STAT 405 – Assignment 4 (65 pts.) Due Friday, Oct. 10th
1.)In a 1985 study of the relationship between contraceptive use and infertility, 89 of 283 case (infertile) women, compared with 640 of 3833 control (fertile) women, had used an intrauterine device (IUD) at some time in their lives.
a)What type of study is this? (1 pt.)
b)Use the normal-theory method to test for significant differences in contraceptive-use patterns between the two groups. Summarize your findings. (5 pts.)
c)Construct a 2 X 2 contingency table of the results and use a chi-square test to compare the proportion of IUD users between the populations of cases and controls. (4 pts.)
d)Use Fisher’s Exact Test to compare the proportion of IUD users between the populations of cases and controls. How do the p-values from these three tests (normal theory, chi-square, and Fisher’s Exact) compare? (3 pts.)
e)Compute a 95% CI for the difference in the proportion of women who have ever used IUDs between the infertile and fertile women. Interpret. (3 pts.)
f)Compute the OR in favor of ever using an IUD for infertile women vs. fertile women.
(3 pts.)
g)Find and interpret a 95% CI for the OR in part (e). How does CI for OR relate to the tests conducted above? Explain. (5 pts.)
2.)Suppose that 200 obese (BMI 25) children and 500 normal-weight (BMI < 25) children are identified in a school-based screening for hypertension. Eighteen of the obese children and 10 of the normal-weight children are hypertensive.
a)What type of study is this? (1 pt.)
b)Conduct an appropriate test to compare the proportion of school-age children with hypertension between the populations of obese and normal-weight children. Summarize your findings. (5 pts.)
c)What is the RR for hypertension associated with obesity in school-age children? Interpret this quantity. (4 pts.)
d)Find and interpret a 95% CI for RR in part (c). How does this CI related to the test conducted in part (b). Explain. (3 pts.)
e)What is the Absolute Risk Reduction (ARR) for this study? Find a 95% CI for the ARR. Interpret. (4 pts.)
f)How does the CI for the ARR in part (e) relate the test conducted in part (b). Explain.
(2 pts.)
g)What is the Number Needed to Harm (NNH) associated with obesity in school-age children? Find a 95% CI for this quantity as well. Interpret. (4 pts.)
h)Suppose that 30% of school-age children in the U.S. are obese by the above definition. What percent of hypertension is attributable to obesity? Provide a 95% CI associated with this estimate. Interpret these results. (4 pts.)
3.)These data are from a study of breast feeding mothers in Western Australia. Earlier research discovered surprisingly high levels of pesticide levels in human breast milk. The research conducted hopes to show that the levels had decreased as a result of stricter government regulations on the use of pesticides on food crops. They did find decreases for several types of pesticides. Levels of the pesticide Dieldrin, however, had substantially increased.
For 45 breast milk donors, we have information on the mother's age in years, whether they lived in a new suburb (New, Old), whether their house had been treated for termites within the past three years (HT = house treated, NT = not treated), and whether their breast milk contained above average levels(> .009 ppm) of the pesticide Dieldrin (High, Low). Note that by law new houses are treated for termites in Australia.
The variables in the Pestmilk.JMPdata file are:
•Age – Age of Mother (yrs)
•New Sub - new suburb indicator (New, Old)
•Treated - house treated for termites in the last 3 years (HT, NT)
•High Dieldrin - Dieldrin level (High, Low)
a)Conduct an appropriate test to compare the proportion of women with high Dieldrin levels in those women living in a new suburb vs. an older suburb. Summarize your findings. (4 pts.)
b)Conduct an appropriate test to compare the proportion of women with high Dieldrin levels in those women living in a home treated for termites with Dieldrin vs. those living in an untreated home. Summarize your findings. (5 pts.)
c)Find estimates and CI’s for the ARR, NNH, and RR for high Dieldrin levels associated with living in a home treated for termites. Interpret each and discuss.
(8 pts.)
d)As stated above, by law new homes in Australia must be treated for termites. Let’s assume that 60% of women in Australia live homes treated for termites. What percent of high Dieldrin levels in breast milk of mothers is attributable to the treatment of homes for termites? Provide an estimate & 95% CI and interpret.
(4 pts.)