Sample Size Rules in Medical Research: Choosing the Right Method by Study Objective

Sample size rules depend on the objective of the research — there is no single universal rule.

Introduction

Sample size calculation is one of the most confusing parts of medical research because there is no single correct rule. The correct approach depends entirely on what the study is trying to achieve. Choose the Rule Based on Your Research Objective

A study may aim to:

• test a hypothesis,

• build a prediction model,

• estimate a parameter precisely,

• evaluate a complex design,

• or handle special data structures.
  

Each objective requires a different logic and different criteria for determining sample size. This article introduces five major objectives in medical research and explains how sample size should be determined for each.

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Objective 1: Hypothesis Testing

“Is there a real effect or difference?”

Purpose

To detect whether an intervention, exposure, or factor has a statistically significant effect.

Sample Size Logic

Sample size is calculated to ensure adequate statistical power to detect a clinically meaningful effect if it truly exists.

Key Framework

BRAVE

• Beta (Power)

• Ratio (group allocation)

• Alpha (Type I error)

• Variability

• Effect size
  

Key Criterion

✔ Power (usually 80–90%)

Typical Use

• Randomized controlled trials (RCTs)

• Group comparisons

• Etiologic association studies

👉 Main question: How many subjects are needed to detect this effect with acceptable error?

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Objective 2: Clinical Prediction Models (CPM)

“Can we predict individual outcomes reliably?”

Purpose

To build a model that predicts risk accurately in new patients, not to test statistical significance.

Sample Size Logic

Sample size is chosen to:

• prevent overfitting

• ensure stable coefficients

• obtain reliable model performance
  

Key Criterion

✔ Model stability and shrinkage ✔ Precision of calibration and discrimination

Modern Approach

• Riley et al. framework

• Implemented via pmsampsize (R / Stata)
  

Typical Use

• Risk scores

• Prognostic models

• Clinical decision tools

👉 Main question: How much data is needed to build a model that works in real patients?

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Objective 3: Estimation / Precision

“How accurately do we want to estimate a value?”

Purpose

To estimate a population parameter (mean, proportion, rate) with acceptable precision.

Sample Size Logic

Sample size is determined by the desired confidence interval width, not by power.

Key Criterion

✔ Margin of error (CI width)

Typical Use

• Prevalence studies

• Surveys

• Descriptive epidemiology
  

👉 Main question: How many subjects are needed so the estimate is precise enough?

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Objective 4: Simulation-Based Studies

“The design is too complex for simple formulas.”

Purpose

To evaluate performance when analytic formulas are unavailable or unreliable.

Sample Size Logic

Repeated computer simulations are used to test whether a given sample size meets performance goals.

Key Criterion

✔ Empirical performance (power, bias, coverage)

Typical Use

• Complex multivariable models

• Adaptive designs

• Machine learning models

👉 Main question: With this sample size, how often does the study succeed under realistic scenarios?

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Objective 5: Specialized Designs

“The data structure changes everything.”

Purpose

To account for non-independent data or time-to-event outcomes.

Sample Size Logic

Sample size must be adjusted for:

• correlation,

• censoring,

• clustering,

• or timing of events.
  

Examples

• Cluster randomized trials → adjust for ICC

• Survival analysis → focus on number of events, not just N

• Non-inferiority trials → larger N required
  

👉 Main question: What design features reduce effective sample size, and how do we compensate?

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Key Teaching Message

Sample size is not one rule — it is a decision driven by the research objective.

Research Objective	Sample Size Based On
Hypothesis testing	Power (BRAVE)
Prediction models	Model stability (pmsampsize)
Estimation	Confidence interval width
Complex designs	Simulation performance
Specialized designs	Design-specific adjustments

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Conclusion

Sample size determination is not a mechanical step but a conceptual decision. Before calculating anything, researchers must ask:

“What is my study trying to achieve?”

Only after the objective is clear can the correct sample size rule be chosen. Teaching sample size this way helps medical graduate students avoid common errors, apply appropriate methods, and design studies that are scientifically sound, efficient, and ethical.