A large number of diseasefree individuals were enrolled in a

A large number of disease-free individuals were enrolled in a study
beginning January 1, 1970, and were followed for 30 years to assess
the age at which they developed breast cancer. Individuals had clinical
exams every 3 years after enrollment. For four selected individuals
described below, discuss in detail, the types of censoring and truncation
that are represented.

(a) A healthy individual, enrolled in the study at age 30, never developed
breast cancer during the study.
(b) A healthy individual, enrolled in the study at age 40, was diagnosed
with breast cancer at the fifth exam after enrollment (i.e., the disease
started sometime between 12 and 15 years after enrollment).
(c) A healthy individual, enrolled in the study at age 50, died from a
cause unrelated to the disease (i.e., not diagnosed with breast cancer
at any time during the study) at age 61.
(d) An individual, enrolled in the study at age 42, moved away from
the community at age 55 and was never diagnosed with breast cancer
during the period of observation.
(e) Confining your attention to the four individuals described above,
write down the likelihood for this portion of the study.

Solution

a)Type 1 censoring,censoring time is 60

since the checkup will go untill age 60

b)Interval censoring:censoring time={52,55}

as the examination will take place until 12 years to 15 years after age 40.

c)Random censoring:censoring time:61

as the patient dies unexpectedly

d)Random censoring:censoring time:55

as the person moves away from cimmunity at 55.so he wont be a part of it anymore.

e)These observations are left truncated at the age 30.40.50 and 42