4. A randomized trial is carried out to compare the hazard for time until infection between treated (Zi = 1) and control (Zi = 0) patients. The following data are observed. 3' l 1 2 3 4 5 6 7 Xi 3 5 6 9 12 15 22 Ag 0 1 1 0 1 D 1 Z; 1 D 1 0 1 D 1 (a) Write out the partial likelihood function, PL(,8). Your nal answer should not have a summation sign or any subscripts. (b) Derive the log partial likelihood function, 06). (c) Derive the score function U(,8). ((1) Based on these data, it is estimated through PL that A(t|Zi = 1) = 1.4 MtlZi : 0) O5 Estimate A0(10). (e) Estimate S(10|Z,; : 1)