[R] A model for disease progression

Damon Wischik djw1005 at cam.ac.uk
Tue Jul 29 15:53:51 CEST 2003

Thank you to the various people who have made suggestions. In particular,
reading the documentation of the addreg package has prompted me to try to
put the question differently. I would be grateful for any comments on the

As I described before, I have a snapshot of a population taken at a
certain time. I am interested in an age-related disease, which progresses
healthy->A->B. (There is no recovery.) For each individual, I know their
age (in years) and the stage of the disease. There are roughly 800 cases,
with ages spanning 40 years.

Suppose I don't distinguish between stages A and B, and all I am
interested in is whether someone has the disease or not. For each
individual, I therefore have a censored observation of a "lifetime" 
random variable:
  if the individual is age t and is diseased, lifetime is in (0,t].
  if the individual is age t and is healthy, lifetime is in (t,inf)

I would like to plot a survival function for this "lifetime" random
variable. According to the documentation (for R1.7.0), the Surv function
does not let me enter left-censored intervals for non-parametric plots. 
Are there ways around this? I could simply estimate

  Prob(lifetime>t) = fraction of cases of age t who are healthy

and take this as my survival curve, but it produces a noisy plot (in
particular, the curve is not monotone). Is there a good way to get a
better estimate of the survival function?

Once I have a good way to estimate survival functions for this sort of
data, I could estimate the distribution of T1 (the time to reach stage A
or B) and of T2 (the time to reach stage B), and thereby estimate the
distribution of T2-T1 (the time to progress from stage A to stage B) by
some sort of convolution, assuming independence.


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