I am facing a problem when I try to calculate the hr from two different survival curves, here is the problem: in the first plot the experimental group's curve is more close to the placebo group then the second plot, even if the first plot's hr is smaller than the second plot. I wonder what the possible reasons are. Can you guys help me to solve this problem? Thanks.
It's hard to help without seeing the survival curves (Kaplan-Meier plot). Do you have one you can show us? Here's a video if you are not sure what I am talking about: https://www.youtube.com/watch?v=XDdytnv6HYE&list=PL64SCLAD3d1GJJrZ63sJGWALO22ZY9erG&index=27&t=1s
Monika Wahi gave a good response. I would always do the confidence bands on K-M curves because that gives a measure of how different they actually are. Some references are given in the attached paper. Best wishes, David Booth
How did you derive the hazard ratios (HRs)? Did you, for example, use some model (e.g. Cox regression) to get the HR for each study/plot? If you used a model, several things might be at play:
- Did you perhaps adjust for covariates in this model? The KM curves are crude in the sense that there's no other controlling than your stratification (= one curve for the intervention group and one for placebo). So, the HR of the intervention likely tells a different story once you control for covariates. Whether that is more correct depends on i.a. whether the covariates are appropriate.
- A model might give incorrect results if your data violate the assumptions (often, the proportional hazards assumption is a frequent culprit).
As Monika Wahi said, it would be a lot easier if you could share the plots (or even similar but artificial ones if you don't feel comfortable sharing your actual data).
Thank you for sharing the drawing; it definitely makes some things clearer. It's a detail, but worth mentioning nonetheless: your curves are not survival curves but probably the cumulative event rate (= 1 - survival) curves. A survival curve always starts in (0, 100%) and is decreasing (although step-wise).
How did you compute the hazard ratios? Reporting a hazard ratio as a meaningful summary statistic assumes that hazards be proportional. It can be difficult to eyeball when this assumption is appropriate (there are diagnostic tests for this purpose), but it is definitely violated when the survival curves cross or converge. The same thing applies to the cumulative event curves, because they are basically just an alternative representation of the same data. As the curves in both your plots cross (the left-hand plot several times, the right-hand plot once in the very beginning), the proportional hazards assumption is violated, and you need to analyse your data differently, for example with time-varying covariates or even discrete-time survival modelling.
I would argue that the curves in the left-hand plot are the same apart from some random noise. In the right-hand plot, it seems the the intervention almost postpones the event (the curves are close initially, and later somewhat parallel with the experimental drug's curve shifted downwards).
Hope it was useful. Let me know if you need other pointers.
Cheers,
Ben
Some potentially useful references:
- https://en.wikipedia.org/wiki/Survival_analysis
- https://en.wikipedia.org/wiki/Proportional_hazards_model
- https://www.rensvandeschoot.com/tutorials/discrete-time-survival/ (nice intro with good references)
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