Please,
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 observed 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.
The proportional hazard model, takes into account the time to estimate
the instantaneous and relative risk:
h(t,x)=ho(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 the relative risk (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 ??
Thank you in advance.
|=======================================================|
| 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 |
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