Sample Size Guidelines for Logistic Regression from Observational Studies with Large Population: Emphasis on the Accuracy Between Statistics and Parameters Based on Real Life Clinical Data

Mohamad Adam Bujang, Nadiah Sa'at, Tg Mohd Ikhwan Tg Abu Bakar Sidik, Lim Chien Joo, Mohamad Adam Bujang, Nadiah Sa'at, Tg Mohd Ikhwan Tg Abu Bakar Sidik, Lim Chien Joo

Abstract

Background: Different study designs and population size may require different sample size for logistic regression. This study aims to propose sample size guidelines for logistic regression based on observational studies with large population.

Methods: We estimated the minimum sample size required based on evaluation from real clinical data to evaluate the accuracy between statistics derived and the actual parameters. Nagelkerke r-squared and coefficients derived were compared with their respective parameters.

Results: With a minimum sample size of 500, results showed that the differences between the sample estimates and the population was sufficiently small. Based on an audit from a medium size of population, the differences were within ± 0.5 for coefficients and ± 0.02 for Nagelkerke r-squared. Meanwhile for large population, the differences are within ± 1.0 for coefficients and ± 0.02 for Nagelkerke r-squared.

Conclusions: For observational studies with large population size that involve logistic regression in the analysis, taking a minimum sample size of 500 is necessary to derive the statistics that represent the parameters. The other recommended rules of thumb are EPV of 50 and formula; n = 100 + 50i where i refers to number of independent variables in the final model.

Keywords: logistic regression; observational studies; sample size.

Conflict of interest statement

Conflict of Interest All authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The comparison of differences of coefficients between results derived from parameters and statistics based on various sample sizes
Figure 2
Figure 2
The comparison of differences of Nagelkerke r-squared between results derived from parameters and statistics based on various sample sizes
Figure 3
Figure 3
The comparison of differences of coefficients between results derived from parameters and statistics based on various sample sizes tested with larger sample

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