Basket Trials in Oncology Research

onto the entire real line:

A normal hierarchical distribution can then be placed on the transformed response probability.

Understanding Shrinkage

Suppose Basket A has only five patients and one response. Its raw response rate is:

Suppose the other baskets have substantially more evidence suggesting that the treatment response is around 30%. A hierarchical model may pull Basket A's posterior estimate toward the overall mean.

This is called shrinkage.

Shrinkage is stronger when:

• The basket contains little information.
• The other baskets are highly consistent.
• The estimated between-basket heterogeneity is small.

Shrinkage is weaker when:

• The basket contains substantial information.
• Other baskets disagree strongly.
• The estimated heterogeneity is large.

Borrowing Can Help—or Hurt

Consider two scenarios.

Scenario A: Similar Treatment Effects

Suppose:

The baskets are reasonably consistent. Borrowing information can stabilize estimates, particularly in baskets with small sample sizes.

Scenario B: Strong Heterogeneity

Suppose instead:

Strong borrowing across all baskets could cause the poorly responding baskets to appear more promising than their own data justify.

This is why basket-trial simulations should evaluate performance under heterogeneous scenarios rather than only under the assumed common-effect scenario.

Borrowing Is a Design Assumption

The most important conceptual point is that borrowing is not simply a computational trick applied after the trial.

It is part of the statistical model.

The model encodes assumptions about how related the baskets are.

Therefore, the operating characteristics should be evaluated under multiple possible patterns of basket similarity and heterogeneity.

A Complete Worked Example

Consider a Phase II basket trial evaluating a targeted therapy in four biomarker-positive tumor types. The primary endpoint is objective response rate assessed according to the protocol-defined response criteria.

For illustration, suppose the investigators define:

The first stage of each basket contains 10 patients. The trial may stop a basket early for futility or continue it to the second stage.

Stage 1 Basket Rule

Suppose the investigators use the following illustrative rule:

This means that each basket operates initially as a screening cohort.

For basket \(j\):

The basket continues if:

Why Use Basket-Specific Stopping?

Suppose the four baskets produce:

The trial does not need to abandon the entire biomarker hypothesis simply because Basket C appears inactive.

Instead:

• Basket A continues.
• Basket B continues.
• Basket C stops.
• Basket D continues.

This is one of the operational advantages of basket trials.

Stage 2 Data

Suppose the three continuing baskets enroll another 10 patients each. The final observed data are:

The crude basket-specific estimates are therefore:

The results suggest considerable heterogeneity. Basket A appears particularly promising, B and D are intermediate, and C shows little evidence of activity.

What Would a Pooled Analysis Show?

Among the completed baskets, the total number of patients is:

The total number of responses is:

The pooled observed response rate is therefore:

or approximately:

That number is useful descriptively, but it hides the important fact that one basket had no responses while another had 35% observed response.

The Clinical Question Is Basket-Specific

Suppose the development question is: Which biomarker-positive tumor types should move forward?

The pooled 24.3% response rate does not answer that question.

The basket-specific estimates provide much more information:

This illustrates why the basket itself is often an important unit of interpretation.

A Bayesian Hierarchical Model for the Example

Now suppose the investigators fit:

with:

The posterior distribution provides:

• A posterior distribution for each basket's response probability.
• A posterior distribution for the overall mean response tendency.
• An estimate of between-basket heterogeneity.
• Posterior probabilities for clinically relevant thresholds.

Posterior Probability of Efficacy

Instead of asking whether a p-value crosses 0.05, a Bayesian analysis might define a clinically meaningful threshold \(p^\ast\). For example:

A basket could then be evaluated using:

A decision rule might be specified such as:

to declare a sufficiently strong efficacy signal.

Why Bayesian Models Are Particularly Useful for Small Baskets

Rare biomarkers can produce very small tumor-specific sample sizes. For example, a basket might contain only 8 or 12 evaluable patients.

A purely independent estimate can be extremely imprecise.

A hierarchical model can use information from related baskets while retaining basket-specific estimates.

This is particularly attractive when the biological mechanism strongly suggests that response should be related across tumor types.

But Biological Similarity Does Not Guarantee Clinical Similarity

A common mutation does not imply identical treatment response. Differences can arise from:

• Tissue-specific biology.
• Differences in pathway dependence.
• Co-occurring mutations.
• Differences in drug exposure.
• Tumor microenvironment.
• Prior therapies.
• Disease burden.
• Mechanisms of resistance.
• Differences in biomarker assay performance.

