We wish to design study to assess risk factors for stroke and dementia. There're two primary outcome measures. The first is measure of neurological function. Patients with normal function typically score 70 with an SD of 15. The second outcome is incident stroke. In the patients over the age of 65, approximately 14% construct stroke over 25 years. How many participants over the age of 65 must be enrolled to ensure the following?
a. That the margin of error in a 95% CI for the difference in mean neurologic function scores between men and women doe not eceed 2 units.
b. That we have 80% power to detect a 20% reduction in incidence of stroke between participants who participate in healthy-aging program compared to those who do not. Assume that the incidence of stroke is 14% in those who do not participate.
c. How many men and women over the age of 65 should be enrolled to satisfy parts (a) and (b) assuming that 15% will be lost to follow-up over the course of 25-year follow up?