Umbrella Trial Design

An umbrella trial enrolls patients with a single disease (typically one tumor type) and stratifies them into biomarker-defined sub-studies, each testing a different targeted treatment against a shared control arm. The central question is whether each biomarker-matched therapy improves outcomes relative to the common standard of care within that disease population.

Landmark Examples

• •LUNG-MAP (S1400): Squamous cell lung cancer patients screened for multiple genomic alterations, each assigned to a matched targeted therapy vs. standard docetaxel. A pioneering public-private partnership demonstrating the umbrella paradigm at scale.
• •NCI-MATCH (EAY131): While primarily a basket trial, certain disease-specific cohorts within MATCH operate as umbrella sub-studies, screening for multiple actionable mutations within a given histology.
• •BATTLE (2011): Biomarker-integrated Approaches of Targeted Therapy for Lung Cancer Elimination. One of the first adaptive umbrella trials in NSCLC, randomizing patients to matched therapies based on real-time tumor profiling.
• •plasmaMATCH (2020): Breast cancer umbrella trial using ctDNA-based biomarker selection to allocate patients to matched targeted therapies, demonstrating feasibility of liquid biopsy-guided umbrella designs.

When to Use an Umbrella Trial

• •Single disease with molecular heterogeneity: The disease population harbors multiple distinct biomarker subgroups, each with a biologically plausible targeted therapy candidate.
• •Shared standard of care: All subgroups have the same control treatment (e.g., standard chemotherapy), making a pooled control arm scientifically defensible.
• •Efficient screening infrastructure: A centralized molecular screening platform can assign patients to sub-studies at enrollment, enabling real-time biomarker-driven randomization.
• •Regulatory efficiency: A single master protocol supports multiple treatment-biomarker evaluations under one IND, with shared infrastructure for data monitoring, safety reporting, and regulatory interactions.

Control Arm Pooling

The defining structural feature of an umbrella trial is the shared control arm. Instead of each sub-study maintaining its own independent control group, a single control arm is randomized from the full disease population. Control patients are assigned irrespective of biomarker status (or may be biomarker-negative patients), and their outcomes are used as the comparator for every sub-study.

Allocation Ratio

Let $J$ denote the number of sub-studies and $r_c$ the fraction of total enrollment allocated to control. The remaining $1 - r_c$ is distributed across treatment arms according to biomarker prevalence. For total sample size $N$:

where $\pi_j$ is the prevalence of biomarker $j$ such that $\sum_{j=1}^{J} \pi_j = 1$. The default control allocation is $r_c = 0.33$.

Sample Size Savings

Compared to running $J$ independent two-arm trials, the shared control design saves substantially on the total control arm enrollment. For independent trials, the total sample size is:

For the umbrella design with a shared control:

The savings come from eliminating $J - 1$ redundant control groups. With $J = 4$ sub-studies and equal allocation, this can reduce total enrollment by approximately 30–40% relative to independent trials.

Per-Sub-Study Hypothesis Testing

Each sub-study $j$ tests its own null hypothesis $H_{0,j}$ against a one-sided alternative. The test statistic and rejection criterion depend on the endpoint type.

Binary Endpoint

For binary outcomes, a two-sample z-test compares the treatment response rate $\hat{p}_{T_j}$ to the shared control rate $\hat{p}_C$:

where $\bar{p}_j = (x_{T_j} + x_C) / (n_{T_j} + n_C)$ is the pooled proportion under the null, $x_{T_j}$ and $x_C$ are the number of responders in the treatment and control arms, and $n_{T_j}$, $n_C$ are the respective sample sizes.

Continuous Endpoint

For continuous outcomes, a two-sample t-test (or z-test with known common standard deviation $\sigma$) is used:

where $\bar{Y}_{T_j}$ and $\bar{Y}_C$ are the sample means for treatment arm $j$ and the shared control, respectively.

Survival Endpoint

For time-to-event outcomes under proportional hazards, the log-rank z-statistic for sub-study $j$ is approximated via the Schoenfeld formula:

where $d_j$ is the number of events in sub-study $j$ (treatment + control) and $\hat{\text{HR}}_j$ is the estimated hazard ratio. The required events per sub-study are computed from the Schoenfeld formula:

where $\alpha^*$ is the multiplicity-adjusted significance level for sub-study $j$.

Multiplicity Correction

Because $J$ sub-studies are tested simultaneously against a shared control, multiplicity adjustment is needed to control the family-wise error rate (FWER). Three options are available:

Bonferroni Correction

The simplest approach divides the overall significance level equally across all sub-studies:

This strongly controls FWER at level $\alpha$ regardless of the correlation structure among test statistics (which arises from the shared control). It is conservative when sub-studies are positively correlated, which they are in umbrella trials due to the common control arm.

Holm Step-Down

The Holm procedure is a uniformly more powerful alternative to Bonferroni. Order the $J$ p-values as $p_{(1)} \leq p_{(2)} \leq \cdots \leq p_{(J)}$:

Testing proceeds sequentially from the smallest p-value. The first time a p-value fails the threshold, that hypothesis and all remaining hypotheses are retained. Holm controls FWER at level $\alpha$ and is never less powerful than Bonferroni.