Consequently, the strength of borrowing should be justified by the scientific context rather than by the desire to increase effective sample size.

Borrowing and Effective Sample Size

Suppose Basket C contains only 10 patients. If the other baskets contain 60 additional patients with highly consistent responses, a hierarchical model may make Basket C's posterior estimate more stable than an independent analysis would.

It is tempting to describe those 60 patients as if they had literally been added to Basket C. That is generally not correct.

Hierarchical borrowing does not necessarily mean that the basket has an actual sample size of 70. Instead, the posterior uncertainty is reduced because information about the shared distribution informs the basket-specific parameter.

Dynamic Borrowing

A particularly useful concept is dynamic borrowing. The amount of information borrowed from other baskets depends on how compatible the observed data are.

If all baskets produce similar results, borrowing can be substantial. If one basket strongly disagrees with the others, the model can reduce the amount of borrowing.

Conceptually:

Basket Heterogeneity

The parameter:

is central to hierarchical basket models. It represents the variability of the transformed basket-specific effects around the overall mean.

Small:

suggests relatively homogeneous effects.

Large:

allows substantial differences.

What Does "Similar Baskets" Actually Mean?

Similarity should be defined scientifically. It might involve:

• The same molecular driver.
• A shared mechanism of action.
• Similar pathway dependence.
• Similar expected pharmacodynamic effects.
• Similar prior-treatment patterns.
• Similar expected sensitivity to the drug.

Simply having the same mutation is not necessarily sufficient evidence that response probabilities should be identical.

Multiplicity and Basket Expansion

Basket trials frequently allow some cohorts to expand while others stop. This creates a sequence of decisions.

For example:

The more adaptive decisions the trial contains, the more important simulation becomes.

Why Simulation Is Essential

Closed-form calculations are useful for simple basket designs. However, real basket trials may include:

• Multiple baskets.
• Unequal basket sizes.
• Staggered enrollment.
• Different stopping boundaries.
• Bayesian borrowing.
• Multiple interim analyses.
• Basket dropping.
• Basket expansion.
• Delayed endpoint assessment.
• Missing data.
• Multiplicity adjustments.
• Correlated biomarkers.

Once several of these features are combined, simulation is usually the most practical way to evaluate operating characteristics.

Operating Characteristics for Basket Trials

A basket trial should be evaluated under many possible response scenarios. Important quantities include:

• Probability of correctly identifying an active basket.
• Probability of incorrectly declaring an inactive basket active.
• Family-wise false-positive probability.
• False discovery rate, when relevant.
• Probability of dropping an active basket.
• Probability of retaining an inactive basket.
• Expected sample size.
• Maximum sample size.
• Posterior probability calibration.
• Coverage of confidence or credible intervals.
• Bias caused by borrowing.
• Operating characteristics under homogeneous effects.
• Operating characteristics under heterogeneous effects.

Scenario-Based Simulation

A useful simulation program might include at least the following scenarios.

The last two scenarios are particularly important for evaluating borrowing.

The All-Inactive Scenario

Under:

the principal concern is false-positive control.

A design should not frequently conclude that one or more baskets are active when every basket truly has an uninteresting response probability.

The All-Active Scenario

Under:

the focus is statistical power.

A hierarchical model can potentially gain substantial efficiency when all baskets are genuinely similar.

The One-Active Scenario

Suppose only Basket A is active:

This is a crucial test of a basket model.

A useful design should be able to identify Basket A without causing the inactive baskets to inherit too much evidence from it.

The Strongly Heterogeneous Scenario

Consider:

This scenario stresses the borrowing mechanism.

If the model assumes excessive similarity, the strong responses in A and B can pull C and D upward.

If the model allows appropriate heterogeneity, borrowing should diminish.

Independent vs. Hierarchical Analysis in the Worked Example

The independent analysis treats the observed basket results separately:

A hierarchical model instead estimates:

jointly.

The resulting posterior estimates will depend on the amount of heterogeneity supported by the data and the prior distribution placed on the hierarchical parameters.

The important point is that the hierarchical analysis should be interpreted as a model-based estimate, not simply as a more powerful version of the independent analysis.

