Mediana Fundamentals

Initialization

data.model <- DataModel()

OutcomeDist - Outcome Distribution

Specifies the distribution of patient outcomes.

OutcomeDist(
  outcome.dist = "NormalDist",   # Distribution type
  outcome.type = "standard"       # "standard" or "event"
)

Supported Distributions:

Multivariate Distributions:

Sample - Treatment Arm Definition

# Normal distribution parameters
outcome.placebo <- parameters(mean = 0, sd = 70)
outcome.treatment <- parameters(mean = 40, sd = 70)

# Define samples
Sample(id = "Placebo",
       outcome.par = parameters(outcome.placebo))

Sample(id = "Treatment",
       outcome.par = parameters(outcome.treatment))

Multiple Scenarios:

# Define multiple effect size scenarios
outcome1.placebo <- parameters(mean = 0, sd = 70)
outcome1.treatment <- parameters(mean = 40, sd = 70)  # Conservative

outcome2.placebo <- parameters(mean = 0, sd = 70)
outcome2.treatment <- parameters(mean = 50, sd = 70)  # Optimistic

Sample(id = "Placebo",
       outcome.par = parameters(outcome1.placebo, outcome2.placebo))

Sample(id = "Treatment",
       outcome.par = parameters(outcome1.treatment, outcome2.treatment))

SampleSize - Balanced Design

SampleSize(c(50, 55, 60, 65, 70))  # Per arm
SampleSize(seq(50, 100, 10))

Event - Event-Driven Design

Event(
  n.events = c(390, 420),      # Total event counts to evaluate
  rando.ratio = c(1, 2)        # Control:Treatment ratio
)

Design - Enrollment and Dropout

# Non-uniform enrollment with beta distribution
# 50% enrolled at 75% of enrollment period
enroll.par <- parameters(
  a = log(0.5)/log(0.75),
  b = 1
)

Design(
  enroll.period = 12,              # Enrollment duration (months)
  study.duration = 36,             # Total study duration
  enroll.dist = "BetaDist",        # Or "UniformDist"
  enroll.dist.par = enroll.par,
  dropout.dist = "ExpoDist",
  dropout.dist.par = parameters(rate = 0.0115)
)

Complete Data Model Example

# Time-to-event trial with PFS and OS
median.pfs.placebo <- 6
median.pfs.treatment <- 9
median.os.placebo <- 15
median.os.treatment <- 19

placebo.par <- parameters(
  parameters(rate = log(2)/median.pfs.placebo),
  parameters(rate = log(2)/median.os.placebo)
)

treatment.par <- parameters(
  parameters(rate = log(2)/median.pfs.treatment),
  parameters(rate = log(2)/median.os.treatment)
)

corr.matrix <- matrix(c(1.0, 0.3, 0.3, 1.0), 2, 2)

data.model <- DataModel() +
  OutcomeDist(outcome.dist = "MVExpoPFSOSDist",
              outcome.type = c("event", "event")) +
  Event(n.events = c(390, 420), rando.ratio = c(1, 2)) +
  Design(enroll.period = 12, study.duration = 30,
         enroll.dist = "BetaDist",
         enroll.dist.par = parameters(a = log(0.5)/log(0.75), b = 1),
         dropout.dist = "ExpoDist",
         dropout.dist.par = parameters(rate = 0.0115)) +
  Sample(id = list("Placebo PFS", "Placebo OS"),
         outcome.par = parameters(parameters(par = placebo.par,
                                             corr = corr.matrix))) +
  Sample(id = list("Treatment PFS", "Treatment OS"),
         outcome.par = parameters(parameters(par = treatment.par,
                                             corr = corr.matrix)))

Analysis Model

Initialization

analysis.model <- AnalysisModel()

Test - Statistical Tests

Test(
  id = "Primary",                           # Unique test ID
  samples = samples("Placebo", "Treatment"), # Samples to compare
  method = "TTest",                          # Test method
  par = parameters(...)                      # Optional parameters
)

Built-in Tests:

Note: Tests are one-sided. By default, larger values expected in Sample 2. Set larger = FALSE if larger values expected in Sample 1.

Statistic - Descriptive Statistics

Statistic(
  id = "Mean Treatment",
  method = "MeanStat",
  samples = samples("Treatment")
)

Built-in Statistics:

MultAdjProc - Multiplicity Adjustment

MultAdjProc(
  proc = "HolmAdj",
  par = parameters(weight = c(0.5, 0.5)),
  tests = tests("Test1", "Test2")  # Optional: applies to all if omitted
)

Built-in Procedures:

Multiplicity Examples

Chain Procedure:

MultAdjProc(
  proc = "ChainAdj",
  par = parameters(
    weight = c(0.5, 0.5),
    transition = matrix(c(0, 1,
                          1, 0), 2, 2, byrow = TRUE)
  )
)

Parallel Gatekeeping:

MultAdjProc(
  proc = "ParallelGatekeepingAdj",
  par = parameters(
    family = families(
      family1 = c(1, 2),    # Primary endpoints
      family2 = c(3, 4)     # Secondary endpoints
    ),
    proc = families(
      family1 = "HolmAdj",
      family2 = "HolmAdj"
    ),
    gamma = families(
      family1 = 0.8,        # Truncation parameter
      family2 = 1
    )
  ),
  tests = tests("Primary1", "Primary2", "Secondary1", "Secondary2")
)

Multiple-Sequence Gatekeeping:

MultAdjProc(
  proc = "MultipleSequenceGatekeepingAdj",
  par = parameters(
    family = families(family1 = c(1, 2), family2 = c(3, 4)),
    proc = families(family1 = "HolmAdj", family2 = "HochbergAdj"),
    gamma = families(family1 = 0.8, family2 = 1)
  )
)

