split population model (long-term survivors)

[morago06]

Hi everyone,

I hope someone can help me with this query. I'm attempting to run a split population model; this is a special type of survival analysis model in which the duration length of some individuals is extremely long or effectively infinite. Goldstein (2011, chapter 11, pp. 226-227), refers to this special case very briefly. Nevertheless, Goldstein does mention that this can be specified as a bivariate model in which we have two responses for the censored cases (one continuous time measure and one binary measure of censoring) and a single response for the uncensored cases.
Another way of looking at this is that duration is an outcome that is only relevant for the censored cases (the sub-population that experience the event); and that the binary measure of censoring is relevant for the whole population.
I thought of one way of specifying this in runmlwin, but I'm unsure whether this is a correct specification:

runmlwin ///
(logtime cons, eq(1)) ///
(censoring cons, eq(2)), ///
level1(id2: (cons, eq(1))) ///
discrete(distribution(normal binomial) link(probit) denom(cons denomb)) ///
nopause forcesort

Logtime is the natural logarithm of the time measure. Logtime is missing for the uncensored cases. A multilevel extension to this should have this specification:

runmlwin ///
(logtime cons, eq(1)) ///
(censoring cons, eq(2)), ///
level2(groupid: (cons, eq(1)) (cons, eq(2))) ///
level1(id: (cons, eq(1))) ///
discrete(distribution(normal binomial) link(probit) denom(cons denomb)) ///
nopause forcesort

Of course, this specification uses MQL1 as the estimator, but it can be changed to MCMC quite easily. What I'm after is knowing if this model would be equivalent to a split population model.

I'd appreciate any feedback on this!

Many thanks!

[GeorgeLeckie]

Hi,

The models look fine from a purely runmlwin perspective, but I'm afraid I can't comment as to whether they are equivalent to the split population models to which you refer.

If you can write your desired model down as a model equation we can then have a think as to whether it can be implemented in runmlwin.

Best wishes

George