Question

-Event time T follows an exponential distribution with a mean of 40
-Censoring time Tc follows an exponential distribution with a mean of 25
-Generate 500 observations, with censoring flag indicating whether censoring happened before events

Question: What do you think the percent of censoring should be? Show your calculation or reasoning.

Answer 1

I have used R to create the actual random sample and censored random sample, and then I flagged them in excel.

Let us start with the data.

We have to use the data snippet as it is exceeding the character limits.

Actual data	Censoring events	Flag (1 = censored)
11.49726987	76.9530783	0
108.0359437	16.75622817	1
87.30937175	10.53936965	1
28.37716795	52.51840041	0
50.44413026	13.69920358	1
39.1176727	78.27119046	0
53.74690909	5.32343887	1
6.175411977	57.61599983	0
10.45824168	9.579730277	1
30.60202226	13.96628568	1
191.8416877	3.719486971	1
23.68727703	7.696135622	1
44.21200581	25.37628167	1
107.1747418	72.07776978	1
1.974580679	12.66587234	0
84.32676456	89.42452943	0
31.8948435	98.25278729	0
39.20494169	0.89817956	1
36.75132677	38.480403	0
55.89845888	36.14671673	1

hence, the percentage of censoring will be 300/500 = 0.6Here we can see that 299 are censored observations, That means, in 299 cases, the censoring has occurred before the events actually happened.

60% of data will be censored if we use the distribution of censoring which is given in the question.

Now, for the R code for reference, I am giving the r code here

T = rexp(500,1/40)
T.c = rexp(500,1/25)
Data = cbind(T,T.c)
C = T - T.c
data = cbind(T,T.c,C)
data