Bayesian Priors

Bayesian basket trials require prior distributions. For example:

and:

The exact prior specification can materially affect inference when basket sample sizes are small.

Noninformative vs. Weakly Informative Priors

A common misconception is that Bayesian analysis is objective only when a completely "noninformative" prior is used.

In practice, the more important question is whether the prior is scientifically defensible and whether the resulting inference is robust to reasonable prior changes.

For basket trials, this is particularly important because the hierarchical prior directly influences the amount of borrowing.

Posterior Probability and Decision Rules

A Bayesian basket trial may define an efficacy threshold:

The basket-level decision could then depend on:

For example, a design might use a prespecified criterion:

where \(c\) is selected during design.

The exact value of \(c\) should be calibrated using simulation to achieve acceptable false-positive and false-negative operating characteristics.

Posterior Probability Is Not Automatically a Frequentist Type I Error

A posterior probability such as:

is a Bayesian probability conditional on the model, prior, and observed data.

It should not automatically be interpreted as equivalent to:

These quantities answer different statistical questions.

Frequentist and Bayesian Basket Trials

Neither framework is universally appropriate. The design should follow the scientific question and the required inferential properties.

Frequentist Hierarchical Models

Borrowing is not exclusively Bayesian. Frequentist hierarchical or mixed-effects models can also model basket-specific effects around a common population mean.

For example:

The distinction lies in how the unknown parameters are estimated and how uncertainty and decisions are interpreted.

Basket Trials with Time-to-Event Endpoints

Not every basket trial uses objective response as its primary endpoint. Possible endpoints include:

• Progression-free survival.
• Overall survival.
• Duration of response.
• Time to progression.
• Event-free survival.

For a time-to-event endpoint, the statistical model may involve basket-specific hazard ratios or survival distributions rather than binomial response probabilities.

For example:

A hierarchical model could then relate the basket-specific treatment effects:

The same conceptual issue remains: how much should the baskets borrow from one another?

Basket Trials with Binary Safety Endpoints

Safety can also be evaluated across baskets. For example, investigators may monitor the probability of a serious treatment related adverse event:

However, safety borrowing requires particular caution. Differences in tumor type, disease burden, concomitant medications, and treatment history can affect adverse-event rates independently of the treatment.

Therefore, efficacy borrowing and safety borrowing need not use the same model.

Biomarker Definition Is Part of the Design

The validity of a basket trial depends on the biomarker definition. Important considerations include:

• Assay platform.
• Analytical validity.
• Clinical validity.
• Biomarker positivity threshold.
• Central versus local testing.
• Sample handling.
• Turnaround time.
• Reproducibility.

If biomarker classification is noisy, the baskets may not contain the biologically intended population.

Biomarker Misclassification

Suppose the true sensitive population is defined by:

but the assay identifies patients with an imperfect classification:

Some biomarker-negative patients may be included, and some biomarker-positive patients may be excluded.

This can dilute the observed treatment effect.

Thus, the statistical design should not be considered separately from the biomarker assay strategy.

Rare Tumor Baskets

One major attraction of basket trials is the ability to investigate rare tumors harboring a common actionable alteration.

Without a basket structure, a single rare tumor type may be difficult to study because recruitment could be extremely slow.

A basket protocol can screen for the biomarker across multiple tumor types and then allocate eligible patients to the relevant cohort.

The result can be substantially more efficient operationally, even when no statistical borrowing is performed.

Basket Trials Do Not Require Statistical Borrowing

This distinction is important. A basket trial can simply be:

The statistical analysis can remain entirely basket-specific.

Borrowing is an additional modeling decision.

Umbrella Trials vs. Basket Trials

Consider the following two structures.

Basket

One treatment is evaluated across several diseases sharing a biomarker:

Umbrella

One disease is divided according to several biomarkers and corresponding treatments:

The distinction is therefore primarily about the direction of stratification.

Basket Trial Accrual

Recruitment can be highly unbalanced. For example, a common tumor type may recruit rapidly while a rare tumor basket takes months to enroll.

Therefore, the protocol should specify:

• Whether baskets enroll concurrently.
• Whether a basket can open later.
• Whether baskets can close early.
• Whether enrollment caps differ by basket.
• How enrollment pauses affect the overall trial.

Statistical planning should reflect the actual expected accrual pattern.

