Re: [R] Survival Regression with multiple events per subject

From: Terry Therneau <therneau_at_mayo.edu>
Date: Mon, 28 Apr 2008 08:22:21 -0500 (CDT)


> I want to process a maximum likelihood estimation for a parametric
> regression survival time model with multiple events per subject.

  Data sets with multiple records per subjects are used for several things, you need to tell me what it is that you want to accomplish. Multiple records is a method, not a goal.   

  1. Robust variance: If each observation is a separate measurement on the subject, with it's own covariates, time 0, and endpoint, and you want a "GEE" type variance that accounts for the fact that multiple observations are for the same subject: survreg(Surv(time, exercise) ~ itm + posret + negret + cluster(id), ... where id is a variable that is unique for unique subjects.
  2. Time dependent covariates: Each subject has one endpoint, but covariates change over time. The bookkeeping for time dependent covariates is reasonably straightforward for proportional hazards models, but a major pain for an accelerated failure time (ACF) model. I've thought about it but never implemented the feature in survreg, though this may change one day due to the increased interest in accelerated aging as a biological model among the researchers I work with (but don't hold your breath). For example, if you smoked in your youth but later quit, in an ACF model this 'adds years' to your biological age which you never lose; the computer code has to keep track of covariate histories. In a proportional hazards model today's risk = function(today's covariates), which is easier. A weibull can be written in either ACF or PH form, survreg uses the acf style, I don't know which stata uses.
  3. Multiple events per subject, with a single time scale per subject. This is seen in reliability analysis where hazard = function of age. Survreg does not handle this case either.

          Terry Therneau



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