Advanced adaptive trials

Advanced Adaptive Trial Designs in R

Overview

Advanced adaptive clinical trial designs including platform trials, basket and umbrella trials, response-adaptive randomization, multi-arm multi-stage designs, Bayesian adaptive methods, and sample size re-estimation techniques.

Platform Trials

Using adaptr Package

library(adaptr)

# Define a platform trial with multiple arms
setup <- setup_trial(
  arms = c("Control", "Arm_A", "Arm_B", "Arm_C"),
  control = "Control",
  true_ys = c(0.30, 0.35, 0.45, 0.32),  # True response rates
  data_looks = seq(100, 500, by = 100),  # Interim analyses
  randomised_at_looks = NULL,            # Equal allocation initially
  min_n = 25                              # Minimum per arm before dropping
)

# Specify stopping rules
setup <- setup |>
  setup_trial_binom(
    highest_is_best = TRUE,
    soften_power = 0.5                    # Softening for allocation
  )

# Add arm dropping rules
setup <- setup_trial_binom(
  arms = c("Control", "Arm_A", "Arm_B", "Arm_C"),
  control = "Control",
  true_ys = c(0.30, 0.35, 0.45, 0.32),
  data_looks = seq(100, 500, 100),
  superiority = 0.99,                     # Probability for superiority
  inferiority = 0.01,                     # Probability for futility
  equivalence_prob = 0.90,
  equivalence_diff = 0.05
)

# Simulate trial
set.seed(123)
sims <- run_trials(setup, n_rep = 1000, cores = 4)

# Summarize results
summary(sims)
plot(sims)

Adding Arms Mid-Trial

library(adaptr)

# Platform trial with arm addition
setup_platform <- setup_trial_binom(
  arms = c("Control", "Arm_A", "Arm_B"),
  control = "Control",
  true_ys = c(0.30, 0.40, 0.35),
  data_looks = seq(100, 1000, 100),
  superiority = 0.99,
  inferiority = 0.01
)

# Add Arm_C at look 3 (n=300)
setup_platform <- setup_platform |>
  add_arm(
    arm = "Arm_C",
    true_y = 0.50,
    start_look = 3              # Add at third interim
  )

# Simulate
sims_platform <- run_trials(setup_platform, n_rep = 500)
summary(sims_platform)

Response-Adaptive Randomization

Thompson Sampling

# Thompson sampling for binary outcomes
thompson_sampling <- function(successes, failures, n_arms) {
  # Sample from posterior Beta distributions
  samples <- sapply(1:n_arms, function(i) {
    rbeta(10000, successes[i] + 1, failures[i] + 1)
  })

  # Probability each arm is best
  prob_best <- colMeans(samples == apply(samples, 1, max))

  # Allocation probabilities (can apply min allocation constraint)
  alloc_prob <- prob_best
  alloc_prob <- pmax(alloc_prob, 0.1 / n_arms)  # Minimum 10% of equal
  alloc_prob <- alloc_prob / sum(alloc_prob)    # Normalize

  return(alloc_prob)
}

# Example: After 100 patients
successes <- c(20, 25, 30)  # Successes in Control, A, B
failures <- c(30, 25, 20)   # Failures

alloc <- thompson_sampling(successes, failures, 3)
cat("Allocation probabilities:", round(alloc, 3), "\n")

RAR with Minimum Allocation

# Response-adaptive randomization with constraints
rar_allocation <- function(posterior_probs, min_alloc = 0.1, control_fixed = TRUE) {

  n_arms <- length(posterior_probs)
  alloc <- posterior_probs

  if (control_fixed) {
    # Fix control allocation
    control_alloc <- 1 / n_arms
    remaining <- 1 - control_alloc
    alloc[-1] <- alloc[-1] / sum(alloc[-1]) * remaining
    alloc[1] <- control_alloc
  }

  # Apply minimum allocation
  alloc <- pmax(alloc, min_alloc)
  alloc <- alloc / sum(alloc)

  return(alloc)
}

Basket Trials

Using basket Package

library(basket)

# Basket trial: One treatment, multiple tumor types/biomarker groups
# Data: responses (r) and sample sizes (n) per basket

basket_data <- data.frame(
  basket = c("Breast", "Lung", "Colon", "Melanoma", "Ovarian"),
  r = c(8, 12, 5, 15, 7),     # Responders
  n = c(20, 25, 18, 30, 22)   # Total patients
)

# Bayesian hierarchical model (MEM - Multisource Exchangeability Model)
fit_mem <- mem_exact(
  r = basket_data$r,
  n = basket_data$n,
  p0 = 0.15,                  # Null response rate
  shape1 = 0.5,               # Beta prior shape1
  shape2 = 0.5                # Beta prior shape2
)

summary(fit_mem)
plot(fit_mem)

