Consider the survival time of the 30 melanoma patients in Table 3.1.

(a) Compute and plot the PL estimates of the survivorship functions S(t) of the two treatment groups and check your results with Table 3.2 and Figure 3.1.

(b) Compute the variance of S(t) for every uncensored observation.

(c) Estimate the median survival times of the two groups.

Table 3.1. Data for 30 Resected Melanoma Patients

Patient	Age	Gender	Initial Stage	Treatment Received	Remission Duration	Survival Time
1	59	2	3B	1	33.7+	33.7+
2	50	2	3B	1	3.8	3.9
3	76	1	3B	1	6.3	10.5
4	66	2	3B	1	2.3	5.4
5	33	1	3B	1	6.4	19.5
6	23	2	3B	1	23.8+	23.8+
7	40	2	3B	1	1.8	7.9
8	34	1	3B	1	5.5	16.9+
9	34	1	3B	1	16.6+	16.6+
10	38	2	2	1	33.7+	33.7+
11	54	2	2	1	17.1+	17.1+
12	49	1	3B	2	4.3	8.0
13	35	1	3B	2	26.9+	26.9+
14	22	1	3B	2	21.4+	21.4+
15	30	1	3B	2	18.1+	18.1+
16	26	2	3B	2	5.8	16.0+
17	27	1	3B	2	3.0	6.9
18	45	2	3B	2	11.0+	11.0+
19	76	2	3A	2	22.1	24.8+
20	48	1	3A	2	23.0+	23.0+
21	91	1	4A	2	6.8	8.3
22	82	2	4A	2	10.8+	10.8+
23	50	2	4A	2	2.8	12.2+
24	40	1	4A	2	9.2	12.5+
25	34	1	3A	2	15.9	24.4
26	38	1	4A	2	4.5	7.7
27	50	1	2	2	9.2	14.8+
28	53	2	2	2	8.2+	8.2+
29	48	2	2	2	8.2+	8.2+
30	40	2	2	2	7.8+	7.8+

Source: Data courtesy of Richard Ishmael.

Gender: 1, male; 2, female.

Treatment: 1, BCG; 2, C. parvum.

Time Unit: Remission and survival times are in months.

5.1. For the survival times given in Table 3.1, compare the survival distributions of the two treatment groups using:

(a) Gehan’s generalized Wilcoxon test

(b) The Cox—Mantel test

5.2. For the remission data given in Table 3.1, compare the remission time distributions of the two treatment groups using:

(a) The logrank test

(b) Peto and Peto’s generalized Wilcoxon test