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st: estimating cumulative hazard


From   Matt Aronson <mattaronson77@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: estimating cumulative hazard
Date   Wed, 5 Jun 2013 16:54:10 -0600

Dear Statalisters:

I have longitudinal education data on which I estimated a discrete time
survival model, with the event of interest being completion of a degree.
Based on those results, I want to estimate for each respondent the
probability that s/he *ever completed the degree* during the time period for
which s/he was observed. (I know I could just use a logistic regression
model for "ever completed"; my goal is in fact to compare with that.)

I have two different ideas of how to use the survival model results, and
I'd like to know which one (or neither) of these is right. My problem is
with the conceptual rather than the software aspects. Both of my approaches
start off by using the model results to calculate each respondent's hazard
values at each point in time, h_t.  I don't have a problem with that.

Here are my two approaches:

1)  Sum up each respondent's predicted hazard values over all of her/his T
periods of observation,

Prob(ever completed degree) =  h_1 + h_2 + ... h_T
   where h_t is the model-estimated Prob( completed at time t, given not
   completed by time t-1).


2) Take the complement of the respondent's estimated survival probability
up through the end of the Tth period of observation,

Prob(ever completed degree) = 1 - S_T
   where S_T  = Prob(did not complete degree by time T) =  (1-h_1) *
   (1-h_2) * ...(1-h_T)


Which one of these is right (if either), and why?

Thanks very much for whatever you can offer!
Matt Aronson
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