Homework 5 . Due Oct. 31, 2016 


(1). [part 2(b) of the test problem] Assume no tie, Verify that

               d[\hat F_{KM} (t_k)] = delta_k/[ n - \sum  (1-delta_i)/(1-\hat F_KM(t_i) ]

where the sum is over all t_i points < t_k and delta_i = 0


(2). Given a hazard function h(t) = 0.1 + 2exp(- 0.6t), for t>=0; and zero otherwise. How would you generate random variables
     that have this hazard function?   [PLEASE NOTE THE CHANGE in h(t) DEFINITION]

(3). Generate 60 iid observations from a distribution with hazard function given in (2), also generate 80
     iid observations from an exponential disrtibution with (lambda = 0.5). Perform a two sample test using
     logrank test.

(3.5). Plot the two Kaplan-Meier curves from t=0, to t=5. on the same page. 

(4). Use the "restricted mean test" to perform the same test. Use the restriction time tau=3.  




====================================================================================



? ? ?  


=========================================================================================