No Correction

Each sub-study is tested at the unadjusted $\alpha$ level. This does not control FWER but maximizes per-sub-study power. Appropriate when each sub-study is viewed as a separate confirmatory question rather than a family of hypotheses.

The Bayesian analysis computes the posterior probability that treatment $j$ is superior to control, using conjugate or asymptotic posteriors depending on the endpoint type. A “Go” decision is declared when this posterior exceeds the decision threshold $\gamma$ (default 0.975).

Binary Endpoint: Beta-Binomial Conjugate

For binary outcomes, each arm receives an independent Beta prior. The posterior for treatment arm $j$ and the shared control are:

where $\alpha, \beta$ are the shared Beta prior hyperparameters (default: $\alpha = \beta = 1$, i.e., uniform prior). The decision criterion is:

This probability is computed analytically via numerical integration of the product of Beta densities, or equivalently through the regularized incomplete beta function.

Continuous Endpoint: Normal-Normal Conjugate

For continuous outcomes with known common variance $\sigma^2$, the posterior for each arm mean is:

The posterior on the treatment difference is also normal:

The decision criterion $P(\mu_{T_j} > \mu_C \mid \text{data}) > \gamma$ reduces to checking whether the z-score of the posterior mean difference exceeds $\Phi^{-1}(\gamma)$.

Survival Endpoint: Asymptotic Posterior

For survival outcomes, the posterior is based on the asymptotic normal approximation to the log-hazard ratio:

where $d_j$ is the observed event count. The decision criterion is $P(\text{HR}_j < 1 \mid \text{data}) > \gamma$, which translates to checking whether $\log(\hat{\text{HR}}_j) / \sqrt{4/d_j} < -\Phi^{-1}(\gamma)$.

Monte Carlo Operating Characteristics

The umbrella trial simulator estimates operating characteristics by repeating the full design—enrollment, biomarker assignment, shared-control randomization, per-sub-study analysis, and multiplicity correction—across many simulated datasets under both null and alternative scenarios.

When simulation is enabled, the calculator computes the following metrics across all Monte Carlo replicates:

Interpretation Guidance

• •FWER control: With Bonferroni or Holm correction, the frequentist analysis controls FWER at the nominal $\alpha$ level. The Bayesian analysis does not explicitly control FWER; the simulation-based FWER should be examined to calibrate the decision threshold.
• •Power-multiplicity tradeoff: Stricter multiplicity correction (Bonferroni) reduces per-sub-study power. Holm provides a modest improvement. No correction maximizes per-sub-study power at the cost of inflated FWER. The Bayesian approach sidesteps formal multiplicity but requires threshold calibration.
• •Scenario sensitivity: Results depend on which sub-studies are truly active vs. null, and on the biomarker prevalence distribution. Always simulate the global null (all sub-studies inactive) to verify FWER, and the global alternative (all active) to assess overall power.
• •Shared control effect: When the shared control arm is large (high $r_c$ or many sub-studies), the control rate estimate has low variance, which benefits all sub-studies. However, any systematic bias in the control arm (e.g., unexpected prognostic imbalance) propagates to all comparisons simultaneously.

When an Umbrella Design May Not Be Appropriate

POST /api/v1/calculators/umbrella

Umbrella trial design and analysis with frequentist or Bayesian methods, supporting binary, continuous, and survival endpoints with optional Monte Carlo simulation for operating characteristics.

Core Parameters

Binary Endpoint Parameters

Continuous Endpoint Parameters

Survival Endpoint Parameters

Simulation Parameters

Example Request (Binary, Frequentist)

{
  "n_substudies": 3,
  "substudy_names": ["EGFR+", "ALK+", "KRAS G12C"],
  "endpoint_type": "binary",
  "analysis_type": "frequentist",
  "total_n": 450,
  "control_allocation": 0.33,
  "biomarker_prevalences": [0.40, 0.30, 0.30],
  "null_rates": [0.15, 0.15, 0.15],
  "alternative_rates": [0.35, 0.40, 0.30],
  "multiplicity_method": "holm",
  "alpha": 0.025,
  "simulate": true,
  "n_simulations": 10000
}

Example Request (Survival, Bayesian)

{
  "n_substudies": 4,
  "substudy_names": ["HER2+", "PIK3CA", "FGFR", "CDK4/6"],
  "endpoint_type": "survival",
  "analysis_type": "bayesian",
  "total_n": 600,
  "control_allocation": 0.30,
  "biomarker_prevalences": [0.25, 0.25, 0.25, 0.25],
  "median_control": 12.0,
  "hazard_ratios": [0.65, 0.70, 0.75, 0.70],
  "accrual_time": 24.0,
  "follow_up_time": 12.0,
  "dropout_rate": 0.05,
  "decision_threshold": 0.975,
  "simulate": true,
  "n_simulations": 10000,
  "simulation_seed": 42
}

Response Fields