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Re: st: interpreting time ratios in survival analysis

From (Roberto G. Gutierrez, StataCorp)
Subject   Re: st: interpreting time ratios in survival analysis
Date   Sun, 23 Jul 2006 17:17:30 -0500

Howard Bodenhorn <> asks:

> In -streg, an option is -tr, which reports time ratios rather than
> coefficients for survival models. My question is about the interpretation of
> a time ratio. If the estimated time ratio equals, say, 0.88, how am I to
> interpret that result? How do I interpret it for a continuous varaible and
> for a dummy variable? Thanks.

A time ratio is a comparison of rates at which subjects traverse the survival
curve.  Imagine a survival function beginning at 100% survival at time zero
and descending towards 0% survival as time increases.  In an accelerated
failure-time model (that for which time ratios are given), everyone has the
same "baseline" survival curve -- it's just that some travel down it faster
than others.  That is, the effects of covariates serve to accelerate the
passage of time.

For a continuous covariate, a time ratio of 88% means that every unit increase
in the variable translates to a subject who traverses the survival curve 12%
slower.  For a dummy variable, those with the dummy equal to one traverse the
survival curve 12% slower than those with the dummy equal to zero.  Those with
the dummy equal to one die at a slower rate.  For example, at real time 10,
those individuals at baseline (all covariates equal to zero) have a survival
percentage given by S(10), where S is the baseline survival function.  Those
with the dummy variable equal to one, however, have a survival percentage for
real time 10 given by S(8.8), which is greater than S(10) since survival 
curves decrease with time.  Hence, this group has a better overall survival

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