Date:         Fri, 21 Dec 2001 09:16:42 -0500
Reply-To:     "Gray, Alex M" <amg5818@GLAXOWELLCOME.COM>
Sender:       "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From:         "Gray, Alex M" <amg5818@GLAXOWELLCOME.COM>
Subject:      Hazard ratio
Content-Type: text/plain; charset=us-ascii

Dear SAS statisticians,

I am looking at a manuscript that is published in the New England J. Med
that used an analysis that looks at the time to an event (dyskinesia) in a
clinical trial over 5 years.  The analysis used a Cox regression model which
produced a Hazard ratio.  There were two drugs in this trial and the
resulting hazard ratio was 7.  Not being a statistician I have poured over
the two survival analysis books (Allison's and Cantor's) have to confirm the
interpretation of the hazard ratio.  What I learned about the hazard
function suggested to me the following interpretation of this hazard ratio.
Namely, that if you had survived to the end of the study without
experiencing a dyskinetic event ( trial was 5 years) then your risk of
experiencing a dyskinesia post 5 years was 7 times higher (or greater) on
one drug than the other?

This study also used a logistic regression model to investigate the onset of
dyskinesias, and the odds ratio was 15.2.  This is saying that your risk of
experiencing a dyskinesia is 15.2 time greater on one drug than the other.
The odds ratio from the logistic regression doesn't look at the length of
the trial (and therefore doesn't have a time component unlike the hazard
ratio????).

If one assumes (or I have assumed) that I have interpreted the hazard ratio
correctly then the reason for the logistic regression analysis and thus the
odds ratio makes sense viz: the hazard ratio explains the risk if you have
survived without failure so we have a measure for future risk relative to
the two drug treatments following 5 years event free, and the odds ratio
explains the overall risk between the two drug treatments.

If the hazard ratio doesn't have an interpretation that includes having
survived to time t and consequently it doesn't represent the risk of
experiencing the event post time t, then how do the these two measures
(hazard ratio and odds ratio) complement one and other.

Please tell me if I have had too much egg nog already and just can't see the
wood for the trees (but be kind!).

Merry Christmas to all.

Kind regards.

Alex.