TAKEHOME FINAL due on or before Thu 12-22 by 5:30 P.M.
(Return to Prof. Sawyer or
to math receptionist in Cupples I Room 100.)
NOTE: There should be NO COLLABORATION on the takehome final,
other than for the mechanics of using the computer.
Open textbook and notes (including course handouts).
In general where the results of a statistical test are asked for,
Problem 1. Walloopia is a small, apocryphal country that is famous for its pure water and mild climate. A total of 1391 Walloopians died during the previous year, amounting to a crude death rate of 1.77 per thousand. The elders of the country feel that this death rate is too high given the relatively young Walloopian population and are concerned about what this says about the Walloopian health infrastructure.
Table 1. Census Data for Walloopia
Age U.S. Walloopian
Range death rate census
0 to 15 0.0016 212000
15 to 30 0.0011 188000
30 to 45 0.0013 162000
45 to 60 0.0029 143000
60 to 75 0.0057 83000
----------------------------------------
Total: 0.0032 788,000
The crude death rate in the climatically matched U.S. population was
0.0032, or 3.2 per thousand, which was nearly twice the Walloopian crude
death rate of 1391/788000=0.00177.
Problem 2. Disease remission times for 40 patients, some of whom were treated and some of whom were not treated, are given in Table 2. A trailing + in Table 2 means a right-censored value. (For example, if a patient withdrew from the study at that time or died due to unrelated causes.)
Table 2. Remission times for two groups.
Control Group (not treated)
14 43 45 52 67 83 111 145 169 175 196 225 103+
108+ 113+ 158+ 164+
Treated Group
20 24 25 25 30 31 41 42 42 45 45 68 70 75 75
91 107 131 9+ 50+ 62+ 63+ 148+
Problem 3. Survival times in days are given in Table 3 below
for patients who had been diagnosed with a particular disease and had
either been given a particular treatment (Treat=1) or no treatment
(Treat=0). Measurements for morphness (Morph), spatility
(Spat), and hypochronicity (Hypo) were also
recorded at the time of diagnosis and are given in Table 3.
Table 3: Survival times in days in terms of treatment status,
morphness, and two other variables.
(Status: 1 if censored, 0 if observed.)
(Treatment: Treat=1 if treated, Treat=0 if not treated.)
Subj Time Status Treat Morph Spat Hypo
1. 35 0 1 496 62 279
2. 60 0 1 838 24 179
3. 96 0 1 740 72 252
4. 114 0 1 511 106 165
5. 165 0 1 982 112 160
6. 173 0 1 607 127 257
7. 178 0 1 1021 115 226
8. 182 0 0 745 21 239
9. 185 0 1 531 76 148
10. 220 0 0 569 47 192
11. 240 0 1 368 93 117
12. 254 0 0 1013 54 145
13. 262 0 1 588 63 210
14. 275 0 0 881 52 144
15. 314 0 0 902 86 236
16. 339 0 1 842 56 201
17. 385 0 1 947 28 51
18. 394 0 0 994 85 221
19. 425 0 0 822 77 194
20. 474 0 1 926 23 104
21. 484 0 1 1238 31 181
22. 595 0 0 1469 48 169
23. 605 0 1 1239 67 146
24. 638 0 1 1321 40 226
25. 732 0 0 1025 89 220
26. 782 0 1 1168 99 155
27. 884 0 0 650 99 114
28. 38 1 0 1171 49 235
29. 75 1 0 436 74 176
30. 165 1 1 543 100 141
31. 179 1 0 522 68 179
32. 219 1 1 893 103 90
33. 321 1 0 906 112 269
34. 493 1 0 1197 48 182
35. 539 1 1 1011 75 173
Problem 4.. Samples of two groups were followed over 17 years. The numbers of deaths and censoring events (that is, individuals who were last seen at that time) over the 17 years are recorded in Table 4. All individuals in Groups O and X are accounted for in Table 4, so that the last 8 individuals in the combined dataset were recorded as censored in Year 17.
Table 4: Survival times in years for two groups.
Group O Group X
Year deaths censored deaths censored
1 21 0 114 0
2 8 2 57 10
3 7 2 38 6
4 6 2 43 6
5 7 2 34 6
6 6 7 31 27
7 5 8 21 33
8 3 8 19 26
9 4 6 13 17
10 3 7 11 16
11 1 6 11 11
12 1 6 9 13
13 1 5 5 8
14 1 2 2 7
15 1 2 2 6
16 1 3 0 0
17 0 0 0 8
ltangina.sas on the Math434 Web site
for clues about how to read tabled data of this form into a useful SAS
dataset. If num is the name of your variable for the counts
in Table 4, DON'T FORGET to include freq num in SAS
procedures that need to know that your data set is describing groups of
individuals and not individual records. See Section 12.1 in the text
for a discussion of tie-correction methods. (See also
phresid.sas on the Math434 web site.) )
ph2samp.sas and in other example SAS datasets on the Math434
Web site.)
Problem 5.. Forty (40) subjects were recruited for a study of the effectiveness of a particular treatment. Remission times for the subjects were recorded over a period of 90 days with all surviving subjects recorded as censored on day 91. It is known that remission is also strongly affected by a variable called X that can vary over time.
Table 5. Remission times in terms of Sex, Treatment status, and
values of X initially (X0), at 30 days (X30), and at 60 days (X60).
(Status: 1 if censored, 0 if observed.)
(Treatment status: Treat=1 if treated, Treat=0 if not treated.)
Subj Time/Status Sex Treat X0 X30 X60
1. 1 0 1 0 41 33 12
2. 2 0 1 0 42 37 30
3. 4 0 0 1 10 44 42
4. 5 0 1 0 24 29 19
5. 10 0 1 1 17 37 36
6. 24 0 0 0 33 31 7
7. 26 0 1 0 26 18 32
8. 29 0 1 1 28 32 9
9. 31 0 1 1 13 42 7
10. 32 0 1 1 8 40 20
11. 32 0 1 0 22 35 36
12. 36 0 1 0 14 11 45
13. 38 0 1 0 40 38 32
14. 44 0 0 0 31 20 44
15. 50 0 1 0 21 40 29
16. 54 0 0 1 33 43 28
17. 59 0 1 1 11 43 39
18. 61 0 1 1 15 31 45
19. 66 0 1 0 10 35 23
20. 67 0 0 0 6 6 40
21. 67 0 0 0 21 24 34
22. 68 0 1 1 7 25 45
23. 68 0 0 1 19 32 42
24. 69 0 0 1 21 23 40
25. 70 0 0 0 5 26 8
26. 74 0 0 1 37 29 20
27. 91 1 1 0 9 16 11
28. 91 1 0 1 10 33 27
29. 91 1 0 1 11 21 32
30. 91 1 0 0 25 25 20
31. 91 1 0 1 27 21 18
32. 91 1 0 0 38 7 12
33. 91 1 1 1 43 16 42
34. 91 1 0 1 44 24 35
35. 91 1 0 1 44 42 6
ph2samp.sas and phresid.sas on the Math434 Web
site for remarks about modeling time-dependent variables.)