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Censored Data
Posterior Predictive Distributions
Recall that the dataset contains some censored values like Patient 25’s survival time.
All we really know about Patient 25’s survival time is that it is longer than 1,799 days
or, equivalently, that the square root of survival time exceeds 42.415. Even though we
do not know the amount by which this patient’s timesqr exceeds 42.415, we can ask
for its posterior distribution. Taking into account the fact that timesqr exceeds 42.415,
assuming that the model is correct, and taking the patient’s age and acceptyr into
account, what can be said about Patient 25’s survival time? To find out:
E Click the Posterior Predictive button .
or
E From the menus, choose View > Posterior Predictive.
The Posterior Predictive Distributions window shows a table with a row for every
person and a column for every observed variable in the model. Looking in the 25
th
row,
we see Patient 25’s age and acceptyr scores. For Patient 25’s timesqr, all we see is the
symbol
<<, which indicates that the data provide an inequality constraint on the timesqr
score and not an actual numeric value.
To see the posterior distribution of Patient 25’s timesqr:
E Click <<. The posterior distribution appears in the Posterior window.