Date:         Fri, 10 Nov 2000 11:38:04 +0100
Reply-To:     Hassane ABIDI <hassanab@LYON-SUD.UNIV-LYON1.FR>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Hassane ABIDI <hassanab@LYON-SUD.UNIV-LYON1.FR>
Organization: Unité d'Epidémiologie,
              Centre Hospitalier, lyon sud
Subject:      logistic regression and Cox model
Content-Type: text/plain; charset=us-ascii

Dear colleagues,

I have a problem to interpret (or to compare) the output of logistic
regression and that of the Cox model.

let :
Y is a binary variable where Y=1 when event is present
and X is a binary explatory variable, X=1 in the exposition case and 0 otherwise
T is the time where the events are oberved or censured.

In logistic case  (independently of time) we estimate:
p(x)=Pr(Y=1/X=x)
Odds(x)=Logit(p(x)) ( = Ln( P(x)/(1-p(x)) )  )
OR=Odds(1)/odds(0)  = Exp(a) where a is the coefficient of X in logistic
regression.

In Cox model (proportional hazard model), we estimate:
h(t,x)=h(t)*Exp(bx) (hazard function)

thus the ratio of estimated hazards for X=1 and X=0 is
h(t,1)/h(t,0)=Exp(b) (presumedly independent of time)

My problems:

1) In which case, Exp(a) (from logistic) estimates P(1)/P(0) ?

2) In which case we expect that Exp(a) = Exp(b) (or approximate) ie
the ratio of two odds estimates the ratio of tow hazards ie
the logistic model and the Cox model give the same (or approximately) results ??



|=======================================================|
| Hassane ABIDI (PhD)                                   |
| Unite d'Epidemiologie; Centre Hospitalier Lyon-Sud    |
| Pavillon 1.M, 69495 Pierre Benite Cedex, France       |
| Tel:  (33) 04 78 86 56 87 ;  Fax: (33) 04 78 86 33 31 |
| E. mail: Hassanab@lyon-sud.univ-lyon1.fr              |
|=======================================================|