Question
Consider the melanoma data (melanoma.csv, melanoma.txt). This data is properly analyzed with what is called a proportional hazards model, but let's use the tools we
Consider the melanoma data (melanoma.csv, melanoma.txt). This data is properly analyzed with what is called a proportional hazards model, but let's use the tools we have: ignore the 'time' variable and assume that the 'status' variable simply reflects the status of the individual at a follow-up time, whenever that was. Let's say we are interested in the relationship between features of a malignant melanoma (its size, operationalized as its thickness, and whether an ulcer was present or not) and whether or not the patient was alive at the time of follow-up. 1. What type of regression model is most appropriate for this question, and why? 2. Do you need to do any data management in order to fit your model? If so, what do you choose to do, and why? 3. What predictor variables will you use in your model? Why did you choose these variables? 4. Estimate your model, present the results in a table, and interpret the results in words (a paragraph or so).
time | status | sex | age | year | thickness | ulcer | |
1 | 10 | 3 | 1 | 76 | 1972 | 6.76 | 1 |
2 | 30 | 3 | 1 | 56 | 1968 | 0.65 | 0 |
3 | 35 | 2 | 1 | 41 | 1977 | 1.34 | 0 |
4 | 99 | 3 | 0 | 71 | 1968 | 2.9 | 0 |
5 | 185 | 1 | 1 | 52 | 1965 | 12.08 | 1 |
6 | 204 | 1 | 1 | 28 | 1971 | 4.84 | 1 |
7 | 210 | 1 | 1 | 77 | 1972 | 5.16 | 1 |
8 | 232 | 3 | 0 | 60 | 1974 | 3.22 | 1 |
9 | 232 | 1 | 1 | 49 | 1968 | 12.88 | 1 |
10 | 279 | 1 | 0 | 68 | 1971 | 7.41 | 1 |
11 | 295 | 1 | 0 | 53 | 1969 | 4.19 | 1 |
12 | 355 | 3 | 0 | 64 | 1972 | 0.16 | 1 |
13 | 386 | 1 | 0 | 68 | 1965 | 3.87 | 1 |
14 | 426 | 1 | 1 | 63 | 1970 | 4.84 | 1 |
15 | 469 | 1 | 0 | 14 | 1969 | 2.42 | 1 |
16 | 493 | 3 | 1 | 72 | 1971 | 12.56 | 1 |
17 | 529 | 1 | 1 | 46 | 1971 | 5.8 | 1 |
18 | 621 | 1 | 1 | 72 | 1972 | 7.06 | 1 |
19 | 629 | 1 | 1 | 95 | 1968 | 5.48 | 1 |
20 | 659 | 1 | 1 | 54 | 1972 | 7.73 | 1 |
