thank you for your explanations, in the last example, the confidence interval include the number 1 but the p value is significant, which parameter should we consider to definitely say that the result is significant. Thank you very much
Hi! Thank you so much for your question, it's a really good one. It's best to follow confidence intervals - they give you a better precision of the estimate (in this case we are estimating the HR). There's a very complete comment with additional links here: www.researchgate.net/post/When_a_confidence_interval_crosses_the_null_hypothesis_1_but_P_value_is_0001_Is_it_significant
Not really, don't follow p-values blindly especially when its so close to your selected threshold. CI are a good guideline when such things happen, and should always be used as part of your model analysis.
thank you for the video! I would like to know what is the best time to collect data for cox regression analysis? in the beginning of treatment, or endpoint (when the event/hazard occurs)?
How to deal with a situation where the value of the covariate changes after the treatment?. For example, a person is smoker at the initial period but he quits after some time.
In your example, is the relation linear and is that always the case ? I think I understand that if the HR for age is 1.2, it means that an increase of one year results in 20% more risk of the event. So what about 2 years older ? Would it mean 1.2*1.2=1.44 so 44% more risk ? Thank you for the video !
Hi, thanks for your comment! Not exactly - if all Cox regression assumptions are met, it would mean that the hazard rate of death increases by 20% for each year increase in age. This paper explains it really nicely - it actually has a very similar example! www.ncbi.nlm.nih.gov/pmc/articles/PMC8651375/ And this other publication has a really clear explanation of HRs and how to interpret them, in case it helps:) www.ncbi.nlm.nih.gov/pmc/articles/PMC5388384/
Hi. Just checking the data in your video, and drug A's HR is e^(-1.8) = 0.1652, not 0.152. I'm guessing a typo with omitted 6? Otherwise, nice explanation, thank you for the videos!
I am a bit confused by the hazard ratio. It seems like its group A is HR times as like to die as group B. So in the smoking example where smoking had a hazard ratio of 7.4. I took non_smokers as 0 being group A and smokers as 1 being group B. Would this mean that non-smokers were 7.4 times as likely to die compared to smokers?
Thanks for your question! The positive HR for smoking means that there is an increase in the hazard for the smoking group compared to the control (non-smoker group) at any given time. Is this what you were asking? As a sidenote: Hazard ratios are a bit different to relative risk - the HR accounts for also the timing of the event (death), whereas the relative risk only checks if it happened or not. An HR = 1 indicates no change in the hazard (probability of death given that you have survived up to a specific time), if HR > 1 it's increased, and if HR < 1 it's decreased. But this does not translate directly to "7.4 times more likely to die", because it's a ratio, not a probability. To get the probability you can use this equation P = HR/(1 + HR). So for example, a hazard ratio of 2 means there's a 67% chance of the smoking group dying first, and a hazard ratio of 3 corresponds to a 75% chance of dying first. A HR of 6.7 means there's an 87% chance a smokers will die before a non-smoker at any given time. Does this make sense? This paper is really useful in case you want to read more about it: www.ncbi.nlm.nih.gov/pmc/articles/PMC478551/
@@biostatsquid Ahhh I think I was not thinking of things in terms of a group vs control, but was thinking of it in terms of the first group and second group which doesnt make as much sense. Lmao also it being called a ratio should make it obvious to me that it is a ratio and not a probability. I appreciate the clarification, this makes a ton more sense now. Time to finish running this cox-prop model on my GBM survival data. Fingers crossed this paper gets out by Oct T-T
Also the Age HR is e^(0.2) = 1.221 (not 1.247) and the 95% CI for Age HR on the slide [0.60 - 0.90] doesn't include the given HR, it should be around [1.034; 1.443]?
