Survival Analysis Part 3 | Kaplan Meier vs. Exponential vs. Cox Proportional Hazards (Pros & Cons)
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- Опубліковано 14 жов 2024
- This video introduces Survival Analysis, and introduces the Kaplan Meier model, the Exponential model, the Weibull model, and the Cox Proportional Hazards model. The details of each model are presented in later videos, and in this video we focus on comparing the pros and cons of each. While it is a bit abstract to compare pros and cons before talking about the details of each model, we do this so that we can then revisit the pros and cons of each model when they are expanded on in later videos. This video is the first in a series of videos covering survival analysis. The series contains videos that explain the concepts as well as vides that show implementation using the statistical software R.
These videos were put together quickly in response to the COVID-19 pandemic, and are being used as we transition classes to be online for the remainder of the year.
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Another comment for potentially confused mathematicans: The hazartd is not actually just the rate of change of the survival function (dS(t)/dt) but it must be further divided by the vylue of S(t) itself. This results from the definition of the conditional probability used in the definition of the hazard ( P(T < t+delta | T > t) = P(T < t+delta and t >t)/P(T>t) = (S(t+delta)-S(t))/S(t) ). Then truely the exponential model has constant hazard. But the video is realy good at explaining the models.
Yes, you are correct. My audience for these are very conceptual so sometimes I cut corners a bit on the math, but you are absolutely right
thank you for your comment, this solves my doubts exactly!
loving the transition sound effects! Thanks for providing free education
Thank you so much, ive been looking for explanation like this everywhere
thank u so much u saved me, from a master student stuck with statistics.
I absolutely love your lectures!
Got a new job in which I have to use this and you are a life-saver! So fun and easy to understand
Subscribing in order to support you. Great job! Thank you for your lectures.
Thank you so much Professor Marine!
Great video. Cleared up a lot of concepts for me!
Thank you for your excellent description
Thanks very much. Grateful for these videos.
Thank you for your lectures!
Why is the CPH model not able to estimate the S(t) function?
When you were talking about the shortcomings of the exponential model, I expected you to mention earthquakes. It doesn't take into account random acute disasters. Tornadoes, hurricanes, war, and other variables can introduce death spikes that the equation would never be able to predict.
That's something that I simply don't trust about physics. At least when taking physics 101, I was very skeptical that anyone could put blind faith into an equation. I want to see everything verified with data.
I owe you a big "thank you"!!
I'm not familiar with Survival Analysis and associated models, but I'd like to check my understanding.
One of the limitations of the Kaplan-Meier "model" is that:
(1): no simple functional form. It's a step/piecewise function so it's non-smooth i.e., no simple function like S(t) e^{=t}
(2): we cannot estimate the Hazard Ratio because the Kaplan-Meier curve is non-smooth. The Hazard (H(t)) is a function of Survival (S(t)) -- namely the derivative of S(t) i.e., H(t) = S'(t) ?
We can only estimate the Hazard Ratio for the exponential survival function or Cox Proportional model?
Yes, all correct :)
so helpful
thankyou
Thanks for the great video. Could you elaborate more specifically on why "no functional form" is a con?
I guess you can't use it to build a 'model' ; so you can't calculate a specific time point in the past or predict the future
Does the exponential model capture progression-free time? It seems that because of the fitted negative exponential curve, it fails. Is that right?
Great explanation!
thank you for your videos, they are so helpful
As always... excellent..
Thank you for sharing information
While explaining KM, you labeled the upper step curve as x=1 and the lower one as x=0. Shouldn't it be the other way around? (as mostly the survival chances of an exposed individual on an average is lesser than an unexposed individual)
I'm assuming you mean by exposure as the exposure to disease. Am i wrong? 🤔
Hi, there I was really just trying to talk about having 2 KM curves, and why you can’t calculate a HR. Comparing group A and B.
You’re right that most often an exposure will reduce survival. There are cases where exposures can be ‘protective’, although this isn’t what I was getting at. My example was just to compare 2 groups without much context. But you’re right that it’s most common for exposure to be thought of as something harmful that will reduce survival
8:45 Whenever you grow up :) :) :)