Asynchronous Basket Decisions

Basket trials often do not reach interim analyses simultaneously. Basket A might reach its first-stage information while Basket D is still recruiting.

This creates an operationally important distinction between:

• Calendar time.
• Information time.
• Basket-specific enrollment.
• Basket-specific endpoint maturity.

A protocol should clearly specify what triggers each decision.

Delayed Responses

Objective response may not be immediately observable after enrollment. If a basket reaches its enrollment threshold before sufficient follow-up has occurred, investigators must decide whether the interim analysis waits for endpoint maturity or uses a different statistical strategy.

This becomes particularly important when early futility decisions are intended to accelerate development.

Time-to-Response and Delayed-Outcome Methods

When outcomes are delayed, designs can use approaches such as:

• Calendar-time rules.
• Information-based interim analyses.
• Time-to-event models.
• Weighted likelihood approaches.
• Joint enrollment-and-outcome simulation.

The chosen approach should be included in operating-characteristic simulations.

Expansion Cohorts

A promising basket may be expanded after an initial signal. For example:

Such a design can be efficient, but the expansion criterion must be prespecified and its operating characteristics evaluated.

Basket Selection vs. Basket Confirmation

An important development distinction is between:

• Signal detection: identifying tumor types that appear sensitive.
• Estimation: quantifying the magnitude and uncertainty of the response.
• Confirmation: establishing a treatment effect with the level of evidence required for the intended claim.

A basket trial may be excellent for signal detection without being sufficient by itself for every confirmatory purpose.

Common Mistakes in Basket Trial Design

1. Assuming a shared biomarker implies identical treatment effects. Biological plausibility supports borrowing but does not prove exchangeability.
2. Pooling all baskets automatically. Pooling can conceal clinically important heterogeneity.
3. Borrowing aggressively without heterogeneity simulations. The model should be tested under scenarios in which baskets truly differ.
4. Ignoring multiplicity. Multiple baskets create multiple opportunities for false-positive findings.
5. Reporting only the pooled response rate. Basket-specific estimates are often essential to the scientific interpretation.
6. Treating posterior probability as a p-value. Bayesian posterior probabilities and frequentist p-values answer different questions.
7. Ignoring prior sensitivity. Small baskets can be strongly influenced by hierarchical priors.
8. Failing to simulate rare-basket scenarios. The very populations that motivate basket trials may have small sample sizes.
9. Ignoring biomarker assay error. Misclassification can dilute or distort the treatment effect.
10. Using a common decision rule without considering basket-specific clinical context. A response rate that is meaningful in one tumor type may not represent the same clinical value in another.
11. Ignoring delayed endpoint assessment. A nominal interim sample size does not necessarily mean that the interim endpoint data are mature.
12. Changing the borrowing assumptions after seeing the data. Post hoc changes can invalidate the planned operating characteristics.

R: Independent Basket Analysis

The simplest implementation begins with basket-specific binomial data.

baskets <- data.frame(
  basket = c("A", "B", "C", "D"),
  n = c(20, 20, 10, 20),
  responses = c(7, 5, 0, 5)
)

baskets$orr <- baskets$responses / baskets$n

baskets

The resulting crude response estimates are:

baskets$orr

# A: 0.35
# B: 0.25
# C: 0.00
# D: 0.25

Exact Binomial Tests

Suppose the null response rate is:

p0 <- 0.10

An exact binomial test can be performed separately for each basket.

binom.test(7, 20, p = p0, alternative = "greater")
binom.test(5, 20, p = p0, alternative = "greater")
binom.test(0, 10, p = p0, alternative = "greater")
binom.test(5, 20, p = p0, alternative = "greater")

The results provide basket-specific evidence against the null response rate.

If formal multiplicity control is required, the resulting p-values can be adjusted.

Multiplicity Adjustment in R

p_values <- c(
  binom.test(7, 20, p = p0,
             alternative = "greater")$p.value,

  binom.test(5, 20, p = p0,
             alternative = "greater")$p.value,

  binom.test(0, 10, p = p0,
             alternative = "greater")$p.value,

  binom.test(5, 20, p = p0,
             alternative = "greater")$p.value
)

p.adjust(p_values, method = "holm")

The Holm procedure is one example of a family-wise error-rate adjustment. The appropriate multiplicity method depends on the intended claim and prespecified testing strategy.

