Clinical Trial Design Guide

Common Designs

Parallel Group (most common Phase III):
  R --> Treatment A --> Outcome assessment
  R --> Treatment B --> Outcome assessment

Crossover:
  R --> Treatment A --> Washout --> Treatment B --> Outcome
  R --> Treatment B --> Washout --> Treatment A --> Outcome

Factorial (2x2):
  R --> Drug A + Drug B
  R --> Drug A + Placebo B
  R --> Placebo A + Drug B
  R --> Placebo A + Placebo B

Adaptive:
  Stage 1: Enroll n1 patients --> Interim analysis
  Stage 2: Modify design (dose, sample size, arm dropping) --> Continue

Design Selection Criteria

Sample Size Calculation

Two-Sample Comparison of Means

from scipy.stats import norm
import numpy as np

def sample_size_two_means(delta: float, sigma: float,
                           alpha: float = 0.05, power: float = 0.80,
                           ratio: float = 1.0) -> dict:
    """
    Sample size for comparing two group means (two-sided test).
    delta: minimum clinically important difference
    sigma: pooled standard deviation
    alpha: type I error rate
    power: desired power (1 - beta)
    ratio: allocation ratio (n2/n1)
    """
    z_alpha = norm.ppf(1 - alpha / 2)
    z_beta = norm.ppf(power)
    effect = delta / sigma

    n1 = ((z_alpha + z_beta) ** 2 * (1 + 1 / ratio)) / effect ** 2
    n2 = ratio * n1

    return {
        "n_per_group_1": int(np.ceil(n1)),
        "n_per_group_2": int(np.ceil(n2)),
        "total": int(np.ceil(n1) + np.ceil(n2)),
        "effect_size": round(effect, 3),
    }

# Example: detect 5-point difference, SD=15, 80% power
result = sample_size_two_means(delta=5, sigma=15)
print(f"Required: {result['total']} total patients")

Sample Size for Survival Endpoints

def sample_size_logrank(hazard_ratio: float, alpha: float = 0.05,
                         power: float = 0.80, ratio: float = 1.0,
                         median_control: float = 12.0,
                         accrual_time: float = 24.0,
                         followup_time: float = 12.0) -> dict:
    """
    Sample size for log-rank test comparing two survival curves.
    hazard_ratio: expected HR (treatment/control), <1 means treatment better
    median_control: median survival in control arm (months)
    """
    z_alpha = norm.ppf(1 - alpha / 2)
    z_beta = norm.ppf(power)

    # Required number of events (Schoenfeld formula)
    d = ((z_alpha + z_beta) ** 2 * (1 + ratio) ** 2) / (
        ratio * (np.log(hazard_ratio)) ** 2
    )
    d = int(np.ceil(d))

    # Estimate probability of event during study
    lambda_c = np.log(2) / median_control
    lambda_t = lambda_c * hazard_ratio

    # Average probability of event (simplified uniform accrual)
    p_event_c = 1 - np.exp(-lambda_c * followup_time)
    p_event_t = 1 - np.exp(-lambda_t * followup_time)
    p_event_avg = (p_event_c + ratio * p_event_t) / (1 + ratio)

    n_total = int(np.ceil(d / p_event_avg))

    return {
        "events_required": d,
        "total_patients": n_total,
        "hazard_ratio": hazard_ratio,
        "p_event_avg": round(p_event_avg, 3),
    }

Randomization Methods

Implementation

import random

def stratified_block_randomization(strata: list[str],
                                     block_sizes: list[int] = [4, 6],
                                     ratio: tuple = (1, 1),
                                     seed: int = 42) -> list[str]:
    """
    Stratified permuted block randomization.
    strata: list of stratum labels for each patient (in enrollment order)
    block_sizes: list of possible block sizes (randomly selected)
    ratio: allocation ratio (e.g., (1,1) for 1:1, (2,1) for 2:1)
    Returns list of treatment assignments ('A' or 'B').
    """
    rng = random.Random(seed)
    stratum_queues = {}
    assignments = []

    for stratum in strata:
        if stratum not in stratum_queues:
            stratum_queues[stratum] = []

        if not stratum_queues[stratum]:
            # Generate new block
            block_size = rng.choice(block_sizes)
            n_a = block_size * ratio[0] // sum(ratio)
            n_b = block_size - n_a
            block = ["A"] * n_a + ["B"] * n_b
            rng.shuffle(block)
            stratum_queues[stratum] = block

        assignments.append(stratum_queues[stratum].pop(0))

    return assignments

Interim Analysis and Monitoring

Group Sequential Design

def obrien_fleming_boundary(n_looks: int, alpha: float = 0.05) -> list[float]:
    """
    Compute O'Brien-Fleming spending function boundaries.
    Provides very conservative early stopping with near-nominal final alpha.
    """
    from scipy.stats import norm
    boundaries = []
    for k in range(1, n_looks + 1):
        info_fraction = k / n_looks
        z_boundary = norm.ppf(1 - alpha / 2) / np.sqrt(info_fraction)
        p_boundary = 2 * (1 - norm.cdf(z_boundary))
        boundaries.append({
            "look": k,
            "info_fraction": round(info_fraction, 3),
            "z_boundary": round(z_boundary, 4),
            "p_boundary": round(p_boundary, 6),
        })
    return boundaries

# Example: 3 interim looks + 1 final
boundaries = obrien_fleming_boundary(4)
for b in boundaries:
    print(f"Look {b['look']}: Z={b['z_boundary']}, p={b['p_boundary']}")

Survival Analysis

Kaplan-Meier and Log-Rank Test

from lifelines import KaplanMeierFitter
from lifelines.statistics import logrank_test

def analyze_survival(time: pd.Series, event: pd.Series,
                      group: pd.Series) -> dict:
    """
    Perform Kaplan-Meier estimation and log-rank test.
    time: follow-up duration
    event: 1=event occurred, 0=censored
    group: treatment group labels
    """
    groups = group.unique()
    kmf_results = {}

    for g in groups:
        mask = group == g
        kmf = KaplanMeierFitter()
        kmf.fit(time[mask], event[mask], label=str(g))
        kmf_results[g] = {
            "median_survival": kmf.median_survival_time_,
            "survival_at_12m": kmf.predict(12),
        }

    # Log-rank test
    mask_a = group == groups[0]
    lr = logrank_test(
        time[mask_a], time[~mask_a],
        event[mask_a], event[~mask_a],
    )

    return {
        "group_results": kmf_results,
        "logrank_statistic": lr.test_statistic,
        "logrank_p_value": lr.p_value,
    }

Regulatory Considerations

Key regulatory documents for clinical trial design:

• ICH E6 (R2): Good Clinical Practice guidelines
• ICH E9 (R1): Statistical Principles, estimands framework
• ICH E8 (R1): General Considerations for Clinical Studies
• FDA 21 CFR Part 312: Investigational New Drug regulations
• EMA Scientific Guidelines: Disease-specific guidance documents

Tools and Software

• R survival package: Kaplan-Meier, Cox regression, log-rank test
• lifelines (Python): Survival analysis library
• gsDesign (R): Group sequential design and monitoring boundaries
• PASS / nQuery: Commercial sample size software
• EAST (Cytel): Adaptive and group sequential design software
• REDCap: Electronic data capture for clinical research
• ClinicalTrials.gov API: Trial registry search and data access