Survival Analysis
Applications
Engineering
Censoring vs Truncation
Modelling
Censoring
Truncation
Left-right
Astronomy
Medical Studies
Functions
For modelling, it is often assumed that the censoring event is independent of the time
Definition: Some information is known about a part of the data. Ex: It is known that patient survived up to 180 days, but no information known beyond that since 180 is the censoring time
No information is known about a subset of the data
Circumstances
Interval censoring
Malaria example: we know the date between negative and positive, but not a precise date
May lead to problem (biased models), if this is not the case
Right - Left
Right: The real value for the variable of interest could not be observed, this may be due to various factors
Types
Left: the beginning of the variable of interest may have been before the current estimate/value
May not be the case: transplant studies, patient may leave because they need another treatment, patients may leave because they got better, administrative reasons
S(t)
H(t)
h(t)
Hazard of event at point t
1 - F(t) (probability of death, event, whatever the nature is)
Models
Parametric
Non-Parametric
Hazard function
Type I
Type II
Random
the start times and end times are random
All have the same censoring time
Example: Patients followed in a study, 40 patients are followed from beggining to end
All start at the same time, but censoring happens after x failures
Following 40 lightbulbs, finish experiment once 5 of them have failed
Long studies where the entrance gap of time varies widely, and patients leave due to random reasons or at different times