Complete Analysis Model Example

analysis.model <- AnalysisModel() +
  # Primary tests
  Test(id = "PFS test",
       samples = samples("Placebo PFS", "Treatment PFS"),
       method = "LogrankTest") +
  Test(id = "OS test",
       samples = samples("Placebo OS", "Treatment OS"),
       method = "LogrankTest") +

  # Fixed-sequence multiplicity adjustment
  MultAdjProc(proc = "FixedSeqAdj") +

  # Descriptive statistics
  Statistic(id = "Patients Placebo",
            samples = samples("Placebo PFS"),
            method = "PatientCountStat") +
  Statistic(id = "Patients Treatment",
            samples = samples("Treatment PFS"),
            method = "PatientCountStat")

Evaluation Model

Initialization

evaluation.model <- EvaluationModel()

Criterion - Success Metrics

Criterion(
  id = "Marginal power",
  method = "MarginalPower",
  tests = tests("Primary"),
  labels = c("Primary Power"),
  par = parameters(alpha = 0.025)
)

Built-in Criteria:

Complete Evaluation Model Example

evaluation.model <- EvaluationModel() +
  Criterion(id = "Marginal power",
            method = "MarginalPower",
            tests = tests("PFS test", "OS test"),
            labels = c("PFS Power", "OS Power"),
            par = parameters(alpha = 0.025)) +

  Criterion(id = "Disjunctive power",
            method = "DisjunctivePower",
            tests = tests("PFS test", "OS test"),
            labels = c("At least one significant"),
            par = parameters(alpha = 0.025)) +

  Criterion(id = "Average patients",
            method = "MeanSumm",
            statistics = statistics("Patients Placebo", "Patients Treatment"),
            labels = c("Mean Placebo N", "Mean Treatment N"))

Running Simulations

SimParameters

sim.parameters <- SimParameters(
  n.sims = 10000,        # Number of simulations
  proc.load = "full",    # Parallelization: "low", "med", "high", "full", or integer
  seed = 42938001        # For reproducibility
)

CSE Function

results <- CSE(
  data.model,
  analysis.model,
  evaluation.model,
  sim.parameters
)

# View summary
summary(results)

Results Structure

The CSE function returns a list with:

• simulation.results: Data frame of results per scenario
• analysis.scenario.grid: Grid of data/analysis combinations
• data.structure: Data model structure
• analysis.structure: Analysis model structure
• evaluation.structure: Evaluation model structure
• sim.parameters: Simulation parameters
• timestamp: Start/end time and duration

Report Generation

PresentationModel

presentation.model <- PresentationModel() +
  Project(username = "Analyst Name",
          title = "Phase III Trial Simulation",
          description = "Power analysis for multi-endpoint trial") +
  Section(by = "outcome.parameter") +
  Subsection(by = "sample.size") +
  Table(by = "multiplicity.adjustment") +
  CustomLabel(param = "sample.size",
              label = paste0("N = ", c(50, 60, 70))) +
  CustomLabel(param = "outcome.parameter",
              label = c("Conservative", "Expected", "Optimistic"))

GenerateReport

GenerateReport(
  presentation.model = presentation.model,
  cse.results = results,
  report.filename = "Simulation_Report.docx"
)

Complete Example: Multi-Endpoint Trial

library(Mediana)

# Data Model
outcome.placebo <- parameters(mean = 0, sd = 1)
outcome.trt.conservative <- parameters(mean = 0.3, sd = 1)
outcome.trt.expected <- parameters(mean = 0.5, sd = 1)

data.model <- DataModel() +
  OutcomeDist(outcome.dist = "NormalDist") +
  SampleSize(seq(80, 120, 10)) +
  Sample(id = "Placebo",
         outcome.par = parameters(outcome.placebo, outcome.placebo)) +
  Sample(id = "Treatment",
         outcome.par = parameters(outcome.trt.conservative, outcome.trt.expected))

# Analysis Model
analysis.model <- AnalysisModel() +
  Test(id = "Primary",
       samples = samples("Placebo", "Treatment"),
       method = "TTest") +
  Statistic(id = "Effect Size",
            samples = samples("Placebo", "Treatment"),
            method = "EffectSizeContStat")

# Evaluation Model
evaluation.model <- EvaluationModel() +
  Criterion(id = "Power",
            method = "MarginalPower",
            tests = tests("Primary"),
            labels = "Primary Power",
            par = parameters(alpha = 0.025)) +
  Criterion(id = "Mean Effect",
            method = "MeanSumm",
            statistics = statistics("Effect Size"),
            labels = "Mean Effect Size")

# Run Simulations
results <- CSE(
  data.model,
  analysis.model,
  evaluation.model,
  SimParameters(n.sims = 10000, proc.load = "full", seed = 12345)
)

# View Results
summary(results)

# Generate Report
presentation.model <- PresentationModel() +
  Project(title = "Sample Size Analysis") +
  Section(by = "outcome.parameter") +
  Table(by = "sample.size") +
  CustomLabel(param = "outcome.parameter",
              label = c("Conservative", "Expected"))

GenerateReport(presentation.model, results, "Analysis_Report.docx")

Best Practices

1. Multiple Scenarios: Always evaluate multiple treatment effect assumptions
2. Sample Size Range: Test a range of sample sizes to build power curves
3. Reproducibility: Always set seed in SimParameters
4. Parallelization: Use proc.load = "full" for large simulations
5. Report Labels: Use CustomLabel for interpretable scenario names
6. Validation: Compare CSE results to analytical formulas where available
7. Multiplicity: Select appropriate procedures based on hypothesis structure