21 | 667 | 1 | 0 | 89 | 1968 | 13.85 | 1 |
22 | 718 | 1 | 1 | 25 | 1967 | 2.34 | 1 |
23 | 752 | 1 | 1 | 37 | 1973 | 4.19 | 1 |
24 | 779 | 1 | 1 | 43 | 1967 | 4.04 | 1 |
25 | 793 | 1 | 1 | 68 | 1970 | 4.84 | 1 |
26 | 817 | 1 | 0 | 67 | 1966 | 0.32 | 0 |
27 | 826 | 3 | 0 | 86 | 1965 | 8.54 | 1 |
28 | 833 | 1 | 0 | 56 | 1971 | 2.58 | 1 |
29 | 858 | 1 | 0 | 16 | 1967 | 3.56 | 0 |
30 | 869 | 1 | 0 | 42 | 1965 | 3.54 | 0 |
31 | 872 | 1 | 0 | 65 | 1968 | 0.97 | 0 |
32 | 967 | 1 | 1 | 52 | 1970 | 4.83 | 1 |
33 | 977 | 1 | 1 | 58 | 1967 | 1.62 | 1 |
34 | 982 | 1 | 0 | 60 | 1970 | 6.44 | 1 |
35 | 1041 | 1 | 1 | 68 | 1967 | 14.66 | 0 |
36 | 1055 | 1 | 0 | 75 | 1967 | 2.58 | 1 |
37 | 1062 | 1 | 1 | 19 | 1966 | 3.87 | 1 |
38 | 1075 | 1 | 1 | 66 | 1971 | 3.54 | 1 |
39 | 1156 | 1 | 0 | 56 | 1970 | 1.34 | 1 |
40 | 1228 | 1 | 1 | 46 | 1973 | 2.24 | 1 |
41 | 1252 | 1 | 0 | 58 | 1971 | 3.87 | 1 |
42 | 1271 | 1 | 0 | 74 | 1971 | 3.54 | 1 |
43 | 1312 | 1 | 0 | 65 | 1970 | 17.42 | 1 |
44 | 1427 | 3 | 1 | 64 | 1972 | 1.29 | 0 |
45 | 1435 | 1 | 1 | 27 | 1969 | 3.22 | 0 |
46 | 1499 | 2 | 1 | 73 | 1973 | 1.29 | 0 |
47 | 1506 | 1 | 1 | 56 | 1970 | 4.51 | 1 |
48 | 1508 | 2 | 1 | 63 | 1973 | 8.38 | 1 |
49 | 1510 | 2 | 0 | 69 | 1973 | 1.94 | 0 |
50 | 1512 | 2 | 0 | 77 | 1973 | 0.16 | 0 |
51 | 1516 | 1 | 1 | 80 | 1968 | 2.58 | 1 |
52 | 1525 | 3 | 0 | 76 | 1970 | 1.29 | 1 |
53 | 1542 | 2 | 0 | 65 | 1973 | 0.16 | 0 |
54 | 1548 | 1 | 0 | 61 | 1972 | 1.62 | 0 |
55 | 1557 | 2 | 0 | 26 | 1973 | 1.29 | 0 |
56 | 1560 | 1 | 0 | 57 | 1973 | 2.1 | 0 |
57 | 1563 | 2 | 0 | 45 | 1973 | 0.32 | 0 |
58 | 1584 | 1 | 1 | 31 | 1970 | 0.81 | 0 |
59 | 1605 | 2 | 0 | 36 | 1973 | 1.13 | 0 |
60 | 1621 | 1 | 0 | 46 | 1972 | 5.16 | 1 |
61 | 1627 | 2 | 0 | 43 | 1973 | 1.62 | 0 |
62 | 1634 | 2 | 0 | 68 | 1973 | 1.37 | 0 |
63 | 1641 | 2 | 1 | 57 | 1973 | 0.24 | 0 |
64 | 1641 | 2 | 0 | 57 | 1973 | 0.81 | 0 |
65 | 1648 | 2 | 0 | 55 | 1973 | 1.29 | 0 |
66 | 1652 | 2 | 0 | 58 | 1973 | 1.29 | 0 |
67 | 1654 | 2 | 1 | 20 | 1973 | 0.97 | 0 |
