Q&A - Censoring Distributions


QUESTION:

When you ask about the censoring, isn't that just the same thing as what we 
have been doing for survival?

ANSWER:

In the standard survival analysis problem, there are two random variables:

T0 = time until death
C = time until we lose track of the patient

We are generally only interested in T0, but occasionally we want to quantify 
the characteristics of our experiment by describing the amount of follow-up we 
have in our experiment.

In any case, we have the problem that we can only observe the smaller of C and 
T0 for each patient:

T = min(C, T0)

We also usually construct an "indicator of death"

d= (0 if T=C, 1 if T=T0)

Then we can use KM to estimate the distribution of T0.

But if we want to discover the distribution of time to follow-up, we have to 
deal with the problem of estimating when C would have occurred for patients 
whose death was observed. We can do this by creating an "indicator of 
censoring"

X= (0 if T=T0, 1 if T=C)

Then we use KM with T and X, and it tells us when we would have probably lost 
patients to follow-up, had they lived.

This relates to statistical precision with which the scientific question can be 
addressed, as well as the limitations of the study. For instance, if we are 
studying the time to death, but our censoring distribution maxes out at 5 
years, we are only comparing the effects of survival over the first 5 years. 
And even then, we need to consider whether most patients would only have been 
followed for 1 year rather than 5 years, etc.

Scott

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Scott S. Emerson, M.D., Ph.D.            Biost Dept: (O) 206-543-1044
Professor of Biostatistics                           (F) 206-543-3286
Department of Biostatistics  Box 357232         ROC: (O) 206-221-4185
University of Washington                             (F) 206-543-0131
Seattle, Washington 98195                   semerson@u.washington.edu
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