R: A Simple Bayesian Hierarchical Model

A Bayesian hierarchical model can be fit using a probabilistic programming framework such as Stan through an R interface. The conceptual model is:

X[j] ~ binomial(n[j], p[j])

logit(p[j]) ~ normal(mu, tau)

mu ~ normal(0, 2.5)
tau ~ normal(0, 1)

A complete implementation depends on the chosen software package and the prior parameterization. The important statistical structure is:

and:

Illustrative Stan Model

data {
  int<lower=1> J;
  array[J] int<lower=0> n;
  array[J] int<lower=0> x;
}

parameters {
  real mu;
  real<lower=0> tau;
  vector[J] theta;
}

transformed parameters {
  vector[J] p;

  for (j in 1:J)
    p[j] = inv_logit(theta[j]);
}

model {

  mu ~ normal(0, 2.5);
  tau ~ normal(0, 1);

  theta ~ normal(mu, tau);

  for (j in 1:J)
    x[j] ~ binomial(n[j], p[j]);
}

This is intentionally a simple teaching model. Production analyses should use a carefully justified prior structure, diagnostic checks, sensitivity analyses, and simulation-based validation.

Posterior Basket Probabilities

After fitting the model, a clinically meaningful decision can be based on:

In R, this can conceptually be calculated from posterior draws:

posterior_prob <- colMeans(
  posterior_p > 0.20
)

posterior_prob

where posterior_p contains posterior draws of the basket-specific response probabilities.

Prior Sensitivity Analysis

Suppose the primary model uses:

A sensitivity analysis might consider a weaker or stronger prior on heterogeneity.

For example:

# Conceptual sensitivity scenarios

prior_tau_1 <- "HalfNormal(0.5)"
prior_tau_2 <- "HalfNormal(1.0)"
prior_tau_3 <- "HalfNormal(2.0)"

The exact implementation depends on the modeling framework. The goal is to determine whether the basket-level conclusions are robust to reasonable assumptions about between-basket similarity.

Simulation: The Basic Algorithm

A simple basket-trial simulation can be constructed as follows.

Simple R Simulation Skeleton

simulate_basket <- function(
  p,
  n1 = 10,
  n2 = 10
) {

  J <- length(p)

  x1 <- rbinom(
    J,
    size = n1,
    prob = p
  )

  continue <- x1 >= 2

  x2 <- rep(0, J)

  x2[continue] <- rbinom(
    sum(continue),
    size = n2,
    prob = p[continue]
  )

  n_total <- rep(n1, J)
  n_total[continue] <- n1 + n2

  x_total <- x1 + x2

  data.frame(
    basket = seq_len(J),
    n = n_total,
    responses = x_total,
    continue = continue,
    orr = x_total / n_total
  )
}

This is only a structural example. A real design simulation should reproduce the exact protocol decision rules, analysis model, endpoint timing, and missing-data assumptions.

Repeating the Simulation

set.seed(2026)

results <- replicate(
  10000,
  simulate_basket(
    p = c(0.30, 0.10, 0.10, 0.10)
  ),
  simplify = FALSE
)

The simulation can then be used to estimate the probability that the active basket is identified and the probability that inactive baskets are incorrectly selected.

What Makes a Basket Trial Statistically Difficult?

The complexity comes from several layers interacting simultaneously.

Selection Effects

Suppose four baskets are initially screened and only the basket with the largest observed response rate is expanded.

The selected basket's observed response rate will tend to be optimistic even if all baskets have the same true response probability.

This is a form of selection bias caused by choosing a basket because of its observed result.

Therefore, an expansion cohort should not simply treat the initial observed response rate as though the basket had been selected independently of the data.

Winner's Curse in Basket Trials

When many baskets are screened, some will look unusually effective simply due to random variation.

The basket with the strongest observed response rate may therefore overestimate its true treatment effect.

This is particularly relevant when:

• There are many baskets.
• Each basket is small.
• Expansion is triggered by the largest observed response.
• There is substantial heterogeneity.

Confirmatory follow-up should account for the selection process.

Response Rate Is Not the Entire Story

A basket can have a high response rate but still require careful interpretation. Investigators may also consider:

• Duration of response.
• Depth of response.
• Progression-free survival.
• Overall survival.
• Time to response.
• Safety.
• Quality of life.
• Subsequent therapy.

For a targeted therapy, a durable response may be much more informative than a short-lived radiographic response.

