Talk:Proportional hazards model

Incomplete sections

It seems that the sections "Multiple and mixed covariates" and "Calculating the baseline hazard" are empty. The sections should either be filled in or removed / moved to drafts. Barbarr (talk) 14:22, 3 November 2022 (UTC)

I've removed them for now. Octagon.pinhole (talk) 17:07, 11 November 2022 (UTC)

Unreadable page, add a normal language explanation

I came to Wikipedia looking for an accessible information about the Cox proportional hazards model. What is here is completely un-understadable to an average reader. Please add common language or example explanation. There must be dozens of such readable explanations in various better statistical books. It is not a spirit of Wikipedia to include only a dry mathematical model, which seems to be rewritten from a student exercise book from a technical university, which author did not understand mathemetics very well himself. your Reader — Preceding unsigned comment added by 87.102.171.116 (talk) 11:32, 8 November 2018 (UTC) Once on a conference I heard such presentation of a mathematical equations about some economic phenomena, then the presenter asked “Are there any questions?” silence… then someone started to ask about the phenomena also used some A(t)+I etc…. The presenter kept silence one minute looked on his formulas and said “Well…. Actually I used another model…” – very fruitful discussion … — Preceding unsigned comment added by 46.186.39.139 (talk) 05:34, 2 April 2019 (UTC)

Agree. I've written some more friendly texts about the Cox model. I've started editing this page to make it less math dense. I imagine the median reader of this page is coming _not_ from a statistics background. Octagon.pinhole (talk) 01:11, 24 August 2022 (UTC)

Add an inuition for the probability that the event occurs in the subject i

Can we make this clearer by adding a phrasing such as: "the probability that the event occurred in subject i out of all the other subjects that survived till time t is"? Ihadanny (talk) 13:00, 14 February 2016 (UTC)

I added a description of the summation in the denominator, paraphrased from Cox, "Partial likelihood" (Biometrika 1975), above his equation (5). Arie ten Cate (talk) 20:46, 21 November 2017 (UTC)

A definition of partial likelihood is needed here

Preferably with links to likelihood...

Internal link added to likelihood page Arie ten Cate (talk) 20:58, 21 November 2017 (UTC)

terrible page

it doesnt describe any details about the model —Preceding unsigned comment added by 212.186.126.215 (talk) 02:11, 24 October 2008 (UTC)

Wikipedia already has a good article on survival analysis, but it does not mention proportional hazards. I hope that this article will supplement that article; and I hope that it will be useful to users who search for proportional hazards, and fail to find even the survival analysis page.

I also hope this page will be expanded by another editor, or merged with the survival analysis page. --Pstevens 17:39, 30 May 2006 (UTC)

Weibull is a special case of Cox (with specified baseline hazard). Also there is new work in time-dependent covariates. Updating. —Preceding unsigned comment added by 128.59.109.171 (talk) 21:46, 13 May 2009 (UTC)

I just donated $35 to Wikipedia, then I went looking for an understandable explantation of what a "Cox proportional hazard model" is; unfortunately, I got sent to this entry, which has succeeded only in deepening my mystification. Please, somebody, take pity on those of us who need more fundamental understanding, and write an introduction to this subject that would be useful and graspable by anybody with the basic interest to look it up. That's how to make Wikipedia better; make it useful.Trigley (talk) 20:02, 12 December 2009 (UTC)

It's not at all clear to me what "PH models" and "GLM models". Can someone familiar with these things clarify that sentence? — Preceding unsigned comment added by 136.152.129.247 (talk) 23:53, 31 October 2011 (UTC)

I've just expanded those initialisms, giving "proportional hazards models" and "generalized linear models." Qwfp (talk) 11:55, 1 November 2011 (UTC)

The score "function" is called the score vector and it should use a nabla ($\nabla$) symbol. Also, while the Newton-Raphson method is certainly applicable, many other numerical optimization routines might be applied. In particular, the BHHH optimization algorithm is applicable, making use of only the outer product of the score vectors in approximating the Hessian. Moreover, it doesn't seem very pedagogical to present the Cox Proportional Hazards model with the partial likelihood function without ever mentioning what the full likelihood for this model is (the full likelihood would need a parametric specification of the baseline function $\lambda _{0}(t)$ as well but maximizing over the partial likelihood gives valid estimates of the parameters). Superpronker (talk) 14:10, 11 April 2012 (UTC)

Proportional Hazards assumptions

There should be a description of the assumptions needed for this model — Preceding unsigned comment added by Bakerstmd (talk • contribs) 19:36, 9 December 2013 (UTC)

The main assumption is the first equal sign in the first equation of the section "The Cox model". Must this be stated explicitly like this? Another assumption, which holds quite general, is the treating of the subjects as statistically independent from each other. Arie ten Cate (talk) 21:10, 21 November 2017 (UTC)

Tied times section unclear

The section describing how to deal with tied times used unclear notation. In particular, it is unknown what the parameters l and m stand for. Furthermore, what does |H| stand for? — Preceding unsigned comment added by 170.194.16.50 (talk) 11:22, 10 August 2015 (UTC)

Problem in the definition of the Cox model

Definition of the Y_j implicit but missing.

The probability that the event occurs for subject i under the condition that Y_i = t (i.e. that the event occuring for subject i occurs at t) and C_i = 1 is 1, and not the Cox formula given. The only condition about t, is that some event happens for any subject at risk at this time and that indeed subject i is at risk (C_i = 1).

Am I missing something?

132.204.100.226 (talk) 16:09, 8 November 2017 (UTC)

Assume I have observed a throw of a dice. I am absolutely sure, one hundred percent sure, about the outcome. But I also know this outcome only had a probability of 1 in 6. I have tried to express this in the phrase "The probability that this happened .." (Revision https://en.wikipedia.org/w/index.php?title=Proportional_hazards_model&oldid=811147935 ) Arie ten Cate (talk) 21:30, 21 November 2017 (UTC)

Ongoing work to lower the "barrier to entry" of this article

As of August 2022, this article was very focused on the mathematics of a very important tool in survival analysis¹. Most of the page was dedicated to the likelihood, which is never used by practitioners (instead the likelihood is implemented by software, and users use that software instead of working with the likelihood). It's often a biology or medical students first encounter with regression, too.

I've taken the first steps to iteratively make this page better able to be understood for more people, especially students. Additional content to be included over the next year (fingers-crossed):

• adding examples
• adding first-class software implementations, as this is how people will use the PH model.
• focusing on interpretations, including common misinterpretations.
• focusing on common "asks" of the PH model:
  • how do I / can I convert to probabilities?
  • how do I check the PH assumptions? What to do if the assumptions fail?
• deemphasizing the mathematics, including the likelihood work, by pushing it further down the article (Not that it isn't important, it's just not important for most people).

¹ The Cox model is second only to the Kaplan-Meier estimator in terms of importance and use in statistics. Octagon.pinhole (talk) 22:49, 27 August 2022 (UTC)

Frailty Model ToDO

Missing frailty model which connects this to mixed-effects models 68.134.243.51 (talk) 15:35, 10 October 2022 (UTC)