Power and sample size evaluation for the McNemar test with application to matched case-control studies

Area of Science:

• Biostatistics
• Epidemiology
• Clinical Trials

Background:

• Sample size calculation is crucial for the statistical power of studies analyzing paired or matched proportions.
• Existing methods for matched case-control studies, particularly using McNemar's test, show variations in sample size expressions.
• Differences often stem from the variance estimation under the alternative hypothesis.

Purpose of the Study:

• To identify and compare various unconditional sample size calculation expressions for McNemar's test in matched designs.
• To evaluate the accuracy and conservativeness of different unconditional sample size formulas.
• To provide a simplified method for calculating sample sizes based on cell probabilities.

Main Methods:

• Comparison of four distinct unconditional sample size expressions against the conditional power function.
• Analysis of Schlesselman's, Miettinen's, Fleiss and Levin's, Dupont's, Connor's, and Mitra's methods.
• Development of a simplified approach using a table of cell probabilities.

Main Results:

• Miettinen's first-order expression tends to underestimate sample size.
• Miettinen's second-order and Connor's multinomial expressions are generally accurate, with slight variations in conservativeness.
• Mitra's local unconditional expression is often excessively conservative.

Conclusions:

• Miettinen's second-order and Connor's multinomial methods provide reliable sample size estimations for matched case-control studies.
• The choice of sample size formula impacts study power and resource allocation.
• A simplified method facilitates the application of various sample size calculations.