Chapter 2 Sample Size Determination

Chapter Objectives

The objective of this chapter is to provide a practical, defensible, and regulator-ready framework for sample size determination in clinical trials.
Upon completing this chapter, the reader should be able to:

  • Understand sample size as a design decision rather than a mechanical calculation
  • Justify assumptions used in sample size determination
  • Evaluate effect size sources critically
  • Account for dropout and multiplicity in planning
  • Produce clear, auditable outputs for Protocols and SAPs

2.1 The Role of Sample Size in Clinical Trial Design

2.1.1 Sample Size Is Designed, Not Calculated

In practice, sample size is not a purely mathematical result.
It is the consequence of multiple design assumptions:

Sample Size = Statistical Hypothesis × Effect Size × Variability × Operational Assumptions

The role of the statistician is not to apply formulas blindly, but to ensure that:

  • The study question is answerable with the proposed sample size
  • Assumptions are scientifically reasonable
  • The design can withstand regulatory scrutiny

2.1.2 Two Dangerous Extremes

Statisticians should actively avoid:

  • Over-optimism: assuming an unrealistically large effect size, leading to underpowered studies
  • Over-conservatism: inflating sample size beyond operational feasibility

The true value of statistical leadership lies in balancing scientific rigor, feasibility, and risk.

2.2 Sample Size Calculation Framework

2.2.1 Core Components

Regardless of endpoint type, all sample size calculations must clearly define:

Component Description
Primary endpoint Sample size must be based on the primary endpoint only
Statistical hypothesis Null and alternative hypotheses
Significance level Type I error rate (α)
Power Probability of detecting the assumed effect
Effect size Mean difference, rate difference, or hazard ratio
Variability Standard deviation or event rate assumptions

2.2.2 Endpoint-Specific Considerations

2.2.2.1 Continuous Endpoints

  • Based on mean differences
  • Requires standard deviation assumptions
  • Highly sensitive to variance misspecification

2.2.2.2 Binary Endpoints

  • Based on response rates or risk differences
  • Requires control group event rate assumptions
  • Low event rates rapidly increase sample size

2.2.2.3 Time-to-Event Endpoints

  • Driven primarily by number of events
  • Dependent on follow-up duration and censoring
  • Assumed hazard ratio is the key driver

2.2.2.4 Repeated Measures Endpoints

  • Correlation structure must be considered
  • Simplified approaches must clearly state assumptions

2.2.3 Transparency of Assumptions

All assumptions used in sample size determination should be explicitly documented, including:

  • Data sources
  • Rationale for chosen values
  • Consequences if assumptions are violated

2.3 Effect Size Justification

2.3.1 Why Effect Size Is the Highest-Risk Assumption

Effect size assumptions directly determine:

  • Required sample size
  • Probability of trial success
  • Interpretability of results

An unrealistic effect size almost guarantees trial failure.

2.3.2 Common Sources of Effect Size Assumptions

2.3.2.1 Published Literature

  • Advantages: peer-reviewed, traceable
  • Risks: differences in population, endpoint definition, or dose

2.3.2.2 Pilot or Phase I/II Studies

  • Advantages: same compound and indication
  • Risks: small sample size and optimistic bias

2.3.2.3 Clinical Assumptions

  • Must be clinically meaningful
  • Must never be selected solely to reduce sample size

2.3.3 Reality Checks by the Statistician

Statisticians should always ask:

  • Is this effect clinically plausible?
  • What happens if the true effect is smaller?
  • Should sensitivity or scenario analyses be conducted?

2.4 Dropout and Attrition Assumptions

2.4.1 Why Dropout Matters

Sample size calculations yield the number of evaluable subjects required for primary analysis, not the number to be randomized.

Dropout assumptions bridge this gap.

2.4.2 Sources of Dropout Assumptions

Common sources include:

  • Historical trials in the same indication
  • Disease severity and patient burden
  • Treatment duration and administration route
  • Frequency of study visits

2.4.3 Common Mistakes

  • Applying a default dropout rate without justification
  • Ignoring differential dropout across treatment arms
  • Failing to consider missingness at critical time points

Dropout assumptions and adjustments must be explicitly stated.

2.5 Impact of Multiplicity on Sample Size

2.5.1 Multiplicity Is Not Only an Analysis Issue

Sample size may be affected when there are:

  • Multiple primary endpoints
  • Multiple dose comparisons
  • Multiple formal hypotheses

2.5.2 Common Strategies

2.5.2.1 Hierarchical Testing

  • Sample size driven by the first primary endpoint
  • No sample size inflation for subsequent tests

2.5.2.2 Bonferroni-Type Adjustments

  • α is divided across comparisons
  • Often leads to substantial sample size increases

2.5.2.3 Composite Endpoints

  • Changes the definition of effect
  • Requires careful clinical interpretation

2.5.3 Key Message to Study Teams

Each additional formal comparison almost always increases the required sample size.

2.6 Deliverable 1: Sample Size Calculation Memo

2.6.1 Purpose of the Memo

The Sample Size Calculation Memo serves as:

  • An internal decision-making document
  • A regulatory defense artifact
  • The foundation for Protocol and SAP text

2.7 Deliverable 2: Sample Size Section in Protocol and SAP

2.7.1 Protocol Writing Principles

  • Concise and regulator-friendly
  • Focused on primary assumptions
  • Avoid excessive discussion of uncertainty

2.7.2 SAP-Level Details

The SAP should include:

  • Detailed calculation methods or formulas
  • Clarification of assumptions
  • Alignment with planned primary analysis methods

2.8 Statistician’s Pre-Finalization Checklist

Before finalizing sample size, confirm that:

2.9 Chapter Summary

Sample size is not about “calculating enough,”
but about committing appropriate resources to answer a meaningful question.