Survival Analysis Part 9 | Cox Proportional Hazards Model

[@charlesp4440]

Excellent. It is astounding how you capture so much detail with lucid explanations in a short time.

[@marinstatlectures]

Thanks :) In about a month I’ll have to record the 9 lectures worth of content that comes before these. These were recorded at the start of Covid, mid Course... in January I teach this course again, and will be recording all course content...so look out for that if you want more on regression models: Linear, Logistic, ...

[@raqvikantbhai]

have never seen such a clarity and simple in teaching of such a complex topic!!

[@federico2064]

Gracias hermano, sos un crá, tenés lo que todo profesor de estadística debería tener, el esfuerzo por ser riguroso e intuitivo a la vez en las explicaciones. Tratás que la gente entienda, y creeeme que en mi caso lo conseguiste.

[@raphaelriviere2506]

There is such a great clarity, pace, and authenticity in your teaching methods. Thank you very much for making these videos. Subscribed!

[@makemymarket1772]

You are so good at teaching, learned so much from your lectures. Thanks!

[@sunsun6360]

It is really helpful! you have a very good way to explain those difficult concepts!

[@janemou7727]

thank you so much!

[@mavis6025]

very helpful to understand PH assumption, thanks!

How do you distinguish ho(t) from random error?

[@ProfFeinman]

What is Hazard? Is that events per unit time? Or what? Example might be easier for beginners

[@AmarinderThind]

Nice!

[@bilalsr632]

In the assumption part what does it mean that "hazard ratios are Proportional?"

[@185283]

Given an observation with duration, event(1 or 0), and x1, how do you calculate HAZ of this observation?

[@ghallab1980]

you are amazing!!

[@DrifterChan]

A question：what's actual difference between Cox and Logistic Model, I thought the baseline hazard function h0(t) in Cox is not that easy to get. So cox model is used to find the key feature of influencing the survival ratio at most time, as same as logistic regression..

[@DrifterChan]

I am not a bioinformatics student, just want to use Cox model to predict the hazard of corporation over the time. Is it realistic Or what else model is better for such condition. Confusing.

[@marinstatlectures]

They’re quite different. Logistic regression is used to model a Y variable that is 0/1 while Survival analysis (like Cox model) is used to model a Y that is a time-till-event variable.

[@Mr1159pm]

6:28 But if the distance is the same then the proportion will change. E.g. For simplicity let's assume that for t0 Yf is 1 and the distance between Ym and Yf is 1. That gives us 2/1 ratio at t0 . Let's assume that at t1 the Yf is 2 then, if the distance is fixed , the ratio will be 3/2. What am I missing here?

[@marinstatlectures]

It is because it is modeled on the log hazard scale. The distance between them is constant, on the log hazard scale. This translates to them being proportional on the scale of the hazard. Hope that helps clarify it. If not let me know and I can elaborate more

[@Mr1159pm]

@@marinstatlectures ah log scale. That makes sense. Thanks!

[@anmolpardeshi3138]

in the initial part you state that the model allows hazard to change over time but then you say that the hazard ratio is constant. How is that ie aren't the two things contradictory?

[@marinstatlectures]

It’s not contradictory. Using made up numbers for ease of calculation, suppose that at time 0 the hazard for group 1 is 0.04 and the hazard for group 2 is 0.02. Their ratio (the hazard ratio) is 2. Now suppose that hazards increase, and at time t=1 the hazard for group 1 is 0.06, and the hazard for group 2 is 0.03. Here the hazards have increased, but their ratio is still 2. The Cox PH model allows the hazards to change over time, but forces the HR to remain constant (also stated as the hazards are proportional). Hope that clears it up

[@anmolpardeshi3138]

@@marinstatlectures i see. Thanks for that. And why do we care so much about survival analysis. Im taking a class and its survival analysis all over the place! KM survival, poisson regression, survival regression (which is the cox). Why do we care sooo much that there are so many approaches to it?

[@marinstatlectures]

Well, it’s used if you want to know anything about “the time until something happens”, and there’s a lot that fits that. There are always many approaches to trying to model something...each of those you mentioned have strengths and weaknesses.

[@anmolpardeshi3138]

@@marinstatlectures sure thanks. Another question is - here you are taking how hazard, between two groups, is proportional or constant. But in earlier videos, I saw that KaplanM and this Cox method are both used for individuals' data in our cohort. So Im unable to get the link between this group level proportionality and individuals' data that will help us do the cox regression based on covarites (assume non-time dependent covariates for now)

[@zainabkhan2475]

Thank you sir, Im your subscriber from India... Can you explain ARIMA both statistically and in R?

[@lilyha2470]

oh thank God

[@rohitpant6473]

Cuti pie