Estimands in Basket Trials

An estimand should specify what treatment effect the trial is intended to estimate. For each basket, this may involve:

• The target population.
• The treatment condition.
• The endpoint.
• The intercurrent-event strategy.
• The summary measure.

For example, an estimand might target the probability of objective response within a prespecified assessment window among eligible biomarker-positive patients receiving the investigational treatment.

The estimand framework becomes especially important when baskets have different clinical characteristics.

Basket-Specific Clinical Thresholds

The null and alternative response rates do not necessarily need to be identical across baskets.

For example:

A 20% response rate might be clinically meaningful in one heavily pretreated tumor type but not in another disease where effective standard treatments already produce substantially higher response rates.

Therefore, a single common threshold should not be imposed simply because the trial is a basket trial.

Heterogeneous Null Hypotheses

A more realistic formulation can be:

The alternative becomes:

This creates basket-specific design targets.

The trade-off is increased design complexity.

When Common Thresholds Are Reasonable

Common \(p_0\) and \(p_1\) values may be reasonable when:

• The clinical value of response is similar across baskets.
• The endpoint is interpreted similarly across diseases.
• Historical control data support a common benchmark.
• The biomarker hypothesis is strongly shared.
• The treatment mechanism is expected to produce comparable activity.

Even then, basket-specific operating characteristics should be examined.

Historical Controls

Single-arm basket trials often rely on historical response rates. The quality of the historical benchmark can strongly influence the design.

Potential problems include:

• Changes in standard of care.
• Differences in eligibility criteria.
• Differences in prior treatment.
• Differences in response assessment.
• Differences in patient prognosis.
• Differences in biomarker testing.

A historical response rate should therefore be treated as a design assumption requiring clinical justification, not as a fixed biological constant.

Basket Trial Decision Matrix

A useful protocol summary can map each basket to its statistical status.

This kind of structure can make complex basket decisions easier to communicate to investigators, clinicians, and data-monitoring groups.

Basket Trials and Regulatory Interpretation

A biomarker-defined treatment effect across several tumor types can potentially support a broader development strategy than a conventional histology-specific trial.

However, the strength of the evidence depends on the design, endpoint, consistency of effects, magnitude of benefit, safety, biological rationale, and the intended claim.

A statistical model that borrows information across baskets should therefore not be interpreted as establishing biological equivalence among diseases.

Basket Trials and Master Protocols

Basket trials are often implemented as master protocols. A master protocol can define:

• Common eligibility procedures.
• Biomarker testing.
• Shared operational infrastructure.
• Common treatment administration.
• Multiple tumor-specific cohorts.
• Predefined rules for opening, closing, or expanding cohorts.

This can reduce duplication compared with conducting separate studies for every tumor type.

Basket Trial Workflow

What Should Be Included in the Statistical Analysis Plan?

A basket-trial SAP should be unusually explicit because the trial contains multiple related populations. At minimum, document:

• Definition of each basket.
• Biomarker definition.
• Primary endpoint.
• Analysis population.
• Basket-specific sample sizes.
• Interim decision rules.
• Final decision rules.
• Null and alternative assumptions.
• Multiplicity strategy.
• Borrowing model, if applicable.
• Prior distributions, if Bayesian.
• Heterogeneity assumptions.
• Missing-data rules.
• Response assessment timing.
• Safety analysis.
• Sensitivity analyses.
• Simulation methodology and operating characteristics.

What Should Be Reported?

A publication should generally allow readers to understand both the basket-specific and overall results.

Useful summaries include:

• Number enrolled in each basket.
• Number evaluable for the primary endpoint.
• Number of responses.
• Objective response rate.
• Confidence or credible intervals.
• Duration of response.
• Progression-free survival where appropriate.
• Safety by basket.
• Results of the prespecified hierarchical analysis.
• Results under alternative borrowing assumptions.

Interpreting a Successful Basket Trial

Suppose three baskets show convincing activity while one does not. There are several possible interpretations.

The simplest is: the treatment appears active in a subset of biomarker-positive tumor types.

Another possibility is that the biomarker is predictive but not sufficient; additional biological factors may determine response.

The appropriate interpretation depends on the magnitude, precision, consistency, and biological plausibility of the observed effects.

What If All Baskets Respond?

