When Is the Target Itself Changing?

The decisive question is whether the rule defining the intended group has changed, not whether the observed enrollment pattern has. If the original target is adults aged 40 through 75 with a specified diagnosis and baseline value of at least 8.0 units, an interim decision to recruit more people near the upper end of that range changes the enrolled mix but leaves the formal target intact. If a protocol amendment changes the minimum to 9.0 units and the intended conclusion is now restricted to people meeting that new threshold, the target definition has changed.

A trial can retain the original target as its primary target while introducing a narrower enrollment rule. But it must then be transparent that the enrolled participants no longer cover the target in the same way. If the protocol instead redefines the target, the revised criteria should be stated, dated, and distinguished from the original definition. Combining data across definitions without recording which rule applied can make it unclear which group a reported conclusion concerns.

The setting and time context also matter. “Adults with the condition” may refer to different populations in primary care and specialist clinics, or under different diagnostic practices. A fixed target should specify relevant context where it affects membership or interpretation. Fixing criteria does not mean that the group can never be described more precisely; it means that any change to the intended group is explicit rather than inferred from who entered the trial.

Diagnostics, Alternatives, and Limitations

Several checks help reveal whether a proposed target definition is stable and usable:

• Check operational clarity. Can the criteria be applied consistently from baseline records? Terms such as “severe,” “recent,” or “high risk” need a specified definition, measurement, and time window.
• Check timing. Are all membership criteria known before randomization? If a criterion depends on later treatment, adherence, response, or follow-up, it is not a baseline eligibility criterion.
• Check versions. Record the criteria in force for each enrollment stage. A protocol amendment that changes eligibility should not silently overwrite the original target description.
• Check coverage. Compare enrolled participants with the target criteria and relevant baseline categories. A fixed target can include people from whom the trial ultimately obtains little or no information.
• Check terminology. Do not call the enrolled cohort “the target population” when it is a selected subset, or treat the analysis population as identical to either without verifying the definitions.

One alternative is to define the target simply as “everyone who enrolled.” That is easy to describe, but it makes the target depend on the adaptation and recruitment process. The group may differ across stages or trial versions, so it is not a stable population definition. Another alternative is a broad clinical label with no operational criteria. That may sound general, but it is difficult to reproduce and may conceal disagreements about who qualifies. A baseline-defined target avoids these ambiguities, though it cannot guarantee that the enrolled sample represents the target.

A further limitation is that criteria alone do not ensure that trial evidence supports conclusions for every member of the target. If an adaptive rule stops enrolling one eligible category, the data may contain little information about that category. The target remains definable, but the evidence available for it may be incomplete. Later methods address how to express or analyze effects for populations with differing covariate distributions; defining the population is the prerequisite, not a substitute for those methods.