Talk:Hazard ratio

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Someone please tell me that

(1 - AUC(treatment)) \over (1 - AUC(control))

is a standard definition!! :-) Wikid

Isn't the AUC of dimension time? Then shouldn't the 1 be replaced by the time period considered? - Patrick 20:36 12 Jul 2003 (UTC)


Okay, just thinking aloud here. The curve has time on the horizontal axis and probability of survival (p) on the vertical axis. The AUC is thus a function of p*time. The hazard however is the hazard of death - 1-survival. So we're actually interested in the "area above the curve". The total available area = 1*time. ... so rather laboriously conclud Ratio of Hazard of Death =

(time - AUC(treatment)) \over (time - AUC(control))

Next question: what's the time? - meaning that when some data are missing or censored, we can't really claim to have followed the whole group for the same length of time. How do we adjust for that? Also, how sensitive are hazard ratios to changing lengths of follow-up - what's the mathematical function that describes this? Thanks Patrick! :-)
Wikid 21:07 12 Jul 2003 (UTC)

Patrick I have to confess I'm struggling a bit on this, and using it partly as an exercise to clarify my own thinking or bait some luminary to come along and set things straight once and for all. The expectations here are supposed to be the "null hypothesis" which says that tretament does not cause any difference between the treated group and controls. So one naturally asks, shouldn't it just be E(controls) in both lines. Answer: not if one can identify other things about the specific sample populations of controls and treated that might condition our expectations of their survival. In other words, the HR seems to be comparing what you might call age-sex-comorbidity standardised natural histories for the two groups. Wrapping this up into a tidy definition could take me some time (I'm not a biostatistician). But at least I can cite a reference this time! I might have a look in the British Medical Journal - they've had some good papers defining all these things. Wikid 13:15 16 Jul 2003 (UTC)

Okay, I think this corresponds with my last edit. - Patrick 13:26 16 Jul 2003 (UTC)

I can't work out exactly how E is calculated but from the textbook account the difference between E(treatment) and E(controls) may reflect nothing so much as the difference in actual numbers between the two groups. Oh & wooah there - the null hypothesis on survival is that natural history is the average survival of controls and treatment group combined. So even if the treated group do appear to do better, the null hypothesis would explain that as simple intrinsic variation in severity of disease.
Anyhow I'll keep plugging on with this until I get it right or it "fixes itself". :-) Wikid 16:15 16 Jul 2003 (UTC)

[edit] example

For non-statistitions an interpretive example of how one would use a real hazard ratio would be helpful. 210.11.82.152 22:12, 21 June 2006 (UTC) Ted Cooper