Consistent responses across several tumor types provide evidence supporting the hypothesis that the shared biological feature is associated with treatment sensitivity.

A hierarchical model may be particularly efficient in this scenario.

However, the final clinical interpretation should still consider:

• Response magnitude.
• Response durability.
• Safety.
• Patient population.
• Prior therapies.
• Available treatment alternatives.

What If Only One Basket Responds?

This is not necessarily a failed basket trial. It may indicate that:

• The biomarker is insufficiently specific.
• The biological mechanism is tissue dependent.
• Co-mutations matter.
• The treatment effect is restricted to one histology.
• Some baskets were underpowered.
• The biomarker assay performed differently across populations.

The result can therefore generate a refined biological hypothesis.

What If No Baskets Respond?

If all baskets show little activity, the biomarker-treatment hypothesis may not be supported.

An important advantage of a basket design is that this conclusion can sometimes be reached more efficiently than through a sequence of separate tumor-specific trials.

What If One Basket Is Much Worse Than the Others?

A markedly poor-performing basket should generally be investigated rather than automatically forced into the common-effect model.

Potential explanations include:

• True biological heterogeneity.
• Different biomarker prevalence or co-mutation structure.
• Different prior therapy.
• Different disease stage.
• Different assay performance.
• Random variation from a small sample.

The hierarchical model can help quantify this uncertainty, but it cannot determine the biological explanation by itself.

Independent, Pooled, and Hierarchical Models: Summary

Choosing the Statistical Model

The choice should begin with the scientific question.

Ask:

1. Are the baskets biologically related enough to justify borrowing?
2. Is the primary goal signal detection or confirmation?
3. Are the baskets sufficiently large for independent inference?
4. Is a pooled effect scientifically meaningful?
5. How important is basket-specific interpretation?
6. What level of false-positive control is required?
7. How much heterogeneity is clinically plausible?
8. Can the design be validated through simulation?

The statistical model should follow from these questions.

Key Design Principle: Separate Structure From Inference

There are two distinct decisions:

The basket structure answers the first question. The statistical model answers the second.

Keeping these concepts separate prevents one of the most common misunderstandings about basket trials.

Basket Trials and Adaptive Design

A basket trial can be non-adaptive. It can also include adaptive features such as:

• Dropping futile baskets.
• Expanding promising baskets.
• Opening new baskets.
• Closing baskets with insufficient recruitment.
• Changing borrowing strength according to prespecified model rules.

Once these features are introduced, the operating characteristics should be evaluated over the entire adaptive pathway.

Adaptive Basket Trial Simulation

A robust simulation framework should generate:

where \(j\) indexes baskets and \(t\) indexes interim stages.

For every simulated trial:

• Generate patient outcomes.
• Apply the actual enrollment rules.
• Apply basket-specific stopping rules.
• Fit the prespecified model.
• Apply the decision rule.
• Record the resulting decisions.

After many simulations, calculate the frequency of each outcome.

Example Simulation Targets

A design might be required to demonstrate:

• High probability of identifying an active basket.
• Low probability of declaring an inactive basket active.
• Acceptable family-wise false-positive probability under global null scenarios.
• Controlled probability of incorrectly dropping an active basket.
• Acceptable expected sample size.
• Acceptable maximum sample size.
• Robustness to substantial basket heterogeneity.

The exact numerical targets depend on the development context.

Global Null vs. Basket-Specific Null

Two different concepts should be distinguished.

The global null might be:

A basket-specific null is:

A trial may be designed to control the probability of making any false basket-specific declaration under the global null, or it may use a different decision framework.

These are different inferential objectives and should not be conflated.

Global Evidence vs. Basket Evidence

A biomarker may show evidence of activity across the overall program while the effect remains concentrated in only a subset of tumor types.

Therefore, basket trials often produce at least two levels of inference:

• Program-level evidence: Is the biomarker-treatment hypothesis broadly supported?
• Basket-level evidence: Which tumor types appear to benefit?

The analysis should make clear which level is being tested.

Common Reporting Table

A useful final-results table might look like:

The exact inferential quantities should be determined by the prespecified analysis.

Safety Across Baskets

Safety should generally be examined both overall and by basket.

For example:

A favorable efficacy signal does not automatically justify expansion if safety is unacceptable.

