New method to estimate the sample size for calculation of a proportion assuming binomial distribution.

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Methods

Background:

• Current sample size calculations for prevalence often rely on the Normal distribution.
• This method may not accurately reflect the underlying Binomial distribution of prevalence data.
• Confidence intervals calculated using the Normal distribution can be less precise.

Purpose of the Study:

• To compare sample size calculation methods for prevalence estimation.
• To evaluate the accuracy of Normal distribution-based formulas versus Binomial distribution methods.
• To propose an improved algorithm for sample size determination.

Main Methods:

• Comparison of sample size formulas based on Normal and Binomial distributions.
• Simulation of an iterative sampling procedure.
• Development of a sample size algorithm utilizing the Wilson Score method.

Main Results:

• The Normal distribution formula shows relevant variations in confidence interval amplitude compared to the Binomial distribution, particularly at the tails and center.
• Simulations revealed underestimation of sample size for prevalence near 0 or 1, and overestimation near 0.5.
• The proposed Wilson Score-based algorithm yields sample size values comparable to simulation results.

Conclusions:

• The Wilson Score method provides a more accurate basis for sample size calculations in prevalence studies.
• The traditional Normal distribution method can lead to inaccurate sample size estimates.
• The developed algorithm offers a reliable alternative for determining optimal sample sizes.