68 | 1654 | 2 | 0 | 67 | 1973 | 1.13 | 0 |
69 | 1667 | 1 | 0 | 44 | 1971 | 5.8 | 1 |
70 | 1678 | 2 | 0 | 59 | 1973 | 1.29 | 0 |
71 | 1685 | 2 | 0 | 32 | 1973 | 0.48 | 0 |
72 | 1690 | 1 | 1 | 83 | 1971 | 1.62 | 0 |
73 | 1710 | 2 | 0 | 55 | 1973 | 2.26 | 0 |
74 | 1710 | 2 | 1 | 15 | 1973 | 0.58 | 0 |
75 | 1726 | 1 | 0 | 58 | 1970 | 0.97 | 1 |
76 | 1745 | 2 | 0 | 47 | 1973 | 2.58 | 1 |
77 | 1762 | 2 | 0 | 54 | 1973 | 0.81 | 0 |
78 | 1779 | 2 | 1 | 55 | 1973 | 3.54 | 1 |
79 | 1787 | 2 | 1 | 38 | 1973 | 0.97 | 0 |
80 | 1787 | 2 | 0 | 41 | 1973 | 1.78 | 1 |
81 | 1793 | 2 | 0 | 56 | 1973 | 1.94 | 0 |
82 | 1804 | 2 | 0 | 48 | 1973 | 1.29 | 0 |
83 | 1812 | 2 | 1 | 44 | 1973 | 3.22 | 1 |
84 | 1836 | 2 | 0 | 70 | 1972 | 1.53 | 0 |
85 | 1839 | 2 | 0 | 40 | 1972 | 1.29 | 0 |
86 | 1839 | 2 | 1 | 53 | 1972 | 1.62 | 1 |
87 | 1854 | 2 | 0 | 65 | 1972 | 1.62 | 1 |
88 | 1856 | 2 | 1 | 54 | 1972 | 0.32 | 0 |
89 | 1860 | 3 | 1 | 71 | 1969 | 4.84 | 1 |
90 | 1864 | 2 | 0 | 49 | 1972 | 1.29 | 0 |
91 | 1899 | 2 | 0 | 55 | 1972 | 0.97 | 0 |
92 | 1914 | 2 | 0 | 69 | 1972 | 3.06 | 0 |
93 | 1919 | 2 | 1 | 83 | 1972 | 3.54 | 0 |
94 | 1920 | 2 | 1 | 60 | 1972 | 1.62 | 1 |
95 | 1927 | 2 | 1 | 40 | 1972 | 2.58 | 1 |
96 | 1933 | 1 | 0 | 77 | 1972 | 1.94 | 0 |
97 | 1942 | 2 | 0 | 35 | 1972 | 0.81 | 0 |
98 | 1955 | 2 | 0 | 46 | 1972 | 7.73 | 1 |
99 | 1956 | 2 | 0 | 34 | 1972 | 0.97 | 0 |
100 | 1958 | 2 | 0 | 69 | 1972 | 12.88 | 0 |
101 | 1963 | 2 | 0 | 60 | 1972 | 2.58 | 0 |
102 | 1970 | 2 | 1 | 84 | 1972 | 4.09 | 1 |
103 | 2005 | 2 | 0 | 66 | 1972 | 0.64 | 0 |
104 | 2007 | 2 | 1 | 56 | 1972 | 0.97 | 0 |
105 | 2011 | 2 | 0 | 75 | 1972 | 3.22 | 1 |
106 | 2024 | 2 | 0 | 36 | 1972 | 1.62 | 0 |
107 | 2028 | 2 | 1 | 52 | 1972 | 3.87 | 1 |
108 | 2038 | 2 | 0 | 58 | 1972 | 0.32 | 1 |
109 | 2056 | 2 | 0 | 39 | 1972 | 0.32 | 0 |
110 | 2059 | 2 | 1 | 68 | 1972 | 3.22 | 1 |
111 | 2061 | 1 | 1 | 71 | 1968 | 2.26 | 0 |
112 | 2062 | 1 | 0 | 52 | 1965 | 3.06 | 0 |
113 | 2075 | 2 | 1 | 55 | 1972 | 2.58 | 1 |
114 | 2085 | 3 | 0 | 66 | 1970 | 0.65 | 0 |
