colon cancer and fat intake

1. An investigator proposes a case control study to assess colon cancer and fat intake. She has a scale that identifies “high-fat consumers”, projected as 28% of the population. She will select cancer cases (annual incidence rate of 3/1000 in this population) from the cancer clinic and hospital controls from the GI clinic. You are asked to write a paragraph regarding the number of cases and controls needed.

2. An investigator is uncertain if the higher rates of bladder cancer among white men can be attributed to smoking. He feels the rate of progression of smoking exposure to the development of bladder cancer varies by race. He has access to a retrospective cohort of 100,000 male smokers (75,000 Caucasian and 25,000 African Americans) who have been followed for 30-years. The overall incidence of bladder cancer is 1.25/1000 among Caucasians and .95/1000 among African Americans. How many subjects need to be included in order to test the hypothesis?

3. An investigator wishes to test the use of vitamin D on carotid thickness among postmenopausal women. She proposes a two armed trial with 1000 mg of vitamin D versus placebo. She would like to detect a 0.2 mm difference in the change of IMT after 3 years. In this population a typical change in two years is 0.5 mm with a standard deviation of 0.1 mm. She is not sure what effect the vitamin D will have on IMT but hopes to slow progression. How many individuals are needed in each arm of the study?

4. An investigator has completed a study of 10 subjects using a cross over design of three treatments? He determined that anxiety was decreased with each therapy independently by 5 units and a standard deviation of 3.0 units. He thinks this is great and sends an abstract to NEJM. He then realized a sample size calculation was never done. Backtracking he comes to you with tears in his eyes and ask what can be done. You suggest a power analysis. He does not know what that means – so please write a paragraph about power for this study.