Correct! Well spotted:) and definitely - sorry for the confusion! The confidence interval should include the hazard ratio as it is a way of expressing the uncertainty around the point estimate of the hazard ratio. Thanks for your comment, I'm sure more people have the same question:)
thank you for your explanations, in the last example, the confidence interval include the number 1 but the p value is significant, which parameter should we consider to definitely say that the result is significant. Thank you very much
Hi! Thank you so much for your question, it's a really good one. It's best to follow confidence intervals - they give you a better precision of the estimate (in this case we are estimating the HR). There's a very complete comment with additional links here: www.researchgate.net/post/When_a_confidence_interval_crosses_the_null_hypothesis_1_but_P_value_is_0001_Is_it_significant
Not really, don't follow p-values blindly especially when its so close to your selected threshold. CI are a good guideline when such things happen, and should always be used as part of your model analysis.
thank you for the video! I would like to know what is the best time to collect data for cox regression analysis? in the beginning of treatment, or endpoint (when the event/hazard occurs)?
nice explanation!!! but you might want to balance the volume
hidden gem of stats
Great explanation! Thanks !
Thank you for this amazing video!
Really helpful, thank you!
Thank you for this simple and short explanation!!!
this video helped me so much!!!!!
Like your videos!
How to deal with a situation where the value of the covariate changes after the treatment?. For example, a person is smoker at the initial period but he quits after some time.
In your example, is the relation linear and is that always the case ? I think I understand that if the HR for age is 1.2, it means that an increase of one year results in 20% more risk of the event. So what about 2 years older ? Would it mean 1.2*1.2=1.44 so 44% more risk ? Thank you for the video !
Hi, thanks for your comment! Not exactly - if all Cox regression assumptions are met, it would mean that the hazard rate of death increases by 20% for each year increase in age. This paper explains it really nicely - it actually has a very similar example! www.ncbi.nlm.nih.gov/pmc/articles/PMC8651375/
And this other publication has a really clear explanation of HRs and how to interpret them, in case it helps:) www.ncbi.nlm.nih.gov/pmc/articles/PMC5388384/
Hi. Just checking the data in your video, and drug A's HR is e^(-1.8) = 0.1652, not 0.152. I'm guessing a typo with omitted 6? Otherwise, nice explanation, thank you for the videos!
Hi, thank you for you for your comment! Yes, just a typo, great that you noticed:)
I am a bit confused by the hazard ratio. It seems like its group A is HR times as like to die as group B. So in the smoking example where smoking had a hazard ratio of 7.4. I took non_smokers as 0 being group A and smokers as 1 being group B. Would this mean that non-smokers were 7.4 times as likely to die compared to smokers?
Thanks for your question! The positive HR for smoking means that there is an increase in the hazard for the smoking group compared to the control (non-smoker group) at any given time. Is this what you were asking?
As a sidenote: Hazard ratios are a bit different to relative risk - the HR accounts for also the timing of the event (death), whereas the relative risk only checks if it happened or not. An HR = 1 indicates no change in the hazard (probability of death given that you have survived up to a specific time), if HR > 1 it's increased, and if HR < 1 it's decreased. But this does not translate directly to "7.4 times more likely to die", because it's a ratio, not a probability. To get the probability you can use this equation P = HR/(1 + HR). So for example, a hazard ratio of 2 means there's a 67% chance of the smoking group dying first, and a hazard ratio of 3 corresponds to a 75% chance of dying first. A HR of 6.7 means there's an 87% chance a smokers will die before a non-smoker at any given time. Does this make sense?
This paper is really useful in case you want to read more about it: www.ncbi.nlm.nih.gov/pmc/articles/PMC478551/
@@biostatsquid Ahhh I think I was not thinking of things in terms of a group vs control, but was thinking of it in terms of the first group and second group which doesnt make as much sense. Lmao also it being called a ratio should make it obvious to me that it is a ratio and not a probability. I appreciate the clarification, this makes a ton more sense now. Time to finish running this cox-prop model on my GBM survival data. Fingers crossed this paper gets out by Oct T-T
Also the Age HR is e^(0.2) = 1.221 (not 1.247) and the 95% CI for Age HR on the slide [0.60 - 0.90] doesn't include the given HR, it should be around [1.034; 1.443]?
Correct! Well spotted:) and definitely - sorry for the confusion! The confidence interval should include the hazard ratio as it is a way of expressing the uncertainty around the point estimate of the hazard ratio. Thanks for your comment, I'm sure more people have the same question:)
And the CI 95% for Gender HR is [0.349; 0.474] and does not include 1.0. There are just too many errors in the data shown in the video.
Yep exactly! Thanks! Hope that despite the errors I still made my point across and the idea behind Cox regression was understandable.