Assigment A (deadline: 04/08/2021)
Question 1
At Miracle Cure hospital a pioneering new surgery was tested to replace human lungs with synthetic
implants. Operations were carried out throughout June 2010. Patients who underwent the surgery
were monitored daily until the end of August 2010, or until they died or left hospital if sooner. The
results are shown below. Where no date is given, the patient was alive and still in hospital at the end of
August.
Patient
A
B
C
D
E
F
G
H
I
J
K
L
M
N
(i)
(ii)
(iii)
(iv)
Date of surgery
June 1
June 3
June 5
June 8
June 9
June 12
June 16
June 17
June 22
June 24
June 25
June 26
June 29
June 30
Date of leaving observation
June 3
July 2
Reason for leaving observation
Died
Left Hospital
July 11
Died
June 21
Aug 12
Died
Left Hospital
June 29
Aug 20
Died
Died
Aug 6
Left Hospital
Explain whether each of the following types of censoring is present and for those present
explain where they occur:
 Right censoring
 Left censoring
 Informative censoring
(3 marks)
Calculate the Kaplan-Meier estimate of the survival function for these patients, stating all
assumptions that you make.
(6 marks)
Sketch, on a suitably labelled graph, the Kaplan-Meier estimate of the survival function.
(2 marks)
Estimate the probability that a patient will die within four weeks of surgery.
(1 mark)
Question 2
A study of the mortality of a certain species of insect reveals that for the first 30 days of life, the insects
are subject to a constant force of mortality of 0.05. After 30 days, the force of mortality increases
according to the formula:
𝜇30+𝑥 = 0.05𝑒 0.01𝑥
Where x is the number of days after day 30.
(i)
(ii)
(iii)
Calculate the probability that a newly born insect will survive for at least 10 days. (1 mark)
Calculate the probability that an insect aged 10 days will survive for at least a further 30
days.
(3 marks)
Calculate the age in days by which 90 per cent of insects are expected to have died.
(4 marks)