115 | 2102 | 2 | 1 | 35 | 1972 | 1.13 | 0 |
116 | 2103 | 1 | 1 | 44 | 1966 | 0.81 | 0 |
117 | 2104 | 2 | 0 | 72 | 1972 | 0.97 | 0 |
118 | 2108 | 1 | 0 | 58 | 1969 | 1.76 | 1 |
119 | 2112 | 2 | 0 | 54 | 1972 | 1.94 | 1 |
120 | 2150 | 2 | 0 | 33 | 1972 | 0.65 | 0 |
121 | 2156 | 2 | 0 | 45 | 1972 | 0.97 | 0 |
122 | 2165 | 2 | 1 | 62 | 1972 | 5.64 | 0 |
123 | 2209 | 2 | 0 | 72 | 1971 | 9.66 | 0 |
124 | 2227 | 2 | 0 | 51 | 1971 | 0.1 | 0 |
125 | 2227 | 2 | 1 | 77 | 1971 | 5.48 | 1 |
126 | 2256 | 1 | 0 | 43 | 1971 | 2.26 | 1 |
127 | 2264 | 2 | 0 | 65 | 1971 | 4.83 | 1 |
128 | 2339 | 2 | 0 | 63 | 1971 | 0.97 | 0 |
129 | 2361 | 2 | 1 | 60 | 1971 | 0.97 | 0 |
130 | 2387 | 2 | 0 | 50 | 1971 | 5.16 | 1 |
131 | 2388 | 1 | 1 | 40 | 1966 | 0.81 | 0 |
132 | 2403 | 2 | 0 | 67 | 1971 | 2.9 | 1 |
133 | 2426 | 2 | 0 | 69 | 1971 | 3.87 | 0 |
134 | 2426 | 2 | 0 | 74 | 1971 | 1.94 | 1 |
135 | 2431 | 2 | 0 | 49 | 1971 | 0.16 | 0 |
136 | 2460 | 2 | 0 | 47 | 1971 | 0.64 | 0 |
137 | 2467 | 1 | 0 | 42 | 1965 | 2.26 | 1 |
138 | 2492 | 2 | 0 | 54 | 1971 | 1.45 | 0 |
139 | 2493 | 2 | 1 | 72 | 1971 | 4.82 | 1 |
140 | 2521 | 2 | 0 | 45 | 1971 | 1.29 | 1 |
141 | 2542 | 2 | 1 | 67 | 1971 | 7.89 | 1 |
142 | 2559 | 2 | 0 | 48 | 1970 | 0.81 | 1 |
143 | 2565 | 1 | 1 | 34 | 1970 | 3.54 | 1 |
144 | 2570 | 2 | 0 | 44 | 1970 | 1.29 | 0 |
145 | 2660 | 2 | 0 | 31 | 1970 | 0.64 | 0 |
146 | 2666 | 2 | 0 | 42 | 1970 | 3.22 | 1 |
147 | 2676 | 2 | 0 | 24 | 1970 | 1.45 | 1 |
148 | 2738 | 2 | 0 | 58 | 1970 | 0.48 | 0 |
149 | 2782 | 1 | 1 | 78 | 1969 | 1.94 | 0 |
150 | 2787 | 2 | 1 | 62 | 1970 | 0.16 | 0 |
151 | 2984 | 2 | 1 | 70 | 1969 | 0.16 | 0 |
152 | 3032 | 2 | 0 | 35 | 1969 | 1.29 | 0 |
153 | 3040 | 2 | 0 | 61 | 1969 | 1.94 | 0 |
154 | 3042 | 1 | 0 | 54 | 1967 | 3.54 | 1 |
155 | 3067 | 2 | 0 | 29 | 1969 | 0.81 | 0 |
156 | 3079 | 2 | 1 | 64 | 1969 | 0.65 | 0 |
157 | 3101 | 2 | 1 | 47 | 1969 | 7.09 | 0 |
158 | 3144 | 2 | 1 | 62 | 1969 | 0.16 | 0 |
159 | 3152 | 2 | 0 | 32 | 1969 | 1.62 | 0 |
160 | 3154 | 3 | 1 | 49 | 1969 | 1.62 | 0 |
