midterm 2022 1 .pdf - Survival Analysis Midterm 2022 Your...

Survival Analysis, Midterm 2022
Your Name:
There are 5 questions in this exam. The total points is 100pt.
Please write page number and question number on all answer sheets.
1.[20 points] Assume that the cumulative hazard function for survival time X is H ( x ) = 4 x
2
.
(a) Find S ( x ) and h ( x ).
(b) Find the median survival time.
2. [20 points] The interest is the distribution of the age of onset of diabetes among the residents
of a town. The following table contains data on 6 randomly selected individuals, including 1) the
age at which each individual was surveyed; 2) whether or not the respondent indicated a diagnosis of
diabetes prior to that age, and 3) the age at which diabetes was diagnosed, if such information was
provided by the respondent.
(a) Describe the types of censoring and (or) truncation present in this dataset.
(b) Suppose the event time follows a Weibull distribution, write down the likelihood based on this
dataset.
(c) If you are only able to observe those with a prior diagnosis of diabetes (i.e., patients 2,3,4,6) ,
what would be the censoring and (or) truncation present in the dataset?
3. [10pt] Write down the mathematical definition and interpretation for the following two statistical
quantities for a continuous failure time X .
• The hazard function h ( x ).
• The mean residual life function mrl ( x ).
1

4. [35 points] The investigator conducted a small study with 7 subjects. The event times were
recorded as follows, where right-censored observations were indicated by a +.
0 . 4; 1 .