OpenEpi, WHO & CDC Statistical Methods

Sample Size Calculator for Cohort, Cross-Sectional & Clinical Trials

Calculate sample size for comparing two proportions in prospective cohort studies, cross-sectional surveys, or randomized controlled clinical trials. Computes exact sample sizes simultaneously using Kelsey et al., Fleiss, and Fleiss with Continuity Correction (CC) formulas.

3 Standard Methods (Kelsey & Fleiss) 4-Way Auto-Synced Effect Measures 1-Click Protocol Methodology Copy
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1

Study Design Parameters

Configure confidence, power, and sample ratio

Usually 95%
Usually 80%
For equal samples, use 1.0
Between 0.1 and 99.9
2

Effect Measure Selection

Fill in ANY ONE of the 4 fields below. The other 3 will auto-calculate!

Editing any field automatically updates the other three in real time.
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Understanding Sample Size Calculation in Cohort & Clinical Studies

In prospective cohort studies, cross-sectional comparative surveys, and randomized controlled clinical trials, the primary objective is frequently to compare two independent binomial proportions (e.g., comparing disease incidence between exposed and unexposed cohorts, or recovery rates between treatment and placebo groups).

This calculator implements the gold-standard methods described by Kelsey et al. and Fleiss et al., matching the official algorithms of OpenEpi, the U.S. Centers for Disease Control and Prevention (CDC), and the World Health Organization (WHO).

Comparison of the Three Calculation Formulas:

1. Kelsey et al. Method

A widely referenced classical formula in clinical epidemiology that utilizes unweighted average proportions for standard error calculation.

2. Fleiss (Standard)

Uses variance terms weighted under both the null and alternative hypotheses, providing robust estimates for clinical trials.

3. Fleiss with CC (Recommended)

Incorporates Yates' continuity correction to account for discrete binomial approximation, ensuring the nominal Type I error rate is never exceeded.

Mathematical Formula Derivations & Notations

Parameters & Notations:

  • • r = Ratio of unexposed to exposed ($n_2 / n_1$)
  • • P1 = Proportion in exposed with outcome
  • • P2 = Proportion in unexposed with outcome
  • • P̄ = Pooled average proportion = $(P_1 + r P_2) / (r + 1)$
  • • Z1-α/2 = Standard normal deviate for two-sided confidence (1.96 for 95%)
  • • Z1-β = Standard normal deviate for statistical power (0.84 for 80%)

Kelsey et al. Formula:

n1 = [ (Zα/2 + Zβ)2 × P̄(1 - P̄)(r + 1) ] / [ r(P1 - P2)2 ]

Fleiss with Continuity Correction:

n1cc = (n1 / 4) × [ 1 + √(1 + 2(r + 1) / (n1 × r × |P1 - P2|)) ]2

Frequently Asked Questions (OpenEpi Cohort Calculator)

Which sample size number should I report in my synopsis or IRB protocol?

Most international epidemiological guidelines, institutional review boards (IRB), and CPSP recommend reporting the Fleiss with Continuity Correction sample size. It provides a conservative and safe buffer against discrete sample fluctuations.

Can I use an unequal ratio of unexposed to exposed subjects?

Yes! If exposed patients are rare or difficult to recruit, you can increase statistical power by selecting a ratio of 2:1, 3:1, or 4:1 (unexposed to exposed). Beyond a 4:1 ratio, statistical efficiency gains become negligible.

What is the difference between Odds Ratio (OR) and Relative Risk (RR)?

Relative Risk ($RR = P_1 / P_2$) directly compares cumulative incidences in prospective cohort studies and clinical trials. Odds Ratio ($OR$) compares odds of exposure and is primarily calculated in case-control studies. When an outcome is rare ($< 10\%$), the Odds Ratio closely approximates Relative Risk.

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Medswrites Biostatistics & Epidemiology Board OpenEpi & WHO Validated

Statistical calculations benchmarked against OpenEpi Version 3.01 (Emory University), Kelsey JL et al. (Methods in Observational Epidemiology), and Fleiss JL (Statistical Methods for Rates and Proportions).

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