Talk:Hazard ratio

I just read this article and it is clearly not written by an expert and would need a thourough re-write.

— Preceding unsigned comment added by 1.53.224.251 (talk) 14:48, 14 June 2016 (UTC)


 * I am writing in 2023, 7 years after the preceding comment, and it's still true.
 * Verytas (talk) 17:06, 30 September 2023 (UTC)

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)

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


 * I too would like to see an example used to clarify. I just glanced at the paper cited in the article |Hazard Ratio in Clinical Trials. Perhaps an example could be taken from this paper? I also scanned the same article for use of the expression of hazard as a limit and did not see it. Note that the denominator in the expression tends toward zero. Johnfravolda (talk) 15:38, 20 July 2010 (UTC)

Help! I clicked on this link to find out what Hazard ratio means. No luck! Need a quick answer for the lay reader (like, >100 is above average...)

Ditto the above. PLEASE could someone who calculates these things for simple, real-world stuff, give a couple of simple, real-word examples. (incl all the calculations of course). ‒ Jaymax✍ 00:08, 7 August 2011 (UTC)

Merger proposal
Rate ratios and hazard ratios are different names for the same quantity. I propose merging the rate ratio page to this one. --Gak (talk) 16:20, 18 September 2011 (UTC) No, they are not. HR can be interpreted as rate ratios, but not the other way round. Rate ratios can be calculated by dividing the number of events by person time whereas HR are calculated eg by Cox Regression. HR's ~ Relative Risk, however this is not in all cases — Preceding unsigned comment added by Epi micki (talk • contribs) 17:40, 20 September 2011 (UTC)

I think this confusion between hazard ratio and risk ratio is already apparent in the current version of this page:

a treatment increasing the number of one-year survivors in a population from one in 10,000 to one in 1,000 has a hazard ratio of 10.

This is not true. The relative risk is 10. With the help a statistical software, I found out that the HR is 4/3.

By contrast, a treatment group in which 50% of infections are resolved after one week (versus 25% in the control) yields a hazard ratio of two.

The OR here is 2.41 indeed.

If it takes ten weeks for all cases in the treatment group and half of cases in the control group to resolve, the ten-week hazard ratio remains at two

No: this is a degenerate case (survival probability is 0 for one group). --Borisba (talk) 10:38, 12 October 2017 (UTC)

New translation of a sample scientific paper's use of "HR" into lay English added to article's intro
I have added a paragraph to the lede that attempts to explain what the Hazard Ratio in a scientific paper might mean, in ordinary non-technical words. I am not a statistician (which is why I went to Wikipedia to find out what a Hazard Ratio is) and I hope that this explanation can be a start at making this article more useful to non-specialists.

I encourage specialists to correct the explanation, or simplify it, or improve it. But please, don't turn it into technical language that would make it useless to lay readers of encyclopedias.

I picked the cited sentence because I happened to be reading it and wondering what it meant. If you can find a simpler sentence to explain, or if its subject (Covid vaccination) is too controversial for this unrelated article, by all means, replace it with a better example. -- Gnuish (talk) 01:53, 14 June 2022 (UTC)