Why Basket Definitions Matter
A basket trial studies one treatment in several disease subgroups, often because patients share a molecular feature or another proposed treatment target. The central design question is not simply how many groups to list. It is which groups have a defensible clinical basis for being modeled as having treatment effects drawn from a common distribution. That decision determines whether borrowing information across baskets is plausible.
A shared target label alone is not enough. Two tumors may carry alterations in the same gene but differ in whether the alteration drives growth, whether the drug inhibits the relevant pathway, or whether patients receive the same treatment regimen. Conversely, distinct disease names may conceal a sufficiently similar mechanism and clinical setting to make a common model reasonable. Subgroup definitions therefore need to connect biology to the treatment effect the trial intends to estimate.
What Exchangeability Requires From a Clinical Definition
Let \(\theta_j\) denote the treatment effect for basket \(j\), defined on a stated scale for a stated population and endpoint. A common random-effects formulation is
where \(F\) is a shared distribution, \(\mu_\theta\) describes its center, and \(\tau\) describes between-basket variation. This formulation says that, conditional on the shared parameters, the effects are modeled as arising from the same distribution. It does not say that every \(\theta_j\) is equal, nor does it say that every patient has the same outcome probability.
The clinical definition matters because the model treats subgroup labels as interchangeable for the purpose of that shared distribution. If the labels were permuted while the shared model and covariates remained fixed, the joint distribution of the effects would not change. That symmetry is difficult to defend when, for example, one subgroup's alteration activates the drug target and another subgroup's alteration is known to bypass it.
Before assigning groups to a common hierarchy, specify the estimand. The treatment effect might be a difference in response probabilities, a log odds ratio, a hazard ratio, or a contrast in mean change. The populations, comparator, follow-up period, endpoint, and treatment regimen must also be sufficiently aligned. Effects on different scales or for different clinical questions are not automatically exchangeable merely because they concern the same drug.
A Structured Clinical Assessment
A useful assessment examines several connected dimensions. No single item is a mechanical pass-or-fail test; the task is to make the assumptions visible and to decide whether any differences call for separate groups, explicit model terms, or a different analysis.
State the endpoint, time horizon, treatment contrast, effect scale, and target patient population. Check that the same quantity is being estimated across baskets.
Record the alteration or phenotype used for eligibility, its functional role, relevant co-alterations, and whether it is thought to drive disease or merely accompany it.
Explain why the treatment is expected to affect the relevant pathway in each subgroup. Identify known resistance mechanisms or contexts in which the target may not be active.
Check disease stage, prior therapies, assay rules, treatment dose, concomitant care, and outcome assessment. Differences that change who is enrolled or how benefit is measured may change the estimand or treatment effect.
Specify which patients belong to each subgroup, how ambiguous or multiple findings are handled, and the rationale for sharing or separating effects. Set the rule before examining subgroup outcomes.
Eligibility criteria are part of the scientific definition, not merely administrative details. A mutation measured by different assays, a different threshold of expression, or a history of prior therapy can select clinically different patients. Such differences do not automatically invalidate borrowing, but they require a reasoned account of why the treatment effect remains plausibly drawn from the same distribution.
Also distinguish prognostic variation from treatment-effect variation. A feature is prognostic if it is associated with outcomes regardless of treatment; it is predictive when the treatment effect differs according to that feature. A subgroup may have worse expected outcomes under either treatment and still have a similar treatment effect. A shared model of treatment effects therefore need not imply equal baseline risk. The relevant question is whether the clinical differences plausibly modify the treatment contrast being modeled.
Worked Examples
Worked Example: Two Alterations With a Shared Target Mechanism
Hypothetical design. A trial studies a targeted drug in two tumor subgroups. Subgroup A has alteration A, and subgroup B has alteration B. Laboratory and clinical evidence available before the trial indicates that both alterations activate the same pathway, that the drug inhibits the pathway at the same dose, and that neither subgroup is defined by a known bypass mechanism. Both groups have the same disease stage criteria, prior-treatment rules, response assessment, and follow-up.
Suppose the planned endpoint is response by 24 weeks and the planned effect is a difference in response probabilities between the drug and a common control condition. The groups are eligible for a common exchangeability class if the clinical team can defend the proposition that their treatment effects arise from a shared distribution, while allowing the effects to differ.
For illustration, imagine the observed drug-arm counts are 6 responses among 12 patients in A and 5 among 10 in B. The empirical response proportions are
These matching proportions are not the reason to define the groups together: the clinical rationale was specified before outcomes. Nor do they establish equal treatment effects, since these are drug-arm proportions, not treatment contrasts against control. The matching endpoint and eligibility rules make the comparison interpretable, while the shared mechanism makes exchangeability plausible. The hierarchical model can still represent uncertainty and genuine between-basket variation.
Worked Example: Similar Target, Different Biological Context
Hypothetical design. A trial considers grouping two cancers because both have a variant in the same signaling gene. In cancer X, the variant is believed to activate the pathway inhibited by the study drug. In cancer Y, the same gene variant is usually accompanied by a documented resistance mechanism that signals through an alternate pathway. Both cancers would receive the same drug and use the same response criteria.
