```Date: Fri, 10 Nov 2000 11:38:04 +0100 Reply-To: Hassane ABIDI Sender: "SPSSX(r) Discussion" From: Hassane ABIDI 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 | |=======================================================| ```

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