# Posterior probabilities of response > p0
fit_mem$post_prob

# Cluster map (which baskets share information)
plot(fit_mem, type = "cluster")

Hierarchical Model for Baskets

library(basket)

# Full Bayesian hierarchical model
fit_hier <- basket(
  r = basket_data$r,
  n = basket_data$n,
  p0 = 0.15,
  method = "hpd",
  alpha = 0.05
)

# Alternative: EXNEX model (exchangeability-nonexchangeability)
# Allows some baskets to be exchangeable, others not

Umbrella Trials

Design Considerations

# Umbrella trial: One disease, multiple biomarker-treatment pairs
# Each stratum has its own comparison

# Example setup
umbrella_design <- data.frame(
  stratum = c("EGFR+", "ALK+", "KRAS+", "Other"),
  treatment = c("Erlotinib", "Crizotinib", "Trametinib", "Chemotherapy"),
  target_n = c(100, 80, 120, 150),
  alpha = 0.025 / 4  # Bonferroni correction
)

# Each stratum can be analyzed separately
# But may share control arm or use master protocol

library(rpact)

# Design for each stratum
designs <- lapply(1:4, function(i) {
  getDesignGroupSequential(
    kMax = 2,
    alpha = umbrella_design$alpha[i],
    beta = 0.20,
    sided = 1,
    typeOfDesign = "OF"
  )
})

Multi-Arm Multi-Stage (MAMS)

Using MAMS Package

library(MAMS)

# Design MAMS trial
mams_design <- mams(
  K = 3,                      # Number of experimental arms
  J = 2,                      # Number of stages
  alpha = 0.025,              # One-sided type I error
  power = 0.90,               # Power
  r = c(1, 1.5),             # Allocation ratio at each stage (exp:control)
  r0 = c(1, 1.5),            # Control allocation ratio
  p = 0.5,                    # Control response rate (continuous: effect size)
  p0 = 0.5,                   # Null response rate
  p1 = 0.65,                  # Alternative response rate
  ushape = "triangular",      # Upper boundary shape
  lshape = "triangular"       # Lower boundary shape
)

summary(mams_design)
plot(mams_design)

# Sample size
mams_design$n          # Per arm per stage
mams_design$N          # Total sample size

MAMS with Continuous Outcome

library(MAMS)

# MAMS for continuous outcomes
mams_cont <- mams(
  K = 4,
  J = 3,
  alpha = 0.025,
  power = 0.90,
  r = c(1, 1, 1),
  r0 = c(1, 1, 1),
  p = 0,                      # Null effect size (standardized)
  p0 = 0,
  p1 = 0.3,                   # Target effect size (standardized)
  ushape = "obf",             # O'Brien-Fleming
  lshape = "fixed"            # Fixed lower boundary
)

summary(mams_cont)

Bayesian Adaptive Designs with RBesT

Historical Data Integration

library(RBesT)

# Meta-analytic predictive (MAP) prior from historical data
hist_data <- data.frame(
  study = paste0("Hist", 1:4),
  r = c(15, 20, 18, 22),      # Responders
  n = c(50, 55, 48, 60)       # Total
)

# Fit MAP prior
map_prior <- gMAP(
  cbind(r, n - r) ~ 1 | study,
  data = hist_data,
  family = binomial,
  tau.dist = "HalfNormal",
  tau.prior = 1,
  beta.prior = 2
)

summary(map_prior)
plot(map_prior)

# Get mixture prior approximation
prior_mix <- automixfit(map_prior)
plot(prior_mix)

Robust Prior (Protect Against Conflict)

library(RBesT)

# Robustify prior (mixture with vague component)
robust_prior <- robustify(
  prior_mix,
  weight = 0.2,           # 20% weight on vague component
  mean = 0.5              # Mean of vague component
)

plot(robust_prior)

# Compare priors
plot_mix <- function(...) {
  priors <- list(...)
  x <- seq(0, 1, 0.01)
  plot_data <- map_dfr(names(priors), function(nm) {
    tibble(x = x, y = dmix(priors[[nm]], x), prior = nm)
  })
  ggplot(plot_data, aes(x, y, color = prior)) + geom_line() + theme_bw()
}

Operating Characteristics

library(RBesT)

# Define decision rules
decision <- decision2S(
  pc = 0.975,             # Success: P(rate > p0) > 0.975
  qc = 0.10,              # Futility: P(rate > p0) < 0.10
  lower.tail = FALSE
)

# Operating characteristics
oc <- oc2S(
  prior_treatment = robust_prior,
  prior_control = robust_prior,
  n1_treatment = 30,      # Stage 1 treatment
  n1_control = 30,        # Stage 1 control
  n2_treatment = 30,      # Stage 2 treatment
  n2_control = 30,        # Stage 2 control
  decision = decision
)

