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

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Survival Analysis, Midterm 2022Your 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 timeXisH(x) = 4x2.(a)FindS(x) andh(x).(b)Find the median survival time.2. [20 points] The interest is the distribution of the age of onset of diabetes among the residentsof a town.The following table contains data on 6 randomly selected individuals, including 1) theage at which each individual was surveyed; 2) whether or not the respondent indicated a diagnosis ofdiabetes prior to that age, and 3) the age at which diabetes was diagnosed, if such information wasprovided 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 thisdataset.(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 andinterpretation for the following two statisticalquantities for a continuous failure timeX.The hazard functionh(x).The mean residual life functionmrl(x).1
4.[35 points] The investigator conducted a small study with 7 subjects.The event times wererecorded as follows, where right-censored observations were indicated by a +.0.4; 1.
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total points, Survival analysis