Researchers are interested in the effects of a prenatal support and education program on preterm birth

Researchers are interested in the effects of a prenatal support and education program on preterm birth. They plan to test the program in a pilot study to determine if they should recommend that the Arizona Department of Public Health and Safety implement the program statewide. The current risk of preterm birth in the state is 11%. For ADPHS to recommend implementing the program throughout the state, they have stated that the risk of preterm birth among those receiving the intervention needs to be 9% or lower. The researchers decide to use a concurrent cohort design to investigate this relationship in the pilot study.

Q1.1

Using a relative measure of association, what is the minimum total sample size needed to detect the association that would support statewide implementation of the program as described above? Note that the exposed group are those who received the intervention. For notation, the exposed will be called "Group 1", and the unexposed will be called group "Group 2". Use a 2-tailed statistical test with an alpha level of 0.05 and 80% power. Fill the values for a) through f) . Show working. 

a) Z1−a/2?:

b) Z1−b?:

c) pGroup1?:

d) pGroup2?:

e) n:

f) Total n:

Q1.2

After establishing the sample size needed from Q1.1, the researchers apply for a grant and receive enough funds to deliver the intervention to 5000 mothers, with 5000 control mothers for comparison. What will happen to the power to detect the association described above, assuming that alpha remains unchanged? 

a)There is no change because power is not relevant to sample size

b)There is no change because power is proportional to the sample size

c)Decrease, as the increase in sample size will increase the variance of the outcome among the groups

d) Increase, as the increase in sample size will decrease the variance of the outcome among the groups

Q1.3

After the research described above, researchers get a CIR = 0.84 with a 95% confidence interval of (0.81, 0.87). Indicate whether the following statements are true or false. 

I)  Over an infinite number of repetitions, the true population CIR will be contained in 95% of the confidence intervals produced. (0.81, 0.87) is one of those confidence intervals.

A. True

B. False

II) There is a 95% chance that the true population CIR is contained in the (0.81, 0.87) interval.

A. True

B. False

III) The CIR=0.84 is statistically significant at ?=0.05.

A. True

B. False