STAT 426 – Categorical Data Analysis Homework 3 2022
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STAT 426 – Categorical Data Analysis
Homework 3
2022
Please submit your HW in output file of R Markdown. Your output file should include all the R codes.
1. The relationship between coffee drinking and myocardial infarction was studied in young women, aged 30-49. This retrospective study included 487 cases hospitalized for the occur- rence of a myocardial infarction (MI). Nine hundred eighty controls hospitalized for some other acute condition were selected as controls. Data for consumption of five or more cups of coffee, stratified by smoking status were:
Nonsmokers
Cups per day |
MI |
Controls |
≥ 5 |
14 |
49 |
< 5 |
75 |
381 |
Smokers
Cups per day |
MI |
Controls |
≥ 5 |
138 |
134 |
< 5 |
260 |
416 |
(i) Compute both conditional odds ratios as well as the marginal odds ratio.
(ii) Do you think that stratification on smoking status was important in this study? Explain. (iii) Explain why the relative risk cannot be directly estimated.
2. Fifty-two males between ages of 11 and 30 were operated on for knee injuries using arthro- scopic surgery. The patients were classified by the type of injury: twisted knee, direct blow, or both. The results of the surgery were classified as either excellent (E), good (G) and fair or poor (F-P).
|
E |
G |
F-P |
Twisted |
21 |
11 |
4 |
Both |
3 |
2 |
2 |
Direct |
7 |
1 |
1 |
(i) Estimate π 1,2 .
(ii) Estimate π 1l3, the chance of an excellent outcome given a direct blow, and π 1l1 the chance of an excellent outcome given a twisted knee.
3. Consider a collapsed version of the data.
|
E or G |
F-P |
Twisted |
32 |
4 |
Direct or Both |
13 |
3 |
(i) Using the 2-by-2 table, compute the sample odds-ratio for an excellent or good outcome when the knee is only twisted compared to when it suffered a direct blow or both.
(ii) Using the 2-by-2 table, compute the relative risk of a fair or poor outcome when the knee is only twisted compared to when it suffered a direct blow or both.
4. The data in the table below are on graduate admissions by sex at the University of California, Berkeley, and are given in Bickel (1972).
|
Admitted |
Rejected |
Male |
1198 |
1493 |
Female |
567 |
1278 |
(i) Evaluate the odds ratio for being admitted for males compared with females. (ii) Do the results conclusively indicate unfairness? Why or why not?
(iii) What are some potentially useful stratification variables to condition on, and how might conditional odds-ratios be used to further investigate possible unfairness? (we will revisit this dataset later in the course to further study this question)
5. A study was done to evaluate the diagnostic value of dyspnea (being out of breath) following exertion for congestive heart failure (CHF). The results are tabulated below.
|
MI |
Controls |
Dyspnea |
41 |
183 |
no Dyspnea |
0 |
35 |
(i) Estimate the sensitivity
(ii) Estimate the specificity
of Dyspnea as a test for CHF.
of Dyspnea as a test for CHF.
2022-02-10