161 | 3180 | 2 | 0 | 25 | 1969 | 1.29 | 0 |
162 | 3182 | 3 | 1 | 49 | 1966 | 6.12 | 0 |
163 | 3185 | 2 | 0 | 64 | 1969 | 0.48 | 0 |
164 | 3199 | 2 | 0 | 36 | 1969 | 0.64 | 0 |
165 | 3228 | 2 | 0 | 58 | 1969 | 3.22 | 1 |
166 | 3229 | 2 | 0 | 37 | 1969 | 1.94 | 0 |
167 | 3278 | 2 | 1 | 54 | 1969 | 2.58 | 0 |
168 | 3297 | 2 | 0 | 61 | 1968 | 2.58 | 1 |
169 | 3328 | 2 | 1 | 31 | 1968 | 0.81 | 0 |
170 | 3330 | 2 | 1 | 61 | 1968 | 0.81 | 1 |
171 | 3338 | 1 | 0 | 60 | 1967 | 3.22 | 1 |
172 | 3383 | 2 | 0 | 43 | 1968 | 0.32 | 0 |
173 | 3384 | 2 | 0 | 68 | 1968 | 3.22 | 1 |
174 | 3385 | 2 | 0 | 4 | 1968 | 2.74 | 0 |
175 | 3388 | 2 | 1 | 60 | 1968 | 4.84 | 1 |
176 | 3402 | 2 | 1 | 50 | 1968 | 1.62 | 0 |
177 | 3441 | 2 | 0 | 20 | 1968 | 0.65 | 0 |
178 | 3458 | 3 | 0 | 54 | 1967 | 1.45 | 0 |
179 | 3459 | 2 | 0 | 29 | 1968 | 0.65 | 0 |
180 | 3459 | 2 | 1 | 56 | 1968 | 1.29 | 1 |
181 | 3476 | 2 | 0 | 60 | 1968 | 1.62 | 0 |
182 | 3523 | 2 | 0 | 46 | 1968 | 3.54 | 0 |
183 | 3667 | 2 | 0 | 42 | 1967 | 3.22 | 0 |
184 | 3695 | 2 | 0 | 34 | 1967 | 0.65 | 0 |
185 | 3695 | 2 | 0 | 56 | 1967 | 1.03 | 0 |
186 | 3776 | 2 | 1 | 12 | 1967 | 7.09 | 1 |
187 | 3776 | 2 | 0 | 21 | 1967 | 1.29 | 1 |
188 | 3830 | 2 | 1 | 46 | 1967 | 0.65 | 0 |
189 | 3856 | 2 | 0 | 49 | 1967 | 1.78 | 0 |
190 | 3872 | 2 | 0 | 35 | 1967 | 12.24 | 1 |
191 | 3909 | 2 | 1 | 42 | 1967 | 8.06 | 1 |
192 | 3968 | 2 | 0 | 47 | 1967 | 0.81 | 0 |
193 | 4001 | 2 | 0 | 69 | 1967 | 2.1 | 0 |
194 | 4103 | 2 | 0 | 52 | 1966 | 3.87 | 0 |
195 | 4119 | 2 | 1 | 52 | 1966 | 0.65 | 0 |
196 | 4124 | 2 | 0 | 30 | 1966 | 1.94 | 1 |
197 | 4207 | 2 | 1 | 22 | 1966 | 0.65 | 0 |
198 | 4310 | 2 | 1 | 55 | 1966 | 2.1 | 0 |
199 | 4390 | 2 | 0 | 26 | 1965 | 1.94 | 1 |
200 | 4479 | 2 | 0 | 19 | 1965 | 1.13 | 1 |
201 | 4492 | 2 | 1 | 29 | 1965 | 7.06 | 1 |
202 | 4668 | 2 | 0 | 40 | 1965 | 6.12 | 0 |
203 | 4688 | 2 | 0 | 42 | 1965 | 0.48 | 0 |
204 | 4926 | 2 | 0 | 50 | 1964 | 2.26 | 0 |
205 | 5565 | 2 | 0 | 41 | 1962 | 2.9 | 0 |
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