# Plot OC curves
plot(oc)

# Type I error and power
summary(oc)

Group Sequential Designs with rpact

O'Brien-Fleming Design

library(rpact)

# O'Brien-Fleming group sequential design
design_of <- getDesignGroupSequential(
  kMax = 3,                   # Number of stages
  alpha = 0.025,              # One-sided alpha
  beta = 0.20,                # Type II error
  sided = 1,
  typeOfDesign = "OF",
  informationRates = c(0.33, 0.67, 1.0)
)

summary(design_of)
plot(design_of)

# Boundaries
design_of$criticalValues    # Z-score boundaries
design_of$alphaSpent        # Cumulative alpha spent

Sample Size Calculation

library(rpact)

# Sample size for survival endpoint
sample_size <- getSampleSizeSurvival(
  design = design_of,
  lambda1 = log(2) / 24,      # Control median = 24 months
  lambda2 = log(2) / 36,      # Treatment median = 36 months (HR = 0.67)
  accrualTime = 24,           # Accrual period
  followUpTime = 12,          # Additional follow-up
  dropoutRate1 = 0.05,        # Control dropout
  dropoutRate2 = 0.05,        # Treatment dropout
  allocationRatioPlanned = 1
)

summary(sample_size)

# Events and sample size at each look
sample_size$eventsPerStage
sample_size$numberOfSubjects

Interim Analysis

library(rpact)

# Perform interim analysis
interim <- getAnalysisResults(
  design_of,
  dataInput = getDataset(
    n = c(100, 100),          # Cumulative n by stage
    events = c(40, 80),       # Cumulative events by stage
    logRanks = c(2.1, 2.8)    # Log-rank Z statistics
  )
)

summary(interim)

# Can the trial stop?
interim$finalStage           # Final stage reached?
interim$futilityStop         # Stopped for futility?
interim$rejectAtFinalStage   # Rejected at final analysis?

Sample Size Re-Estimation

Blinded SSR

library(rpact)

# Sample size re-estimation based on interim data
ssr <- getSampleSizeReestimation(
  design_of,
  stageResults = interim,
  conditionalPower = 0.80     # Target conditional power
)

summary(ssr)
ssr$sampleSizeNew             # New sample size recommendation

Unblinded SSR

library(rpact)

# Conditional power at interim
cp <- getConditionalPower(
  design = design_of,
  stage = 2,
  stageResults = interim,
  nPlanned = c(50, 50),       # Planned future n per arm
  assumedEffect = 0.67        # Assumed treatment effect (HR)
)

summary(cp)

# If CP too low, calculate required sample size
if (cp$conditionalPower < 0.50) {
  # Increase sample size
  new_n <- getSampleSizeReestimation(design_of, interim, conditionalPower = 0.80)
}

Graphical Multiplicity with gMCP

library(gMCPLite)

# Define hypothesis graph
# H1, H2: Primary endpoints; H3, H4: Secondary endpoints
m <- matrix(
  c(0, 0.5, 0.5, 0,
    0.5, 0, 0, 0.5,
    0.5, 0, 0, 0.5,
    0, 0.5, 0.5, 0),
  nrow = 4, byrow = TRUE
)

weights <- c(0.5, 0.5, 0, 0)  # Initial alpha allocation

# Create graph
graph <- gMCP::matrix2graph(m, weights)
nodeNames(graph) <- c("H1_Primary", "H2_Primary", "H3_Secondary", "H4_Secondary")

# Plot
plot(graph)

# Test with p-values
pvalues <- c(0.01, 0.03, 0.02, 0.04)
result <- gMCP::gMCP(graph, pvalues, alpha = 0.025)
print(result)

# Which hypotheses rejected?
result@rejected

Key Packages Summary

Package	Purpose
adaptr	Platform trial simulation
basket	Basket trial analysis
MAMS	Multi-arm multi-stage designs
rpact	Group sequential and adaptive designs
RBesT	Bayesian evidence synthesis
gMCPLite	Graphical multiplicity procedures
gsDesign	Group sequential designs
gsDesign2	Enhanced group sequential
Mediana	Clinical trial simulations

Best Practices

1. Pre-specification: Define adaptation rules before trial starts
2. Type I error: Ensure strong control under all adaptations
3. Operating characteristics: Simulate extensively under various scenarios
4. Blinding: Maintain blinding where possible during adaptations
5. Documentation: Document all decision rules in protocol
6. Regulatory: Engage regulators early for complex adaptive designs
7. Implementation: Plan for operational complexity of adaptations
8. Analysis: Plan for potential biases from adaptations