Decision-Making Is Multidimensional

A practical basket decision may therefore depend on:

Advantages of Basket Trials

• Efficient evaluation of rare biomarker-defined populations.
• Shared infrastructure across tumor types.
• Ability to investigate a common biological hypothesis.
• Potential for partial borrowing across related cohorts.
• Basket-specific stopping and expansion.
• Potentially faster signal detection.
• Ability to reveal tumor-specific differences in biomarker response.

Limitations of Basket Trials

• Small sample sizes within individual baskets.
• Potentially substantial tumor-specific heterogeneity.
• Multiplicity from multiple baskets.
• Complexity of hierarchical modeling.
• Sensitivity to assumptions about exchangeability.
• Potential selection bias when baskets are expanded based on observed results.
• Biomarker assay variability.
• Unequal recruitment rates.
• Potentially different clinical meanings of response across diseases.

When a Basket Trial Is Especially Useful

A basket structure can be particularly useful when:

• A biologically compelling target occurs across multiple cancers.
• Some individual tumor types are rare.
• The treatment mechanism is expected to operate across histologies.
• A common biomarker assay can identify eligible patients.
• The study can recruit several tumor types under one infrastructure.
• The development strategy requires rapid identification of responsive populations.

When a Basket Trial May Be Less Appropriate

A basket design may be less compelling when:

• The biomarker has very different biological implications across diseases.
• Standard-of-care response rates vary dramatically and require different benchmarks.
• The drug's mechanism is strongly tissue-specific.
• The eligible population is large enough for efficient conventional trials.
• The intended claim is inherently tumor-specific.
• There is little scientific justification for borrowing information.

Practical Basket Trial Checklist

The Most Important Statistical Concept

The central statistical challenge in basket trials is not simply estimating a response rate.

It is determining how much information should be shared across biologically related but clinically distinct populations.

At one extreme:

At the other:

Hierarchical models occupy the middle:

The correct amount of borrowing is therefore a design question—not merely a technical modeling choice.

Worked Example Summary

The illustrative four-basket trial can be summarized as follows.

The example demonstrates why a pooled response rate alone can be inadequate. The clinically relevant information lies in both the overall biomarker signal and the heterogeneity among individual tumor types.

A Practical Basket Trial Workflow

Bottom Line

A basket trial is a precision-oncology design in which patients with different tumor types are studied together because they share a molecular or biological characteristic believed to be relevant to treatment response.

The defining statistical problem is deciding how the information from these different baskets should be combined.

Independent analyses preserve basket-specific information but can be inefficient when cohorts are small. Complete pooling is efficient when the treatment effects are genuinely similar but can obscure clinically important heterogeneity. Hierarchical models provide a middle ground by allowing basket-specific effects while permitting partial borrowing of information.

The major risks are equally important:

• Over-borrowing when baskets are heterogeneous.
• Ignoring multiplicity across many baskets.
• Failing to account for selection when promising baskets are expanded.
• Using poorly justified biomarker assumptions.
• Ignoring small-sample uncertainty.
• Confusing statistical exchangeability with biological equivalence.

References

Berry, D.A. (2012). The Bayesian approach to basket trials. Clinical Trials.
Lee, J.J., and Chu, C.T. (2012). Bayesian clinical trials in action. Statistics in Medicine.
Neuenschwander, B., et al. (2016). Critical aspects of the Bayesian design of clinical trials. Clinical Trials.
Park, J.W., Liu, M.C., Yee, D., et al. (2017). Adaptive randomization of neratinib in HER2-mutant breast cancer. Journal of Clinical Oncology.
Cunanan, K.M., Iasonos, A., Shen, R., Gönen, M., and others. Assessing the value of basket trials in precision oncology. Clinical Cancer Research.
Hobbs, B.P., Landin, R., and others. Hierarchical Bayesian models for basket trials. Statistics in Medicine.
Berry, S.M., Carlin, B.P., Lee, J.J., and Muller, P. (2010). Bayesian Adaptive Methods for Clinical Trials. CRC Press.
Thall, P.F., Wathen, J.K., and others. Practical Bayesian designs for clinical trials with multiple treatment populations. Clinical Trials.
FDA. Master Protocols: Efficient Clinical Trial Design Strategies to Expedite Development of Oncology Drugs and Biologics. U.S. Food and Drug Administration.
FDA. Clinical Trial Endpoints for the Approval of Cancer Drugs and Biologics. U.S. Food and Drug Administration.