Machine learning, Optimization technique, Weibull, Survival, R codes.

Question ti Placebo dii 1 1 1 1 1 1 LO 1 6 6 1 0 1 0 2 3 1 1 1 1 1 4 0 1 6-MP di 6 6 6 6 7 9 10 10 11 13 16 17 19 20 22 23 25 32 0 5 5 8 1 1 0 00 00 00 11 11 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 0 12 12 15 32 17 34 22 1 35 23 1 Gehan (1965) and others have discussed the results of a clinical trial in which the drug 6-mercaptopurin (6-MP) was compared to a placebo with respect to the ability to maintain remission in acute leukemia patients. Table 1 gives the remission times for two groups of 21 patients each, one group given the placebo and the other drug 6-MP. i Consider fitting a Weibull model to the data for each group separately. Find the maximum likelihood estimates of a and B. ii) For each group, find the Weibull estimates of the survival probabilities S(t), and plot the two survival curves on the same graph. Comment on the effectiveness of the drug 6-MP based on the estimated survival curves. Hint: Weibull estimates of the survival probabilities are given by S(t) = exp[-(tl]. # Estimate of sigma2. 52