The shared gene name and matched assessment do not resolve the key issue: the drug may engage the relevant biology in X but not in Y. If the trial estimates response probability on drug, suppose 8 of 16 patients in X and 3 of 12 in Y respond. Then
The observed 25-percentage-point difference is uncertain and does not by itself establish a biological distinction in treatment effects; these are small hypothetical samples and there is no comparator in this calculation. However, the prespecified resistance mechanism is a clinical reason to question a shared distribution. A defensible plan might define separate exchangeability classes, or model the resistance context explicitly if that approach has a sound scientific basis and adequate design support. It would not be defensible to merge the groups solely because the gene symbol matches.
Worked Example: Eligibility Differences That Change the Target Population
Hypothetical design. A basket trial includes two disease subgroups with a similar proposed drug mechanism. One subgroup enrolls only patients who have not received prior systemic therapy; the other enrolls only patients whose disease progressed after two prior regimens. The trial reports response within 12 weeks using the same criteria.
The endpoint and treatment mechanism are aligned, but the enrolled populations differ in treatment history. Suppose 9 of 15 patients respond in the first group and 4 of 16 in the second. Their observed proportions are
The 35-percentage-point contrast is not a clean estimate of a treatment-effect difference: it compares two drug-arm groups with different prior-treatment histories and no control contrast. Prior therapy could affect prognosis, drug sensitivity, or both. The design team should ask whether the target effect is intended for each subgroup's distinct eligible population, and whether prior treatment is believed to modify that effect. If the groups remain in one hierarchy, the protocol should explain why their effects are still plausibly exchangeable after the planned adjustment or stratification. If that rationale is weak, distinct classes are more transparent than assuming a common distribution without qualification.
Justification: Why Coherent Definitions Support Borrowing
Suppose a set of clinically coherent subgroups has treatment effects modeled as conditionally independent draws from the same distribution \(F(\mu_\theta,\tau)\). Their joint conditional density is
For any permutation \(\pi\) of the subgroup labels, the density becomes
The equality holds because multiplication is unchanged by reordering its factors. Thus the model does not privilege one subgroup label over another in the distribution of effects. Clinical coherence makes that symmetry more plausible: each label represents a group for which the same effect-generating assumptions are reasonable. If a subgroup has a distinct treatment mechanism or a different estimand, the symmetry is harder to defend, and shared borrowing may pull estimates toward an inappropriate common center.
Common Mistakes, Alternatives, and Limits
- Using a shared biomarker name as the whole rationale. A label may encompass variants with different functional consequences. Specify the variant, biological role, and treatment-mechanism link.
- Equating similar prognosis with exchangeable treatment effects. Similar untreated outcomes do not establish similar treatment response, and different baseline risks do not automatically imply different treatment effects.
- Defining groups after seeing the outcomes. Outcome-driven regrouping can make the clinical rationale circular and overstate how well the model represents a prespecified design. Use prespecified, reproducible rules.
- Assuming a common model means equal effects. Exchangeability permits heterogeneity under the shared distribution. It is a structured assumption about how effects relate, not a claim of identity.
- Ignoring incompatible estimands. Different endpoints, follow-up periods, comparators, or treatment regimens may mean the baskets are not estimating the same quantity.
The main alternatives are to place clinically distinct subgroups in separate exchangeability classes, analyze them independently, or use a model that represents a scientifically justified effect modifier. Each choice has costs. Separate analyses reduce borrowing and may be imprecise with sparse data; a shared class can be more efficient but risks inappropriate borrowing; an adjustment requires a clear variable definition and enough information to support it. No modeling choice can compensate for unclear eligibility or an ill-defined treatment effect.
Clinical definitions are also limited by uncertainty in the biology itself. Mechanistic evidence may be incomplete, assays may classify patients imperfectly, and treatment effects may vary for unanticipated reasons. A coherent subgroup definition therefore makes the modeling assumption more defensible; it does not guarantee it. The protocol should record the evidence and unresolved uncertainties so that later interpretation can distinguish a design assumption from an established clinical fact.
Check Your Understanding
Answer each question, then compare with the brief solutions below.
- Two subgroups have the same target-gene label, but only one has evidence that the alteration activates the pathway inhibited by the drug. Is the gene label alone sufficient to justify a shared exchangeability class?
- A biomarker is associated with poor outcomes in both treatment and control groups, but there is no evidence that it changes the treatment contrast. Is this necessarily a reason to separate treatment effects?
- In a hypothetical drug arm, 7 of 14 patients respond in subgroup A and 6 of 12 in subgroup B. Calculate both response proportions. Do these values demonstrate equal treatment effects?
- Name three design features, apart from the biological mechanism, that should be checked before sharing a treatment-effect distribution.
- Why should basket boundaries be specified before examining subgroup outcomes?
Solutions. (1) No. The functional role of the alteration and its connection to the treatment mechanism matter; a shared label does not establish that the effects are exchangeable. (2) No. That describes prognostic association. Separation is more directly motivated if the biomarker plausibly modifies the treatment effect, although other clinical differences may still matter. (3) \(\hat{p}_A=7/14=0.500\) and \(\hat{p}_B=6/12=0.500\). These are drug-arm response proportions, not treatment contrasts, so they do not demonstrate equal treatment effects. (4) Examples include the endpoint and assessment time, eligibility and prior-treatment rules, treatment regimen and comparator, and the effect scale. (5) Prespecification prevents outcome patterns from creating a post hoc rationale for grouping and makes the clinical assumptions transparent.