Thank you for the continued comments on this problem. I think I have a solution, which I thought I'd share here, in the hope that any obvious errors or inefficiencies can be pointed out.
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. Suppose I'm interested in the transition healthy->A. For each individual I have a censored observation of the "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) The Surv function in R does not deal with this sort of censored data. Happily, Mai Zhou has written a package called dblcens, available on CRAN, which will estimate the survival curve. So I can work out the lifetime T0A for the transition healthy->A, and the lifetime T0B for the transition healthy->B. I would like to know about the time for the transition A->B, where T0B = T0A + TAB. This is a deconvolution problem. It cannot be solved in general, because knowing T0A and T0B is insufficient to determine the joint distribution of (T0A,TAB). If I assume that T0A and TAB are independent, it can be solved. I used an ad-hoc solution: find the estimated distribution TABe which minimizes the mean-square-error distance between the survival function for T0B and that for T0A+TABe (i.e. the convolution of T0A+TABe, for which R has a handy function convolve). I did this by optimizing over positive measures for TABe with optim, and tweaking a Lagrange multiplier to make the the optimum be a distribution. I can then plot survival curves for T0A, T0B and T0A+TABe. This lets me visualize whether the assumption of independence is good. Damon. ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help
