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Suppose we want to design a new study to assess the implications of childhood obesity on poor health outcomes in adulthood. In the study we will consider total cholesterol at age 50 and incident cardiovascular disease by age 50 as the key outcomes. We will compare normal versus overweight/obese children. Assume that the standard deviation in total cholesterol is 35. You must manually calculate all parts of this problem.
a. How many normal and overweight/obese children are required to ensure that a 95% confidence interval estimate for the difference in total cholesterol has a margin of error not exceeding 5 units?
b. How many normal and overweight/obese children are required to ensure 80% power to detect a 4% difference in incident cardiovascular disease between groups? Assume that approximately 3% of normal weight children will develop cardiovascular disease by age 50 and that 7% of overweight/obese children will develop cardiovascular disease by age 50 and that a two sided test with a=0.05 will be used.
c. How many normal and overweight/obese children should be enrolled to satisfy (a) and (b) assuming that 20% will be lost to follow-up over the course of the study?
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