Sample size and power estimation for comparison of two binom

Sample size and power estimation for comparison of two binomial probabilities with significance level and statistical power 1 – : To test the null hypothesis H0: 1 = 2 versus the alternate hypothesis H1: 1 2, the estimated sample size in each group can be calculated using the formula n = ((_1 (1-_1)+_2 (1-_2)) (z_(1-2)+z_(1-) )^2)/^2 where is the magnitude of the effect of interest to detect, which in this case is the absolute value of a difference between the two probabilities.

Suppose there are 150 incident cases of a particular disease each year among 100,000 persons at risk. For a randomized, one-year trial of a new dietary intervention to prevent the disease, what sample size per arm do you estimate would be needed to detect a 50% reduction in risk with the intervention. Assume two-sided testing, equal allocation of participants to the two trial arms, = 0.10, and 1 – = 0.90.

What sample size per trial arm would be needed to detect a 20% reduction in risk holding everything else constant?

If 70% of invited participants are expected to participate in the trial, how many must be invited to attain the sample sizes in (a) and (b)?

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