Re: Comparison of Logistic regression and Cox regression

Richard Ulrich wrote:

> On 7 Jul 2005 03:48:16 -0700, ramsathish@xxxxxxxxx wrote:
>
>> Respected Sir,
>>
>> I am Ramsathish S doing M.Phil (STATISTICS) in Loyola
>> College, Chennai, India. I have one doubt sir, How to compare the odds
>> ratio from logistic regression and the hazard ratio from the cox
>> regression.
>
> Logistic regression has a single dichotomous outcome.
> Cox regression models a survivorship curve.
>
> The data are different. What other comparison do you need?
>
>
> I am curious if anyone can describe the difference between
> the Cox regression hazard ratio and the Mantel-Haenszel (1959)
> odds ratio (called at the time, relative risk).
> - MH computes across 2x2 tables. Do I remember right, that
> there is a version valid for survivorship data across time?
> - The MH statistic uses Pearson-type Expected-Observed for
> computing a test. I think the Cox procedure is maximum
> likelihood: Is that so? Is there any other difference?

You are correct that the two estimates are different. To be
precise, the Cox model uses partial maximum likelihood.
However, for a Cox model with a single dichotomous covariate,
the MH procedure carried out stratifying by the unique event
times is equivalent to the score test obtained from a cox
model. There are various estimators of the hazard ratio that
can be obtained from the MH procedure. There is the MH estimate
and also a procedure due to Pike.

--
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Department of Public Health Sciences
Faculty of Medicine, University of Toronto

.

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