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Survival Analysis - Time to the occurance of a given event
Exposure
(Cancer)
Event
(DEATH)
time
It occurs when we don't even know the exact time-to-event for an included observations.
LEFT INTERVAL RIGHT
We know the time- to - event is LESS THAN some value
We know time-to-event is BETWEEN 2 VALUES
We know that the time-to-event is GREATER THAN some value
ti < x
ti > x
x1 < ti < x2
An epidemiologist wishes to know the age at diagnosis in a follow-up study of diabetic retinopathy. At the time of the examination, a 50 year old participant was found to have already developed retinopathy , but there is no record of the exact time at which initial evidence is found.
Let's denote x=retinopathy
x found on 50 years :
X
50
If the initial records indicate that at age of 45, the patient in the example above did not have retinopathy.
X
45
50
Estimating Survival time after diagnosis of pancreatic cancer (Wahutu, 2016)
1997
2012
X
O
- The people stay alive at the end of study
- People lost to follow up
Type I Censoring
6 months
6 animals
died (uncensored observation)
survive - killed as sacrifice (censored observation)
wait until a fixed portion of animals died (80/100 died for example).
Then, the surviving anias are sacrificed.
- The patients enter the study at diff times during this period.
- some may die beofre the end of the study (exact survival times are known).
- Some may lost / withdraw before the end of the study(Censored Observations).
15 years
1) ti < x = LEFT CENSORING
2) x1 < ti < x2 = INTERVAL CENSORING
3) ti > x = RIGHT CENSORING
Inspired by Madison Beer's song 'Reckless'
1) Madison Beer found out her boyfriend was cheating. But she doesn't know since when did her boyfriend cheating her. What type of Censoring is this?
Answer : Left Censoring
2) Madison Beer know the girl her boyfriend was cheating on before. They've met before this. But during that time, her boyfriend meeting the girl for the first time. So we can say that the duration when her boyfriend starts cheating on her can be from the moment they know till she found out.
Answer : Interval Censoring
3) After breaking up, her boyfriend (now EX BOYFRIEND) is with that girl. She hope her boyfriend was not happy and eventually break up with that girl too. But we're not sure either they will break up or not as she don't know what happened to them after she broke up with him.
Answer : Right Censoring