Suppose we know from Connecticut tumor-registry data that the incidence rate of breast cancer over a 1-year period for initially disease-free women ages 4549 is 150 cases per 100,000 [1]. We wish to study whether ingesting large doses of vitamin E in capsule form will prevent breast cancer. The study is set up with 

(1) a control group of 45- to 49-year-old women who are mailed placebo pills and are expected to have the same disease rate as indicated in the Connecticut tumor-registry data and 

(2) a study group of similar-age women who are mailed vitamin E pills and are expected to have a 20% reduction in risk.

 

How large a sample is needed if a two-sided test with a significance level of .05 is used and a power of 80% is desired?

What is the type of the study design?

What is the type of the variable of interest?

What is the hypothesis test you have to conduct based on 1) and 2) (i.e. sample means, sample proportions)?

Write the Null and the Alternative Hypotheses for this hypothesis testing and identify the type of the hypothesis test ( i.e. two-sided or one-sided - left or right).

Identify the appropriate sample size formula and compute the sample size.

Use PROC POWER in SAS to compute the sample size.

Compute the powerof the statistical test for a sample size=100 using SAS Proc POWER

Compute the power of the statistical test for a sample size=100 using the appropriate formula.

 Conduct a simulation study to compute the empirical power for the statistical test for a sample size=100 using SAS.