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st: Are Anderson-Gill and Cox Models the Same with single-event data in STATA?


From   "Hugh Robinson" <hugh.robinson@umontana.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Are Anderson-Gill and Cox Models the Same with single-event data in STATA?
Date   Wed, 5 Nov 2008 15:16:52 -0700

Recent papers in wildlife ecology (Delgiudice et al. 2002, Journal of Wildlife Management JWM 66:698-717 and Johnson et al. 2004, JWM 68:966-978) discuss advantages of using the Andersen-Gill extension to the Cox proportional hazards model when dealing with staggered entry, left-truncated and right-censored survival data in wildlife studies.  However, A-G models are typically discussed with regards to recurring-event data.  Therneau & Grambsch (2000) state that the A-G model is "formally identical to the Cox model for survival data" (page 186), which are inherently single-event data.
 
In STATA it appears that you use the same command (stcox) to execute both Cox and A-G models, with the data set-up to accordingly allow time to either stop or continue after the first failure (using stset).  I have data setup with multiple records per individual in which each record is a monitoring interval from "tstart" to "tstop", with censor (0) or failure (1) dictated by "status" and animal id as "id".   I could use stset as:
 
stset tstop , fail(status) exit(failure) id(id) enter(tstart)
 
Using this code, and single event (survival) data, I am running stcox with covariates (var1, var2) such as:
 
stcox variable1 variable2, nohr nolog
 
With data setup in this way, I'm assuming this will run a standard Cox PH model.  In order to run an A-G model, I expect that I would use the same code except with recurring events in my "status" field per individual, and my exit code in stset adjusted to continue until each individual runs out of data:
 
stset tstop , fail(status) exit(time .) id(id) enter(tstart)
 
However, I am reading about uses of A-G models specifically for survival data.  Any guidance on how Cox PH and A-G PH models differ with single-event (survival) data and/or how one would execute each would be greatly appreciated. 


Hugh S Robinson Ph.D.
Postdoctoral Researcher
Wildlife Biology Program
College of Forestry and Conservation
University of Montana
Missoula, MT 59802
(406) 243-2931


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