Bioequivalence and Bioavailability Forum

Hi Mohamed,

❝ […] how to calculate the sample size and power for clinical trials (CROs) as I want to know the basis for calculating sample size for assessing safety and efficacy of one test drug compared to control.

That’s a terribly wide field where different hypotheses are tested (time to event / survival, dose-response, superiority, non-inferiority, equivalence,…) based on different types of data (discrete: nominal and ordinal scale, continuous: interval and ratio scale), different distributions (normal, lognormal, binomial,…). There’s not enough space here to list the number of statistical models/tests.  All them them require different methods for sample size estimation.

❝ Any equations, guidelines, references, software recommended would be an asset.

See the respective sections in ICH E8 and E9.
Be warned about Chow et al.¹ Although the book gives a good overview it contains a lot of typos. Always cross-check the formulas with other references. Julious² is a nice appetizer. My favorite is the comprehensive book by Julious³ which covers practically everything. If you need something else, consult with a qualified biostatistician.
Due to the high variability and/or small effects in phase III sample sizes generally are so large that approximations by the normal distribution can be used. Makes life easier.

---

1. Chow S-C, Shao J, Wang H. Sample Size Calculations in Clinical Research. New York: Marcel Dekker; 2003.
   
2. Julious SA. TUTORIAL IN BIOSTATISTICS. Sample sizes for clinical trials with Normal data. Stat Med. 2004;23(12):1921–86. doi:10.1002/sim.1783.
   
3. Julious SA. Sample Sizes for Clinical Trials. Boca Raton: Chapman & Hall/CRC; 2010.