Question 4

Suppose that a survival dataset contains data on n individuals, where n is divisible by 3. Suppose that (a) one third of the individuals are observed only up until time 0.4, while (b) the other two thirds are observed forever. So, for the individuals in case (a), we observe their complete lifetime if they die before time 0.4, otherwise they are rightcensored at 0.4. For individuals in case (b), we observe their complete lifetime. Let Ti be the complete lifetime for individual i, and let CI? = 7n,in(fl}a Ki) be the censored lifetime, where Ki = GA for i=1, n/3 and Ki = 00 for i=n/3+1, n. Consider two naive estimators of 5(1): 0 The proportion of the n individuals whose value of T: is greater than or equal to 1. (This means we are treating censored lifetimes as if they were complete lifetimes.) 0 The proportion of the individuals not subject to censoring (i.e. those individuals with T: