4.1 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. Estimate the median survival times of the two groups. C. Use the data in Table 3.2 or the SAS file in your notes. Remission Time Uncensor Uncensor Stage-11 Stage-III A Stage-III B Stage-IVA Treatment 0 1 0 1 0 0 o o 1 1 1 33.7 3.8 6.3 1 Oo od 1 o od 1 1 1 1 1 2.3 1 1 0 1 0 1 1 1 Survival Time 33.7 3.9 10.5 5.4 19.5 23.8 7.9 16.9 16.6 33.7 17.1 1 1 0 0 6.4 23.8 1.8 5.5 1 Patient Age Gender 1 59 2 50 3 76 1 4 66 0 5 33 1 6 23 0 7 40 0 8 34 1 9 34 1 10 38 11 54 0 12 49 1 13 35 1 14 22 1 15 30 1 16 26 0 1 1 1 1 0 o o o o o o 1 0 0 16.6 33.7 0 0 0 0 17.1 0 0 1 1 1 1 0 0 1 4.3 26.9 21.4 18.1 5.8 0 0 8.0 26.9 21.4 18.1 16.0 6.9 1 0 7 a 7 7 0 1 1 0 17 27 1 1 1 1 18 45 0 1 O O O O O O O O O O O O O O O O O O O O 0 0 3.0 11.0 22.1 23.0 0 0 1 0 19 20 21 76 48 1 0 0 0 91 O O O O O O O O OPPO O O O O O O 1 0 1 6.8 1 1 0 1 10.8 0 0 22 23 24 82 50 0 1 1 0 2.8 9.2 40 1 0 1 1 11.0 24.8 23.0 8.3 10.8 12.2 12.5 24.4 7.7 14.8 8.2 8.2 7.8 0 1 1 0 15.9 1 1 O O O O O 1 0 1 4.5 1 25 34 26 38 27 50 28 53 1 1 1 0 9.2 1 0 0 8.2 0 0 0 0 0 29 30 48 40 1 1 8.2 7.8 0 0 0 1MA Table 3.2 Kaplan-Meier Product-Limit Estimate of Survival Function S(t) BCG Patients Death time (t) (t) 3.9 0.909 5.4 0.818 7.9 0.727 10.5 0.636 19.5 0.477 C. parvum Patients Death time (t) (t) 6.9 0.947 7.7 0.895 8.0 0.839 4.1 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. Estimate the median survival times of the two groups. C. Use the data in Table 3.2 or the SAS file in your notes. Remission Time Uncensor Uncensor Stage-11 Stage-III A Stage-III B Stage-IVA Treatment 0 1 0 1 0 0 o o 1 1 1 33.7 3.8 6.3 1 Oo od 1 o od 1 1 1 1 1 2.3 1 1 0 1 0 1 1 1 Survival Time 33.7 3.9 10.5 5.4 19.5 23.8 7.9 16.9 16.6 33.7 17.1 1 1 0 0 6.4 23.8 1.8 5.5 1 Patient Age Gender 1 59 2 50 3 76 1 4 66 0 5 33 1 6 23 0 7 40 0 8 34 1 9 34 1 10 38 11 54 0 12 49 1 13 35 1 14 22 1 15 30 1 16 26 0 1 1 1 1 0 o o o o o o 1 0 0 16.6 33.7 0 0 0 0 17.1 0 0 1 1 1 1 0 0 1 4.3 26.9 21.4 18.1 5.8 0 0 8.0 26.9 21.4 18.1 16.0 6.9 1 0 7 a 7 7 0 1 1 0 17 27 1 1 1 1 18 45 0 1 O O O O O O O O O O O O O O O O O O O O 0 0 3.0 11.0 22.1 23.0 0 0 1 0 19 20 21 76 48 1 0 0 0 91 O O O O O O O O OPPO O O O O O O 1 0 1 6.8 1 1 0 1 10.8 0 0 22 23 24 82 50 0 1 1 0 2.8 9.2 40 1 0 1 1 11.0 24.8 23.0 8.3 10.8 12.2 12.5 24.4 7.7 14.8 8.2 8.2 7.8 0 1 1 0 15.9 1 1 O O O O O 1 0 1 4.5 1 25 34 26 38 27 50 28 53 1 1 1 0 9.2 1 0 0 8.2 0 0 0 0 0 29 30 48 40 1 1 8.2 7.8 0 0 0 1MA Table 3.2 Kaplan-Meier Product-Limit Estimate of Survival Function S(t) BCG Patients Death time (t) (t) 3.9 0.909 5.4 0.818 7.9 0.727 10.5 0.636 19.5 0.477 C. parvum Patients Death time (t) (t) 6.9 0.947 7.7 0.895 8.0 0.839