1 Background Story:

One day, my boss asked me to check if the data has a certain number of events to perform an efficacy analysis. I was curious how did he come up with the number, later I know he must have done the Sample Size Calculation.Today we will go over the basics and R applications for sample size calculation.

2 Five components of Sample Size:

Sample Size: N

Type I error rate: α- level (2-sided 0.05)

Mean under the null and alternative: μ0 and μa

Variance: σ²

Power: 1-β

We can use any four of these five factors to calculate the fifth one.

3 Two methods to calculate the sample size:

Hypothesis testing: a specific null and alternative hypothesis

Confidence interval: an estimated interest

Hypothesis testing approach:

State the null and the alternative hypothesis

Specify standard deviation

Decide the power and alpha level

State the test

R/ SAS program

  1. H0: mean=80, Ha: mean1= 70 2. standard deviation =20, d=(80-70)/20 3. Power=0.8 , Alpha=0.05 for two-sided test
## 
##      One-sample t test power calculation 
## 
##               n = 33.36713
##               d = 0.5
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided

4 Advanced Sample Size:

Two Sample T-test Comparison of proportions

## 
##      Two-sample t test power calculation 
## 
##               n = 26.26343
##               d = 0.7882
##       sig.level = 0.05
##           power = 0.8
##     alternative = two.sided
## 
## NOTE: n is number in *each* group

5 Summary of Sample Size variations:

Variance σ² increase, the sample size N increase

Difference between groups increases (μ1-μ2), sample size N decrease

Type I error rate (α) increase, sample size N decrease

Power (1-ß) increases sample size N increase.

Thanks 77 for sharing the Havard Catalyst class material!

Happy Studying!